Toshima kida

Transcrição

Toshima kida

ORGANIC AND PHYSICAL CHEMISTRY
USING CHEMICAL KINETICS:
PROSPECTS AND DEVELOPMENTS
ORGANIC AND PHYSICAL CHEMISTRY
USING CHEMICAL KINETICS:
PROSPECTS AND DEVELOPMENTS
Y.G. MEDVEDEVSKIKH
ARTUR VALENTE
ROBERT A. HOWELL
AND
G.E. ZAIKOV
EDITORS
Nova Science Publishers, Inc.
New York
Copyright © 2007 by Nova Science Publishers, Inc.
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LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA
Organic and physical chemistry using chemical kinetics : prospects and developments / Y.G.
Medvedevskikh ... [et al.], editors.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-1-60692-749-6
1. Chemical kinetics. 2. Chemistry, Organic. 3. Chemistry, Physical and theoretical. I.
Medvedevskikh, Y. G.
QD502.O74 2007
541'.394--dc22
2007017506
Published by Nova Science Publishers, Inc.
New York
CONTENTS
Preface
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
ix
Conformation and Deformation of Linear
Macromolecules in Concentrated Solutions and
Melts in the Self–Avoiding Random Walks Statistics
Yu. G. Medvedevskikh
1
Thermodynamics of Osmotic Pressure
of Polymeric Solutions
Yu. G. Medvedevskikh, L. I. Bazylyak and G. E. Zaikov
23
Generalization of Data Concerning to the Coal
Swelling in Organic Solvents and Their Extraction
Using the Linear Multiparametric Equations
L. I. Bazylyak, D. V. Bryk, R. G. Makitra,
R. Ye. Prystansky and G. E. Zaikov
35
New Silazane Oligomers and Polymers with
Organic-Inorganic Main Chains: Synthesis,
Properties and Application
N. Lekishvili, Sh. Samakashvili,
G. Lekishvili and G. Zaikov
51
To Question about Influence of Solvent on Interaction
Propanethiole by Chlorine Dioxide
R. G. Makitra, G. E. Zaikov and I. P. Polyuzhyn
65
Mathematical Modelling of Thermo-Mechanical
Destruction of Polypropylene
G. M. Danilova-Volkovskaya,
E. A. Amineva and B. M. Yazyyev
Energy Criterions of Photosynthesis
G. А. Коrablev and G. Е. Zaikov
69
73
vi
Contents
Chapter 8
Spatial-Energy Interactions of Free Radicals
Chapter 9
Poly(Vinyl Alcohol)[PVA]-Based Polymer Membranes:
Synthesis and Applications
Silvia Patachia, Artur J. M. Valente,
Adina Papancea and Victor M. M. Lobo
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
89
103
The Research on the Process of Thermo-Mechanical
Destruction in Polypropylene
G.M. Danilova-Volkovskaya and E. A. Amineva
167
Zinccontaining Polymer - Inorganic Composite as
Vulcanization Active Component for Rubbers of
General and Special Assignment
V .I. Ovcharov, I. A. Kachkurkina,
O. V. Okhtina and B. I. Melnikov
173
Formation of Carbon Nanostructures and
Spatial-Energy Stabilization Criterion
G. А. Korablev and G. E. Zaikov
187
The Structural Treatment of Limiting Conversion
Degree for Solid-State Imidization
L. Kh. Naphadzokova, G. V. Kozlov and M. A. Tlenkopachev
201
A Solid-State Imidization and Heterogeneity
of Reactive Medium
L. Kh. Naphadzokova, G. V. Kozlov and G. E. Zaikov
207
Fractal-Like Kinetics of Reesterification
Reaction in Catalyst Presence
217
Description of the Model Reesterification Reaction
within the Framework of a Strange Diffusion Concept
225
Estimation of Vapor Liquid Equilibrium of Binary
Systems Tert-Butanol+2-Ethyl-1-Hexanol and
N-Butanol+2-Ethyl-1-Hexanol Using
Artificial Neural Network
H. Ghanadzadeh and A. K. Haghi
Liquid-Liquid Equilibria of the MME (Methylcyclohexane
+ Methanol + Ethylbenzene ) System
H. Ghanadzadeh and A. K.Haghi
Sugar Carbamides
J. A. Djamanbaev, J. A. Abdurashitova
and G. E. Zaikov
233
243
251
Contents
Chapter 20
Index
Impact of Chain-End Structure, Basic Comonomer
Incorporation and Pendant Structure on the Stability
of Vinylidene Chloride Barrier Polymers
Bob A. Howell, Adeyinka O. Odelana
and Douglas E. Beyer
vii
257
279
PREFACE
If it’s green or wiggly, it’s Biology
If it’s stinky, it’s Chemistry
If it doesn’t work, it’s physics.
(Definitions of sciences on the back of Sasha Zaikova’s sweatshirt
High School, Perry, Ohio, U.S.A.)
“Inevitability (verity) is something that nobody knows;
the truth everybody knows but each has his or her own truth”
Proverb
The word truth is a multi-meaning word which can be applied both to science and life.
We will not raise social problems but we will go down to the science, particularly chemical
science (organic and physical chemistry). We choose chemical kinetics as a method of
research because chemical kinetics is a science about chemical processes, mechanisms of
reactions, and about possibilities of directing reactions. Parts of the articles in this volume
deal with chemical physics, biochemical physics, and physical organic chemistry. All of these
fields of science are interconnected with each other.
The authors and editors are all part of an international effort to bring these fields of
knowledge to readers around the world. All these efforts are collected at symposia to share
and exchange knowledge. Symposium is defined as a convivial meeting, usually following a
dinner, for drinking and intellectual conversation. It is derived from ancient Greek word
sympósion, which means drinking party, and where ancient philosophers gathered to discuss
ideas. It is well-known that the ancient Greek philosopher and scientist Plato loved to attend
symposiums very much and he even died during a symposium on his birthday, at the age of
81. These are just fun facts on the background of symposia and none of this concerns the
authors and editors of this volume. The papers of this volume focus on the different states of
modern chemistry (both reviews and original papers.) Editors and authors will be grateful to
the readers for valuable remarks that will be taken into account in further work and research.
In the U.S.A., in the times of the Wild West, there was a proverb, stating that “A good
word is appreciated, but a good word with a gun behind it is even better.” Interpreting and
applying this proverb to modern times and situations, one can say that new hypotheses and
x
Y.G. Medvedevskikh, Artur Valente, Robert A. Howell, et al.
ideas are always appreciated, but new hypotheses and ideas with experimental data and other
proof behind them are better.
In the words of an engineer-mechanic of the Russian aviation, Vitalii K. Petukhov, said
“Try your best to do your best, because bad things will happen on their own”
We would like to accept this idea, because our dream is good volume for readers.
However, the last decision (the volume is good or bed) will be done by our readers.
Editors
Prof. Yurii G.Medvedevskikh
Branch of L.V.Pisarzhevskii Institute of Physical Chemistry
National Academy of Sciences
L’viv, Ukraine
Dr. Artur Valente,
Coimbra University
Coimbra, Portugal
Prof. Bob Howell
Central Michigan University
Mount Pleasant, Michigan, USA
Prof. Gennady Zaikov
N.M.Emanuel Institute of Biochemical Physics
Russian Academy of Sciences
Moscow, Russia
Chapter 1 - It was proposed a strict statistics of self–avoiding random walks in the d–
measured lattice and continuous space for intertwining chains in the concentrated solutions
and melts. On the basis of this statistics it was described the thermodynamics of conformation
and isothermal and adiabatic deformation of intertwining chains. It has been obtained the
equation of conformational state. It was shown, that in the field of chains overlap they are
stretched increasing its conformational volume. In this volume there are others chains with
the formation of m–ball. Free energy of a chain conformation does not depend upon the fact,
if the chains intertwined or they are isolated in the m–ball. Mixing entropy is responsible to
the chains interweaving in the m–ball. Dependencies of the conformational radius, free
energy and conformation pressure on respective concentration of polymeric chains have been
determined. Using the thermodynamics of intertwining polymeric chains of m–ball
conformational state and also the laws of isotropic media deformation into linear differential
form it were obtained the theoretical expressions for elasticity modules (namely, volumetric
volume, Young’s module and shift’s module) and for the main tensions appearing at the
equilibrium deformation of the m–ball. Poisson’s coefficient is a function only on the
Euclidean’s space and for the real 3–dimensional space is equal to 3/8. It was proposed a
simple model explaining the tensile strength of the m–ball by the chains intertwining effect
and, thereafter by the loss of the mixing entropy, but not by the chemical bonds breaking.
Preface
xi
Calculations of the elastic properties, the main tensions and tensile strength of natural rubber
carried out without using the empirical adjusting parameters are in good agreement with the
experimental data.
Chapter 2 - It was proposed the analysis of osmotic pressure for diluted, semi–diluted and
concentrated polymeric solutions based on the taking into account a free energy of
macromolecules conformation as a component of their chemical potential. It was shown, that
only into diluted solutions a free energy of macromolecules conformation does not contribute
into osmotic pressure and it is described by Vant–Goff’s equation. In a case of semi–diluted
and concentrated solutions the contribution of the conformative component of chemical
potential of macromolecules into osmotic pressure is dominate. Obtained expressions for the
osmotic pressure in a cases of semi–diluted and concentrated solutions are more general than
proposed ones in the scaling method and self–consistent field method; generally they are in
good agreement with the experimental data and don’t contain the empirical constants. It was
discussed the especial role of the critical concentration c* of the polymeric chains
intertwining. It was shown, that in this point a free energy of the conformation and also
osmotic pressure were determined uniquely, whereas for their derivatives upon the
macromolecules concentrations the jump is observed. On the basis of these peculiarities the
concentration c* is the critical point of the second order phases transition for the polymeric
solutions. This in accordance with the de Clause assumes the Scaling’s ratios application near
c*, although does not establish the criteria for the indexes of corresponding power functions
estimation.
Chapter 3 - Approaches to the consideration of a coal swelling process, which were used
up to now and based on the theory of regular solutions, do not give the possibility to
generalize quantitatively the experimental data. Adequate relation between the physical–
chemical properties of the solvents and the degree of a coal swelling in them can be obtained
only with the use of linear multiparametric equations which take into account the effects of
the all processes proceeding in the system; besides, the basicity and a molar volume of the
liquids are determinative. Such approach is effective at the generalization of data concerning
to extraction of a coal.
Chapter 4 - On the basis of the diallylsilazanes, α,ω-dihydrideoligoorganosiloxanes and
1,4-bis(dimethylhydridesilyl)benzene, new polyfunctional siliconorganic polymers have been
synthesized. General regularities and feasible mechanism of the reaction for obtaining diallylsilazanes have been studied. Based on data of elemental, IR and NMR 1H spectral analysis,
the composition and structure of synthesized polymers have been established.
The kinetics of polyhydrosailylation reactions has been studied. Quantum-chemical
calculations of the model system and data of NMR 1H spectra of the real products of the polyaddition reaction have confirmed probability of passing polyhydrosilylation reaction according to the aforementioned two concurrent directions obtaining both α and β adducts. For the
evaluation of relative activity for selected monomers the algebraic-chemical approach has
been used.
Using Differential Scanning Calorimetric and Roentgen-phase analyses methods it has
been established that synthesized polymers are amorphous systems. Thermal (phase) transformation temperatures of synthesized polymers have been determined. Thermooxidation
stability of the synthesized polymers has been studied. There was shown that their
thermooxidation stability exceeded the analogical characteristic of polyorganocarbosiloxanes.
xii
Y.G. Medvedevskikh, Artur Valente, Robert A. Howell, et al.
Using synthesized diallylsilazanes modification of the properties of some important industrial
polymer composites based on phenolformaldehide resins has been carried out. Preliminary
investigations showed that synthesized polymers in combination with phenolformaldehyde
resins were successfully used as binding-components for polymer/graphite and
polymer/carbon black electro-conducting composites.
Chapter 6 - There has been provided mathematical description of the processes of
thermonuclear destruction in deformed polypropylene melts; the aim was to use the criterion
of destruction estimation in modelling and optimising the processing of polypropylene into
products.
Chapter 7 - The application of methodology of spatial-energy interactions (P-parameter)
to main stages of photosynthesis is given. Their energy characteristics are calculated. The
values obtained correspond to the reference and experimental data.
Chapter 8 - Spatial-energy characteristics of many molecules and free radicals are
obtained. The possibilities of applying the P-parameter methodology to structural interactions
with free radicals and photosynthesis energetics evaluation are discussed. The satisfactory
compliance of calculations with experimental and reference data on main photosynthesis
stages is shown.
Chapter 10 - There has been investigated the effect of thermo-mechanical impact
conditions on destruction kinetics in polypropylene melts. The conditions served as a basis
for obtaining quantitative dependencies and mathematical expressions aimed at describing
destruction processes.
Chapter 11 - In work the synthesis technology of zinccontaining polymer - inorganic
composite on the basis of products of secondary raw material processing at joint precipitating
with carbamide and formaldehyde (ZnCFO) is described.
The structure and properties of ZnCFO are investigated by the differencial-thermal
analysis, electronic microscopy and IR-spectroscopy.
The ZnCFO action as vulcanization active component of elastomeric compositions on the
basis of rubbers of general and special assignment with various vulcanization systems is
investigated.
The comparative estimation of ZnCFO efficiency depending on type of vulcanization
system is given.
The ZnCFO influence on character of formed morphological structure of rubbers is
determined by the method of percalation analysis.
Chapter 12 - Spatial-energy criterion of structure stabilization was obtained. The
computation results for a hundred binary systems correspond to the experimental data. The
basic regularity of organic cyclic compound formation is given and its application for carbon
nanostructures is shown.
Chapter 13 - It was shown, that limiting conversion (in the given case - imidization)
degree is defined by purely structural parameter – macromolecular coil fraction, subjected
evolution (transformation) in chemical reaction course. This fraction can be correctly
estimated within the framework of fractal analysis. For this purpose were offered two
methods of macromolecular coil fractal dimension calculation, which gave coordinated
results.
Chapter 14 - It was shown, that the conception of reactive medium heterogeneity is
connected with free volume representations, that it was to be expected for diffusioncontrolled solid phase reactions. If free volume microvoids were not connected with one
Preface
xiii
another, then medium is heterogeneous, and in case of formation of percolation network of
such microvoids – homogeneous. To obtain such definition is possible only within the
framework of the fractal free volume conception.
Chapter 15 - It was shown, that the reesterification reaction without catalyst can be
described by mean-field approximation, whereas introduction of catalyst
(tetrabutoxytitanium) is defined by the appearance of its local fluctuations. This effect results
to fractal-like kinetics of reesterification reaction. In this case reesterification reaction is
considered as recombination reaction and treated within the framework of scaling approaches.
Practical aspect of this study is obvious-homogeneous distribution of catalyst in reactive
medium or its biased diffusion allows to decrease reaction duration approximately twofold.
Chapter 16 - It is shown, that there is principal difference between the description of
generally reagents diffusion and the diffusion defining chemical reaction course. The last
process is described within the framework of strange (anomalous) diffusion concept and is
controled by active (fractal) reaction duration. The exponent α, defining the value of active
duration in comparison with real time, is dependent on reagents structure.
Chapter 17 - Vapor-liquid equilibrium (VLE) data are important for designing and
modeling of process equipments. Since it is not always possible to carry out experiments at
all possible temperatures and pressures, generally thermodynamic models based on equations
on state are used for estimation of VLE. In this paper, an alternate tool, i.e. the artificial
neural network technique has been applied for estimation of VLE for the binary systems viz.
tert-butanol+2-ethyl-1-hexanol and n-butanol+2-ethyl-1-hexanol. The temperature range in
which these models are valid is 353.2-458.2K at atmospheric pressure. The average absolute
deviation for the temperature output was in range 2-3.3% and for the activity coefficient was
less than 0.009%. The results were then compared with experimental data.
Chapter 18 - The determination region of solubility of methanol with gasoline of high
aromatic content was investigated experimentally at temperature of 288.2 K. A type 1 liquidliquid phase diagram was obtained for this ternary system. These results were correlated
simultaneously by the UNIQUAC model. By application of this model and the experimental
data the values of the interaction parameters between each pair of components in the system
were determined. This revealed that the root mean square deviation (RMSD) between the
observed and calculated mole percents was 3.57% for methylcyclohexane + methanol +
ethylbenzene. The mutual solubility of methylcyclohexane and ethylbenzene was also
demostrated by the addition of methanol at 288.2 K.
Chapter 19 - The results of experimental researches on the synthesis of sugars derivatives
with glycosylamide and thioamide bonds have been presented in this work. The possibility of
using their in the preparative chemistry of sugars, some fields of medicine and agriculture has
been shown.
In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0
Editors: Y.G. Medvedevskikh, et al. pp. 1-21
© 2007 Nova Science Publishers, Inc.
Chapter 1
CONFORMATION AND DEFORMATION OF LINEAR
MACROMOLECULES IN CONCENTRATED SOLUTIONS
AND MELTS IN THE SELF–AVOIDING RANDOM
WALKS STATISTICS
Yu. G. Medvedevskikh*
Physical Chemistry of Combustible Minerals Department;
L. M. Lytvynenko Institute of Physical–Organic Chemistry
and Carbon Chemistry; National Academy of Sciences of Ukraine
ABSTRACT
It was proposed a strict statistics of self–avoiding random walks in the d–measured
lattice and continuous space for intertwining chains in the concentrated solutions and
melts. On the basis of this statistics it was described the thermodynamics of conformation
and isothermal and adiabatic deformation of intertwining chains. It has been obtained the
equation of conformational state. It was shown, that in the field of chains overlap they are
stretched increasing its conformational volume. In this volume there are others chains
with the formation of m–ball. Free energy of a chain conformation does not depend upon
the fact, if the chains intertwined or they are isolated in the m–ball. Mixing entropy is
responsible to the chains interweaving in the m–ball. Dependencies of the conformational
radius, free energy and conformation pressure on respective concentration of polymeric
chains have been determined. Using the thermodynamics of intertwining polymeric
chains of m–ball conformational state and also the laws of isotropic media deformation
into linear differential form it were obtained the theoretical expressions for elasticity
modules (namely, volumetric volume, Young’s module and shift’s module) and for the
main tensions appearing at the equilibrium deformation of the m–ball. Poisson’s
coefficient is a function only on the Euclidean’s space and for the real 3–dimensional
space is equal to 3/8. It was proposed a simple model explaining the tensile strength of
the m–ball by the chains intertwining effect and, thereafter by the loss of the mixing
entropy, but not by the chemical bonds breaking. Calculations of the elastic properties,
*
Yu. G. Medvedevskikh: 3a Naukova Str., 79053, Lviv, UKRAINE; e–mail: [email protected]
2
the main tensions and tensile strength of natural rubber carried out without using the
empirical adjusting parameters are in good agreement with the experimental data.
Key words: intertwining chains, SARW statistics, conformation, polymer chain, random
walks, lattice, thermodynamics, modules of elasticity, forces, work..
1. INTRODUCTION
Self–avoiding random walks (SARW) statistics has been proposed [1] for single that is for
non–interacting between themselves ideal polymeric chains (free–articulated Kuhn’s chains
[2]) into ideal solvents, in which the all–possible configurations of the polymeric chain are
energetically equal. From this statistics follows, that under the absence of external forces the
conformation of a polymeric chain takes the shape of the Flory ball, the most verisimilar
radius Rf of which is described by known expression [3, 4]
R f = aN 3 /( d + 2 )
(1)
Here: a is statistical length of the chain’s link; N is number of the links in chain or its length;
d is the dimension of the Euclidean’s space.
Polymeric chains in the concentrated solutions and melts at molar–volumetric
concentration c of the chains more than critical one c* = (NARfd)-1 are intertwined. As a result,
from the author’s point of view [3] the chains are squeezed decreasing their conformational
volume. Accordingly to the Flory theorem [4] polymeric chains in the melts behave as the
single ones with the size R = aN1/2, which is the root–main quadratic radius in the random
walks (RW) Gaussian statistics.
SARW statistics leads to other result.
2. SARW STATISTICS FOR INTERTWINING CHAINS
IN D–DIMENSIONAL LATTICE SPACE
Let us introduce the d–dimensional lattice with the cell’s parameter equal to the statistical
length a of the chain’s link; let us notify, that Z is number of cells in a space and m chains are
represented in it; every chain has the length N. As same as earlier [1], we will disregard the
energetic effects considering the all–possible configurations of the chains as equivalent.
We appropriate the random chain and notify as ni the numbers of steps of the end of chain
random walk along i–directions of d–dimensional lattice. At this,
∑n
i
=N,
i = 1, d
(2)
i
The probability
ω ( n ) that at given ni the end of chain draws si = ni + − ni − efficient
steps is subordinated to Bernoulli’s distribution [1]
Conformation and Deformation of Linear Macromolecules…
⎛1⎞
ω( N ) = ⎜ ⎟
⎝2⎠
N
∏ {n ! /[( n + s ) / 2 ]! [( n − s ) / 2 ]!}
i
i
i
i
3
(3)
i
Change of a sign si in eq. (3) doesn’t change the value
ω ( n ) ; that is why this probability
represents the probability of fact, that the RW trajectory per ni steps along i–directions of the
d–dimensional space will be finished in one of the 2d cells M(s), position data of which are
given by vectors s = (si), i = 1, d differing only by the signs of own components si.
Condition of the self–avoiding RW trajectories absence on the d–dimensional lattice
demands the circumstance at which more than one link of the chain can not be stood in every
cell. Links of the chain are inseparable; they cannot be divided one from another and located
into the cells in random order. Thereby, number of different methods of mN differing links
location per Z identical cells under condition that in every cell more than one link of the chain
cannot be stood is equal to Z! / (Z – mN)!.
By identify of the cells the antecedent probability of fact that the cell will be occupied by
presented link equal to 1/Z, and when will be not occupied – then (1 – 1/Z). Consequently,
probability ω ( z ) of mN differing links distribution per Z identical cells is determined by
Bernoulli’s distribution
Z!
⎛1⎞
ω( z ) =
⎜ ⎟
( Z − mN )! ⎝ Z ⎠
mN
⎛ 1⎞
⎜1 − ⎟
⎝ Z⎠
Z −mN
(4)
Distribution (3) describes the RW trajectory of one random chain whereas the expression
(4) assigns the links distribution of all m chains. That is why, the probability ω ( s ) of
common event consisting of the fact that the RW trajectory of random chain is also the SARW
trajectory and at given Z, n, N and ni will turned out by its own last step in one among 2d
equiprobable cells M(s) will be equal to
ω ( s ) = ( ω ( z ))1 / m ω ( n )
(5)
Using the Stirling’s formula under condition Z >> 1, N >> 1, ni >> 1 and factorizations ln(1–1/Z) ≈
–1/Z, ln(1–mN/Z) ≈ –mN/Z, ln(1±si/ni) ≈ ± si/ni–(si/ni)2/2 accordingly to condition si << ni, mN
<< Z and also assuming N(N–1) ≈ N2, we find the asymptotic (5) with accuracy to the
constant multiplier:
⎧ mN 2 1
⎫
2
− ∑ si / ni ⎬ ,
2 i
⎩ Z
⎭
ω ( s ) ≈ exp⎨−
m ≥1
(6)
As same as earlier [1], let us assume, that the fiducial cells M(s) generally appertain to
ellipsoid surface. Then we have [1]
4
Z = d d / 2 ∏| si |
(7)
i
Determination (7) means, that the d–dimensional space consisting of Z cells is disposable
for any random chain; this demands of their full mixing.
Combining the expressions (6) and (7) we will obtain
⎧
ω ( s ) = exp⎨− mN 2 / d d / 2 ∏| si | −
⎩
Function
i
⎫
1
2
si / ni ⎬
∑
2 i
⎭
(8)
ω ( s ) determines the probability that the RW trajectory of the random walk is
simultaneously also by SARW trajectory and by its own last step realizes the state M(s).
Hence, it is numerically equal to part of these SARW trajectories among general number (2d)N
of RW trajectories which realize the state M(s). Number L(s) of such SARW trajectories
determines the thermodynamical probability of the realization M(s):
L( s ) = ( 2d )N ω ( s )
(9)
By summing L(s) upon the all set of possible state of the chain’s end we find general
number L of SARW trajectory:
L = ( 2d ) N c( s )
(10)
where
⎧
⎫
1
2
c( s ) = ∑ exp⎨− mN 2 / d d / 2 ∏| si | − ∑ si / ni ⎬
2 i
s
i
⎩
⎭
(11)
Then function
w( s ) =
⎧
⎫
1
1
2
exp⎨− mN 2 / d d / 2 ∏| si | − ∑ si / ni ⎬
c( s )
2 i
i
⎩
⎭
(12)
normalized per unity and determines the end of chain distribution upon states M(s) of d–
dimensional lattice. It equal to ratio of number L(s) of SARW trajectories realizing the state
M(s) to general number L of SARW trajectories: w( s ) = L( s ) / L .
In turn, the ratio L/(2d)N equal to part of general number of SARW trajectories among
general number of RW trajectories in accordance with the adopted terms [3] is the fatigue
function g(N) of the SARW trajectories: g(N) = L/(2d)N = c(s).
5
3. SARW STATISTICS FOR INTERTWINING CHAINS
IN CONTINUOUS D–DIMENSIONAL SPACE
Let us introduce the variable of displacement xi, which is by semi–axis of conformational
ellipsoid; the state M(s) appertains to the surface of this ellipsoid [1]
xi = a | si | d 1/ 2
and parameter
(13)
σ i is a standard deviation of the Gaussian part of the distribution (12)
σ i 2 = a 2 ni d
(14)
In accordance with the expression (2) the following connection is imposed on the values
σi
∑σ
2
i
= a 2 Nd
(15)
i
Since si / ni = xi / σ i , d
2
2
2
d/2
∏| s |= a ∏ x
−d
i
i
i
ω( x ) =
the eq. (12) can be re–written as
i
⎧
1
1
2
2⎫
exp⎨− a d mN 2 / ∏ xi − ∑ xi / σ i ⎬
2 i
c( x )
i
⎩
⎭
⎧
1
2
2⎫
c( x ) = ∫ exp⎨− a d mN 2 / ∏ xi − ∑ xi / σ i ⎬dx
2 i
i
⎩
⎭
(16)
(17)
At this, c(x) is d–multiple integral upon all possible values xi, dx =
∏ dx . Since
i
i
c( x ) = a d d d / 2 c( s ) we have g(N) = c(x)/addd/2.
Integral c(x) can be taken with the adequate accuracy by saddle–point technique [1, 5].
Change of (13) introduces an essential difference between w( s ) and w( x ) : the last
determines the probability w( x )dx of fact that the SARW trajectory at given values m, N and
σ i will finished in the elementary volume dx = ∏ dxi lying on the surface of the ellipsoid
i
with the semi–axes xi, i = 1,d.
6
4. THERMODYNAMICS OF CONFORMATION AND DEFORMATION
OF INTERTWINING CHAINS
Maximum w( x ) at given m, N and
σ i determines the most expected or equilibrium
state of the polymeric chain. Semi–axes xi of equilibrium conformational ellipsoid we will
found from the condition ∂ ln w( x ) / ∂xi = 0 at xi = X i :
1 /( d + 2 )
⎛
⎞
X i = σ i ⎜⎜ a d mN 2 / ∏ σ i ⎟⎟
i
⎝
⎠
(18)
In the absence of external forces the all directions of the end of chain walking are
equiprobable accordingly to condition ni = N / d ; so
σ i 2 = σ 02 = a2 N
(19)
Substitution of (19) into (18) makes the semi–axes Xi of equilibrium ellipsoid the same
and equal to radius Rm of the conformational sphere; the same distribution density ω ( x )
corresponds to the surface of this conformational sphere:
Rm = aN 3 /( d +2 )m
1 /( d + 2 )
(20)
Expression (20) determines not only the conformational radius of one random chain, but
due to the chains intertwining effect also the conformational radius of all m chains. Thereby
Rmd is the conformational volume of m–ball disposable for every among the intertwining
chains. As we can see, m–ball is a fractal with two fractal indexes: first is 3/(d+2) and
determines the dependence Rm on the chain N, the second is 1/(d+2) and determines the
dependence on number of chain in m–ball.
We can see from the comparison of (20) and (1), that the conformational radius Rm of m–
ball and respectively of any random chain in it is more than the conformational radius Rf of
random chain: in m–ball the chains are stretched but are not twisted. The presence of other
chains diminishes the number of free cells of d–dimensional lattice accessible for SARW
trajectory of presented chains enforcing it to encroach more volume of the space.
In the presence of external forces acting along i–axes of the d–dimensional space,
σ i ≠ σ 0 and m–ball is deformated into the ellipsoid with semi–axes Xi accordingly to (18). It
is convenient to introduce the following variables as a measure of m–ball deformation
Λi = X i / Rm
(21)
7
which characterize the multiplicity of the linear deformation of m–ball along i–direction of a
space.
Next, let us determine the multiplicity Λv of volumetric deformation via expression
Λv = ∏ X i / Rmd = ∏ Λi
i
Λv
(22)
i
Due to (2) [1] at any deformations of the m–ball its conformational volume is decreased:
≤ 1 . The connection equation between Λi corresponds to connection equation (2):
∑Λ
i
i
2
= d / ∏ Λi
(23)
i
In continuous space the thermodynamical probability W ( x ) of the realization of state in
which the end of chain is located on the surface of the ellipsoid with the semi–axes Xi is equal
to
W ( x ) = Lω ( x )
(24)
As same as for the lattice space, general number L of SARW trajectories in continuous
space let us determine in the form (10), that is L ≈ ( 2d ) c( x ) . That is why
N
⎧
1
2
2⎫
W ( x ) ≈ ( 2d ) N exp⎨− a d mN 2 / ∏ xi − ∑ xi / σ i ⎬
2 i
i
⎩
⎭
(25)
Entropy S of presented conformational state is equal to S = k ln W ( x ) , free energy
F = −TS or F = −kT ln W ( x ) . From (25) follows F = F0 + F ( x ) where
F0 ≈ −kTN ln 2d ≈ −
d
kTN
2
⎧
1
2
2⎫
F ( x ) = kT ⎨a d mN 2 / ∏ xi + ∑ xi / σ i ⎬
2 i
i
⎩
⎭
(26)
(27)
Thereby, F0 represents by itself a free energy of random walks independent on the
conformational state of a chain; F(x) brings a positive contribution into F and the sense of this
consists in a fact that the terms F(x) and S(x) represent the limitations imposed on the
trajectories of random walk by request of the self–avoiding absence. These limitations form
the self–organization effect of the polymeric chain: the conformation of polymeric chain is
the statistical form of its self–organization.
8
Since F0 doesn’t depend on the conformational state of a chain we assume that the free
energy of a polymeric chain conformation is equal to F = F(x) accordingly to (27).
Expression for the free energy of equilibrium conformation of polymeric chain we will obtain by
substitution of the values xi = Xi in (27) in accordance with the (18):
2
⎛ d⎞ ⎛R ⎞
Fm = ⎜1 + ⎟kT ⎜⎜ m ⎟⎟ / Λv
⎝ 2 ⎠ ⎝ σ0 ⎠
For non–deformated m–ball we have
⎛ d⎞ ⎛R ⎞
F = ⎜1 + ⎟kT ⎜⎜ m ⎟⎟
⎝ 2 ⎠ ⎝ σ0 ⎠
(28)
Λv = 1 and
2
0
m
(29)
From this the expression follows for the deformation work ( A = ΔFdef in the system of
the mechanics signs) of m–ball into ellipsoid in calculation per one chain
⎛ d⎞ ⎛R ⎞
ΔFdef . = ⎜1 + ⎟kT ⎜⎜ m ⎟⎟
⎝ 2 ⎠ ⎝ σ0 ⎠
Since
2
⎛ 1
⎞
⎜⎜ − 1⎟⎟
⎝ Λv
⎠
(30)
Λv ≤ 1 , a work of the deformation is positive ΔFdef ≥ 0 , that is realized above the
0
polymeric chain. Let us compare a free energy Fm of the polymeric chain in non–deformated
m–ball with a free energy Ff of single deformated polymeric chain [1]
⎛ d⎞ ⎛R
F f = ⎜1 + ⎟kT ⎜⎜ f
⎝ 2 ⎠ ⎝ σ0
Here
2
⎞
⎟⎟ / λv
⎠
(31)
λv is a multiplicity of the volumetric deformation of Flory ball.
Let us assume that the chains in m–ball aren’t intertwined, every among them occupies
the isolated volume equal to Rmd/m. Then the multiplicity of the volumetric deformation of
Flory ball into m–ball will be equal to
λv = Rm d / mR f d = m −2 /( d +2 )
(32)
We will obtain for the conformation free energy of isolated chain into m–ball
⎛ d⎞ ⎛R
F f = ⎜1 + ⎟kT ⎜⎜ f
⎝ 2 ⎠ ⎝ σ0
2
⎞ 2 /( d +2 )
⎟⎟ m
⎠
(33)
that
is
equal
to
Fm0
accordingly
( Rm / σ 0 ) = ( R f / σ 0 ) m
2
2
2 /( d + 2 )
to
(29)
with
taking
into
9
account
that
.
Thereby, free energy of the conformation of single chain into m–ball for intertwining or
isolated one from another chains is the same. Free energy of the conformation is not the
factor, which facilitates or prohibits the chains intertwining.
In the absence of energetic interaction such factor is the entropy of mixing. It can be
estimated via the numbers of displacement methods of the all chains links into m–ball with
the exception of a displacement links in every chains: (mN)!/(N!)m. From this under the
Stirling’s approximation we will obtain the expression for the entropy of mixing ΔS c in
calculation per one chain,
ΔSc = kN ln m , and, respectively we will obtain for free energy
ΔFc of mixing
ΔFc = −kTN ln m
The value
(34)
ΔFc < 0 and can be sufficiently big per absolute value, for instance for melts,
in order to provide the chains intertwining of their mixing in m–ball.
6. EQUATION FOR THE CONFORMATIONAL STATE OF M–BALL
Let us determine the pressure P of a conformation via the ordinal thermodynamic ratio
(∂F / ∂V )T = − P as a connection measure between the free energy and the volume of
conformation. Taking into account the all chains into m–ball, we have F = mFm ,
V = Rmd Λv , that is why P = −m∂Fm / ∂Λv Rmd . By differing the eq. (28) we have
2
⎛ d⎞ ⎛R ⎞
P = ⎜1 + ⎟kT ⎜⎜ m ⎟⎟ m / Rmd Λ2v
⎝ 2 ⎠ ⎝ σ0 ⎠
(35)
By multiplying (35) on V = ( Rm Λv )
2
d
2
we will obtain the equation of the
conformational state of m–ball:
PV 2 = mkTβ
(36)
2
⎛ d ⎞⎛ R ⎞
β = ⎜1 + ⎟⎜⎜ m ⎟⎟ Rmd
⎝ 2 ⎠⎝ σ 0 ⎠
(37)
10
From the comparison of (35) and (28) it follows, that the pressure of the conformation
numerically is equal to the density of free energy of the conformation of m–ball P = mFm/V.
That is why we have
FmV = kTβ
(38)
Thereby, the values PV2 and FmV are integrals of the process of equilibrium deformation of m–
ball.
7. ADIABATIC EQUATION FOR EQUILIBRIUM
DEFORMATION OF M–BALL
It is well–known [6, 7], that at the adiabatic deformation of rubber its temperature is
increased. The analysis of this phenomenon in the works [6, 7] is not quite correct. That is
why let us consider the adiabatic deformation of the m–ball with the use of obtained
thermodynamic ratios.
For elementary adiabatic process Cv dT = −δA , where Cv is the heat of the m–ball, δA
is the elementary work in the systems of the thermodynamics signs. Due to determination of
the conformation pressure we can write δA = PdV and, thereby
Cv dT = − PdV
(39)
Using the equation of the conformational state (36) let us divide the variables in (39)
Cv dT / T = −mkβdV / V 2
(40)
Integration of (40) at Cv = const for low–temperature interval in a ranges from V = Rmd
and V = Rm Λv and from T0 till T corresponding to the temperatures of the start and the finish
d
of the adiabatic process gives
Cv ln
T mkβ
= d ( 1 / Λv − 1 )
T0
Rm
(41)
We can see from this, that the adiabatic equation is as follow
{
}
T exp − mkβ / Cv Rmd Λv = const
(42)
In accordance with the experimental data the temperature change at the adiabatic
deformation of rubber is slight, that is why it can be assumed that ΔT = T − T0 << T0 ; this
permits to re–write (41) with taking into account the expression (37) for
β in following form
11
2
⎛ d ⎞ kT ⎛ R ⎞
ΔT ≈ ⎜1 + ⎟ 0 ⎜⎜ m ⎟⎟ ( 1 / Λv − 1 )
⎝ 2 ⎠ cv ⎝ σ 0 ⎠
(43)
Here it was assumed that Cv = mcv, where cv is a heat of one chain.
8. EXPRESSION OF THE THERMODYNAMIC FUNCTIONS
VIA RELATIVE CONCENTRATION OF MACROMOLECULES
In the field of the chains overlapping at c ≥ c = ( N A R f )
*
d
−1
their molar–volumetric
concentration into m–ball and in all volume of the solution or melt is the same:
c = m / N A Rmd .
It is more convenient for the melts to use the other determination of concentration since
ρ = mM / N A Rmd , where M is a molar mass of the chain and is experimentally determined
by a specific density of the melt. Speculative critical density
ρ * = M / N A R df corresponds
to it.
From this follows
ρ / ρ * = c / c* = m 2 /( d +2 )
(44)
The ratio (44) permits to determine the following dependencies, which with the aim of
* 1/ 2
the shortness can be represented in the form of the commensurability: Rm ~ ( c / c )
*
*
,
2
Fm ~ c / c and P ~ ( c / c ) .
9. FORCES AND WORK OF THE DEFORMATION
Let us introduce one more parameter for characteristics of m–ball deformation with the
aim of convenient description of elastic properties of the intertwining chains
ψi = σi / σ0
(45)
Due to the ratio (15) the following connection exists between ψ i
∑ψ
2
i
=d
(46)
i
We determine from the analysis of (18) and (20), and also from the determinations (21)
and (22)
12
ψ i = Λi Λv1/ 2
(47)
In the system of the mechanics signs the deformation forces acting on the random chain
into m–ball along i–axes of the d–dimensional space are equal to f i = ∂F ( x ) / ∂xi . By
differing (27) we will obtain
⎛
2⎞
f i = kT ⎜⎜ − a d mN 2 / xi ∏ xi + xi / σ i ⎟⎟
i
⎝
⎠
(48)
However, under the equilibrium deformation in every current conformational state the
forces should be equal to zero; just this is expressed via the equilibrium condition
∂F ( x ) / ∂xi = 0 at xi = Xi. Thereby, the substitution of the values xi = Xi into (48) draws fi
into zero. That is why the external deformation force along i–direction let us determine as the
force, which should be imposed on the non–deformated m–ball with the conformation radius
Rm, which is equilibrium with respect to the values σ i = σ 0 in order to transform it into the
deformated state of the ellipsoid with the semi–axes Xi equilibrium with respect to the values
σ i ≠ σ 0 , i = 1,d. In accordance with this determination in the expression (48) in the second
term it is necessary to put
σ i = σ 0 but the values xi to change on Xi accordingly to (18) at
σ i ≠ σ 0 . Making the corresponding substitution we will obtain the following expression for
the external main forces of a deformation
(
1 /( d + 2 )
)
⎛R ⎞
⎛
⎞
2
f i = kT ⎜⎜ m2 ⎟⎟ ψ i − 1 / ψ i ⎜⎜ ∏ψ i ⎟⎟
⎝ i
⎠
⎝σ0 ⎠
In the adopted systems of signs fi > 0 at the stretching
contraction
(ψ i < 1) .
(49)
(ψ i > 1)
and fi < 0 at the
With taking into account the connection (47) the force can be determined via the
multiplicities of linear and volumetric deformation of m–ball
(
)
⎛R ⎞
2
f i = kT ⎜⎜ m2 ⎟⎟ Λi Λv − 1 / Λi Λv
⎝σ0 ⎠
(50)
The work of the deformation A in calculation per one chain into m–ball along the all main
directions can be written in accordance with the mechanics rules in form:
Xi
A = ∑ ∫ f i dxi
i
Rm
(51)
13
Substitution of (49) in (51) with taking into account the connection (47) leads to the
expression for A which is identical to the expression (30) for Fdef: A = ΔFdef in the systems
of the mechanics signs. The agreement confirms the truth of the determination of external
forces of deformation accordingly to (49).
10. ELASTICITY MODULES OF M–BALL
Taking into account the big sizes of polymeric chains deformation and their non–linear
relation with the tension let us express the relative linear deformation dxi/xi along i–direction
of d–dimensional space under the action of all main forces fi, i = 1,d under the approximation
of m–ball isotropy via the differential form [8]
Y∂xi / xi = ∂f i / ∏ x j + γ ∑ ∂f j / ∏ xk
j ≠i
j ≠i
Here: Y is Young’s module;
(52)
k≠ j
γ is Poisson’s coefficient;
∏x
j
and
j ≠i
∏x
k
are the values of
k≠ j
the sites in d–dimensional space normal to the forces fi and fj correspondly.
Let us re–write the (52) relative to Young’s module
Y=
x x ∂f i
∂f i
+γ ∑ i j
∏ xi ∂xi j≠i ∏ xi ∂xi
xi
2
i
(53)
i
At equilibrium deformation the forces fi are equal to zero, but not their derivatives
∂f i / ∂xi and ∂f i / ∂x j . That is why by differing (48) upon xi and xj and by substituting the
equilibrium values xi = Xi into obtained expressions we will obtain
∂f i / ∂xi = 3kT / σ 0 ψ i
2
2
(54)
∂f i / ∂x j = ∂f j / ∂xi = kT / σ 0 ψ iψ j
2
(55)
Derivatives in (54) and (55) have been written in accordance with the determination (48)
for one random chain. However, as same as the conformation pressure the elastic properties
of the intertwining chains in m–ball need the taking into account the all m chains. That is why
by multiplying the right terms of (54) and (55) on m and by substituting the result in (53) we
will find
2
⎛R ⎞
d
2
Y = mkT [3 + γ ( d − 1 )]⎜⎜ m ⎟⎟ / Rm Λv
⎝σ0 ⎠
(56)
14
From the comparison of (35) and (56) follows, that the Young’s module of m–ball and the
conformation pressure are differed only by the coefficient and
Y=
2[3 + γ ( d − 1 )]
P
d +2
(57)
In general case of the d–dimensional space the connection between the Young’s module
and the pressure is expressed via the volumetric module E = –VdP/dV by ratio [8]
E = Y / d [1 − γ ( d − 1 )]
(58)
From the equation of a state (12) follows
E = 2P
(59)
By comparing the (57) – (59) we will obtain the expression for Poison’s coefficient
γ = ( d + 3 ) /( d + 1 )2
(60)
Thereby, as same as for the random chain [1], the Poison’s coefficient for intertwining
chains is determined only by the dimensionality d of the Euclidean’s space an at d = 3 is
equal to γ = 3 / 8 .
Via the Young’s module and the Poison’s coefficient we find the shift module
μ = Y / 2( 1 + γ )
at d ≥ 2
μ [2]:
(61)
which is also easy expressed via the conformation pressure
μ=
3 + γ ( d −1)
P
( d + 2 )( 1 + γ )
(62)
11. MAIN TENSIONS AND THE TENSILE STRENGTH
Connection between the tension Gi in planar surface normal to i–direction of the
deformation and between its relative value ∂xi / xi also let us write in differential form
∂Gi = Y∂xi / xi
(63)
In general case this equation hasn’t a simple analytical solution, but permits with the use
of (23) and (46) easy to obtain the constraint equation between Gi. By acting analogously to
the developed algorithm [1], we will obtain
∑G
i
i
(
)
1
2
= − Y 0 1 / Λv − 1
2
15
(64)
Λv = 1 , that is for non–deformated m–ball.
where Y0 = Y at
The sign “minus” signifies, that a sum of the main tensions is subzero (that is negative) at
any deformations of m–ball through its volume decreasing.
For analytical demonstration of Gi at equilibrium deformation, that is at xi = Xi let us re–
write the (63) with taking into account the ratio Y = Y /
0
Λv 2 and substitute in it the
expression ∂ ln xi = ∂ lnψ i − 1 d ln Λv which follows from the connection (47). Then we
2
will obtain
4 / d +2
⎤
⎡
⎛
⎞
1
3
∂Gi = Y ⎢∂ψ i/ ψ i ⎜⎜ ∏ψ i ⎟⎟
− ∂Λv / Λv ⎥
2
⎝ i
⎠
⎥⎦
⎢⎣
0
In the starting non–deformated state of m–ball the all
(65)
ψ i = 1 , Λv = 1 and Gi = 0. By
integrating the (65) accordingly to these conditions we will find
(
)
⎤
⎡1
2
Gi = Y 0 ⎢ 1 / Λv − 1 + I i ⎥
4
⎦
⎣
ψ
i
⎛
⎞
I i = ∫ ∂ψ i / ψ i ⎜⎜ ∏ψ i ⎟⎟
⎝ i
⎠
1
(66)
4 /( d + 2 )
(67)
From this follows, that for the calculation of Ii and respectively Gi the constraint equation
(46) between ψ i is insufficiently; additional information about the character of deformation
is needed in order to determinate the additional connection between
ψ i . One among the
variants of the Gi calculation is considered in the next chapter.
At the m–ball stretching along the i–direction such critical tension is beginning at which
m–ball is broken into two parts. Such critical tension Gicr is the numerical estimation of m–
ball tensile stretch. Its mechanism likes sufficiently complicating, but we will propose a
simple model for the Gicr calculation. Accordingly to this model we assume, that the break of
m–ball into two parts at Gicr proceeds at the expense of the chains fraying, that is at the
expense of the process inverse to their intertwining, in the issue of which the physical
network of the linkings is destroyed. Crosslinking of the chains at rubber vulcanization blocks
the chains intertwining and that is why increases the stability of the vulcanized rubber. The
chains intertwining in m–ball decreases the entropy of mixing. For non–deformated m–ball
the entropy of mixing ΔS c for all m chains determined as
ΔSc = kNm ln m
(68)
16
Let in the deformated m–ball in a moment of break the part of the residual intertwining
chains is equal to α . Then the entropy of mixing will be equal to
ΔSc = kNmα ln( mα ) ,
mα > 1
(69)
The break of m–ball we consider as such equilibrium transition at which m–ball with the
intertwining parameter α is divided by the plane of fracture into two m/2–balls with the same
intertwining parameter. The entropy of mixing into two m/2–balls will be equal to
αm
ΔSc' = kNαm ln( αm / 2 ) ,
2
>1
(70)
The loss of the entropy of mixing at the m–ball braking will be
thereafter the work of a break
Δ( ΔS c ) = ΔSc' − ΔSc ;
ΔFbr = −TΔ( ΔS c ) will be
ΔFbr = kTNαm ln 2
(71)
At breaking the m–ball into two parts it can be assumed that
α = 1 / 2 . Then
ΔFbr = ( 1 / 2 )kTNm ln 2
(72)
This work of the break is created by the work of the m–ball deformation at some critical
value of the multiplicity of volumetric deformation Λ vcr . That is why by equating a work of
the deformation
ΔFdef accordingly (30) multiplied on m– in calculation per all m–ball at
some critical value
Λv to the work of a break ΔFbr accordingly to (72) we will find Λv :
cr
2
⎤
⎡
1 ⎛σ0 ⎞
⎜⎜
⎟⎟ N ln 2⎥
Λvcr = ⎢1 +
⎥⎦
⎢⎣ d + 2 ⎝ Rm ⎠
Knowing the
cr
−1
(73)
Λv , we can calculate the tensile strength Gi at the m–ball stretching
cr
cr
along the i–direction.
12. CALCULATIONS AND ILLUSTRATIONS
For calculations let us consider the real d = 3–dimensional space assuming that among
three main tensions fx, fy and fz only one, for example fz is independent variable, that is
external force, and fx, and fy are reaction forces on fz. At the isotropy of m–ball the forces and
17
multiplicities of linear deformations along the x and y axes will be equal: f x = f y ,
In this case the conformational volume of the m–ball shapes the elongated
or strangulated ( f z < 0 , Λz < 1) along z–axis the ellipsoid of rotation.
Λx = Λ y .
( f z > 0, Λz > 1)
For the ellipsoid of rotation the general constraint equations (23) and (46) take on the
particular form
2Λv + Λz Λv − 3Λz = 0
(74)
2ψ x + ψ z = 3
(75)
2
2
3
2
By assigning the values
Λz as to singular independent variable the values Λv have been
calculated and further Λx = Λ y = ⎛⎜ Λv ⎞⎟
Λ
1/ 2
⎝
z
⎠
.
For the shortness let us confine to the numerical analysis of the isothermal and adiabatic
deformation of natural rubber, which at comparatively low chains cross–linking can be
described as a melt.
For natural rubber – polyisoprene (C5H8)N – the following parameters have been chosen:
number–average molar mass of the chain M = 2·106 g/mole and average length of the chain N
= 2,9·104; ρ = 0,91·106 g/m3, a = 0,125 nm. On the basis of these parameters ρ* = 1,54·104 g/m3 and
ρ/ρ* = 59,1 were determined.
The work of the isothermal deformation in units kT has been calculated in accordance
with the equation (30) converted to a form
ΔFdef / kT =
5 1/ 5 ⎛ ρ
N ⎜⎜ *
2
⎝ρ
⎞
⎟⎟(1 / Λv − 1)
⎠
(76)
Results of the calculations are represented on figure 1.
Dependence of ΔFdef / kT for one chain of the natural rubber on
Λz is the same as for
the Flory’s ball [1], but numerically exceeds the last in ρ/ρ* times. Let us notify also, that in spite
of the “very much” value ΔFdef / kT for one chain in calculation per one link, this magnitude
has an order equal to 1.
Temperature change at adiabatic deformation of natural rubber was calculated
accordingly to eq. (43) which under assumption cv = cv N , where cv = c p is molar heat
0
0
0
of the isoprene carries to
⎛ ρ ⎞
RT
ΔT = 5 2 00 N −4 / 5 ⎜⎜ * ⎟⎟(1 / Λv − 1)
cp
⎝ρ ⎠
(77)
where R is universal gaseous constant. At the calculation accordingly to (77) it was assumed
in accordance with the reference data for the isoprene cp0 =152,3 J/moleK, T0 = 300 K.
18
(
)
(
Figure 1. The work of the natural rubber deformation at its stretching Λz > 1 and squeezing Λz
along z axis. Calculation has been done in accordance with the eq. (76) (see the explanations in text).
'
'
)
<1
Results of the calculations are represented on figure 2. They are in good agreement with
the experimental data [6, 7].
5
ΔT, K
4
3
2
1
0
0
1
2
3
4
Λz
5
Figure 2. Temperature increasing at adiabatic deformation of natural rubber at its stretching
(
)
(Λz > 1) and
squeezing Λz < 1 along z axis. Calculation has been done in accordance with the eq. (77) (see the
explanations in text).
Young’s module has been calculated in accordance with the eq. (56) by taking into
account (44) and γ = 3 / 8 :
19
2
⎛ ρ
kT
Y = 3,75 3 N −8 / 5 ⎜⎜ *
a
⎝ρ
⎞
2
2
⎟⎟ / Λv = Y 0 / Λv
⎠
(78)
where Y0 = 1,97 MPa is Young’s module of non–deformated rubber at T = 300 K. Results of
the calculations are represented on figure 3.
For the ellipsoid of rotation Gx = Gy, that is why we can write in accordance with the (66)
(
)
(79)
(
)
(80)
⎡1
⎤
2
Gx = Y 0 ⎢ 1 / Λv − 1 + I x ⎥
⎣4
⎦
⎡1
⎤
2
Gz = Y 0 ⎢ 1 / Λv − 1 + I z ⎥
⎣4
⎦
Due to connection (75) every from integrals Ix and Iz can be balanced to one own
variable. In accordance with the (67) and (75) we have
ψx
(
/5
I x = ∫ dψ x / ψ 13
3 − 2ψ x
x
)
2 2/ 5
(81)
1
Iz = 2
ψz
4/ 5
∫ dψ
z
/ψz
9/ 5
(3 −ψ )
2 4/ 5
(82)
z
1
At this, superior limits of the integration are given by the ratios
ψ x = Λx Λv1 / 2 and
ψ z = Λz Λv1 / 2 following from (47).
Results of the calculations accordingly to eq. (79) – (82) at Y0 = 1,97 MPa are
represented on figure 4.
Needed for the estimation of Gzcr value of critical multiplicity of volumetric deformation
Λv was calculated accordingly to eq. (73) by transforming it to a form
cr
⎡ 1
⎛ ρ*
Λvcr = ⎢1 + N 4 / 5 ⎜⎜
⎝ ρ
⎣ 5
⎤
⎞
⎟⎟ ln 2⎥
⎠
⎦
As a result, we have obtained
−1
(83)
Λv = 0,103 , respectively Λz = 5,39 , Λx = 0,138 .
cr
Gzcr = 48 MPa corresponds to these values.
cr
cr
20
150
Y, MPa
100
50
0
0
1
2
3
Λz
4
5
Figure 3. Dependence of the Young’s module on the multiplicity of linear deformation Λz at stretching and
squeezing of natural rubber along z axis. Calculation has been done in accordance with the eq. (78) (see the
explanations in text).
50
Gz,Gx, MPa
Gz
25
Gx
0
Gz
-25
Gx
-50
0
1
2
3
4
Λz
5
Figure 4. Dependence of the main tensions Gz and Gx on the multiplicity of linear deformation Λz at
stretching and squeezing of natural rubber along z axis. Calculation has been done in accordance with the eq.
(79) – (82) (see the explanations in text).
As we can see from the figure 4, calculated dependence of the tension Gz on the
multiplicity of natural rubber stretch is in good agreement with the experimental data [6, 7,
21
9]. However, the numerical values Gz and Gzcr are in whole rather higher than the
experimental ones. It is connected with fact, that the last represent by themselves not faithful,
but conventional tensions and tensile strengths, which were estimated with not taking into
account the volumetric deformation of the rubber [6, 7, 9].
CONCLUSION
Accordingly to the self–avoiding random walks statistics in the field of the chains
intertwining that is in concentrated solutions and melts the polymeric chains are stretched
increasing its conformational volume. In this volume other chains are also represented
forming the m–ball. Free energy of the chain conformation doesn’t depend on a fact if chains
are intertwined or they are isolated in m–ball. The entropy of mixing is responsible for the
chains intertwining in m–ball, but not free energy of the chains conformation. Dependencies
of the conformational radius, free energy and conformation pressure on relative concentration
of the polymeric chains into solution or melt have been determined. Thermodynamical
analysis of the isothermal and adiabatic deformation of m–ball has been done.
Self–avoiding random walks statistics for intertwining polymeric chains and based on it
thermodynamics of their conformational state in m–ball permitted to obtain the theoretical
expressions for elasticity modules and main tensions appearing at the equilibrium
deformation of m–ball. Calculations on the basis of these theoretical expressions without
empirical adjusting parameters are in good agreement with the experimental data.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
Medvedevskikh Yu. G. // Condensed Matter Physics, 2001, v. 4, № 2 (26), P. P. 209,
219
Kuhn W. Koll. Zs. // 1934, B. 68, S. 2.
De Gennes P. G. Scaling Concepts in Polymer Physics // Ithaca: Cornell Univ. Press.,
1979.
Flory P. J. Statistical Mechanics of Chain Molecules // M.: Myr, 1971.
Fedoryuk M. V. Saddle–Point Technique. Moscow, Nauka, 1977, 254 p. (in Russian)
Treloar L. The Physics of Rubber Elasticity. Oxford, 1949
Askadskiy A. A. Deformation of Polymers. Moscow, Chimiya, 1973, 448 p.
Feynman R., Leighton R., Sands M.. The Feyman Lectures of Physics. // V. 7. Physics of the
Continuous Media (Russian translation, Moscow, Mir, 1977), 288 p.
Bartenev G. M., Frenkel C. Ya. Physics of Polymers. L.: Chimiya, 1990, 429 p.
Chapter 2
THERMODYNAMICS OF OSMOTIC
PRESSURE OF POLYMERIC SOLUTIONS
Yu. G. Medvedevskikh*1, L. I. Bazylyak1 and G. E. Zaikov*2
1
Physical Chemistry of Combustible Minerals Department
L. M. Lytvynenko Institute of Physical–Organic Chemistry and
Carbon Chemistry; National Academy of Sciences of Ukraine
2
N. Emmanuel Institute of Biochemical Physics
ABSTRACT
It was proposed the analysis of osmotic pressure for diluted, semi–diluted and
concentrated polymeric solutions based on the taking into account a free energy of
macromolecules conformation as a component of their chemical potential. It was shown,
that only into diluted solutions a free energy of macromolecules conformation does not
contribute into osmotic pressure and it is described by Vant–Goff’s equation. In a case of
semi–diluted and concentrated solutions the contribution of the conformative component
of chemical potential of macromolecules into osmotic pressure is dominate. Obtained
expressions for the osmotic pressure in a cases of semi–diluted and concentrated
solutions are more general than proposed ones in the scaling method and self–consistent
field method; generally they are in good agreement with the experimental data and don’t
contain the empirical constants. It was discussed the especial role of the critical
concentration c* of the polymeric chains intertwining. It was shown, that in this point a
free energy of the conformation and also osmotic pressure were determined uniquely,
whereas for their derivatives upon the macromolecules concentrations the jump is
observed. On the basis of these peculiarities the concentration c* is the critical point of
the second order phases transition for the polymeric solutions. This in accordance with
the de Clause assumes the Scaling’s ratios application near c*, although does not establish
the criteria for the indexes of corresponding power functions estimation.
*
*
Yu. G. Medvedevskikh; L. I. Bazylyak: 3a Naukova Str., 79053, Lviv, UKRAINE; e–mail: [email protected];
G. E. Zaikov: 4 Kosygin Str., 117977, Moscow, RUSSIA; e–mail: [email protected]
24
Key words: osmotic pressure, polymeric solutions, free energy of conformation.
1. INTRODUCTION
Osmose plays an essential role in a wide technological and especially in biological
systems represented by solutions of biopolymers. That is why understandable is interest of
scientists to the problem of osmotic pressure of polymeric solutions which permits
comparatively easy experimentally to determine the advantages and deficiencies of theoretical
imaginations about thermodynamical properties of polymeric solutions.
Two main approaches for osmotic pressure of polymeric solutions theoretical description
can be distinguished. First is Flory–Huggins method [1, 2], which afterwards has been
determined as method of self–consistent field. In the initial variant the main attention has
been paid into pair–wise interaction in the system “gaped monomeric links – molecules of
solvent”. Flory–Huggins parameter χ was a measure of above–said pair–wise interaction and
this limited application of presented method by field of concentrated solutions. In subsequent
variants such method was extended on individual macromolecules into diluted solutions with
taken into account the tie–up of chain links by Gaussian statistics [1].
For description of the osmotic pressure π of polymeric solutions the virial
decomposition is used in the Flory–Huggins method
π = RT
c⎛
c⎞
⎜1 + A ⎟
N⎝
N⎠
(1)
in which c is the molar–volumetric concentration of monomeric links; N is the polymerization
degree or length of a chain; A is the second virial coefficient which is the main object of
analysis of multiple following variants of Flory–Huggins method.
It was discovered, that the expression (1) for the description of π into diluted and semi–
diluted solutions required of different values of virial coefficient A. In particular, for the
estimation of A in a field of diluted solutions it would be better to accept the whole
3
conformation volume of macromolecule as excluded volume, that is RF , and in the field of
semi–diluted solutions – the value a (1 − dχ ) [3] where a is a length of a chain link and
3
R f = aN ν
(2)
is the conformation radius of Flory ball with the index ν = 1/2 or 3/5.
Further development of the Flory–Huggins method in direction of taking into account the
effects of far interaction, swelling of polymeric ball in “good” solvents [4, 5], difference of
free volumes of polymer and solvent [6, 7] leaded to complication of expression for virial
coefficient A and to growth of number of parameters needed for its numerical estimation, but
weakly reflected on the possibility of equation (1) to describe the osmotic pressure of
polymeric solutions in a wide range of concentrations.
It was admitted that the best variant for the diluted solutions is the Vant–Goff equation
Thermodynamics of Osmotic Pressure of Polymeric Solutions
π
RT
=
c
N
25
(3)
and for semi–diluted solutions – Fixman equation [8] or Yamakawa equation [9] differing
only by the sense of virial coefficient B
π
RT
=
c
N
⎡
⎛ c ⎞⎤
⎢1 + B⎜ c* ⎟⎥
⎝ ⎠⎦
⎣
(4)
here c = N / N A RF is critical concentration of monomeric links corresponding to the start
3
*
of the polymeric balls intertwining.
From the point of view [3, 10] the main deficiency of the self–consistent field method is
fact, that it does not take into account the fluctuative properties of the polymeric solutions and
correlations appearing due to the difference of the energies of pair–wise interaction into
system monomeric links – solvent tie–up of links into chain. It is considered that these
deficiencies somehow are eliminated by Scaling method [3] which is based on the principle of
scaled invariance of polymeric solution properties as function of some characteristic
parameters, for example length of chain N, relative concentration c/c* and conformation
radius RF of Flory ball. Ideology of method conformably to polymer solutions was appeared
from the assumption about the analogy of fluctuative behaviour of polymeric chains in semi–
diluted solutions and magnetic in external field near the point of change of phase [11].
Analysis of osmotic pressure of semi–diluted polymeric solutions by Scaling method is
based [3] on two positions. Accordingly to the first one it is assumed that the polymeric chain
is in “good” solvent for which χ < 1 / 2 . This position is necessary in order to index ν in the
expression (2) will be determined by the ratio
ν=
3
(d + 2)
(5)
which is correct for swelling ball and gives the value ν = 3/5, but not ν = 1/2 for d = 3–
measured space.
The second position assumes that in semi–diluted solutions the polymeric chains are as
much strong intertwined that the all thermodynamic values, in particular the osmotic pressure,
achieve the limit (at N → ∞) depending only on the concentration of monomeric links, but not
on the chain length.
The following expression is initial for the determination of osmotic pressure of semi–
diluted polymeric solutions accordingly to Scaling method:
π
RT
=
c ⎛c⎞
f⎜ ⎟
N ⎝ c* ⎠
(6)
26
in which the dimensionless function f(c/c*) has two asymptotics. It is assumed for the diluted
solution (c/c* << 1), that f(c/c*) = 1 or f(c/c*) = 1 + const(c/c*), that leads respectively to the
expressions (3) or (4).
Power law depentanizer f(c/c*) = const(c/c*)m is postulated for the semi–diluted solution
*
(c/c >> 1), in which the unknown index m accordingly to the second position of the Scaling
method is from independence π on the length of a chain. This leads to the value m = 1/(3ν –
1), that is m = 4/5 for d = 3–dimensional space. That is why the expression (6) is as follow
π
RT
= const ⋅ c
or, assuming
π
RT
9
4
(7)
ϕ = a 3c as volumetric part of polymer into solution
= const' ⋅ϕ
9
4
(8)
From the point of view [3] the experiments [12] confirm the correctness of the expression
(8).
However, let note, that the assumption about independence of the osmotic pressure of
semi–diluted solutions on the length of a chain is not physically definitely well–founded; per
se it is equivalent to position that the system of strongly intertwined chains is
thermodynamically equivalent to the system of gaped monomeric links of the same
concentration. Therefore, both Flory–Huggins method and Scaling method do not take into
account the conformation constituent of free energy of polymeric chains.
In presented work the analysis of osmotic pressure of the polymeric solutions has been
done with taken into account the thermodynamics of conformation state of macromolecules
following from the self–avoiding random walks statistics [13, 14].
2. STARTING POSITIONS
The following expression is stringent thermodynamical determination of the osmotic
pressure
μs
π = − ∫ dμ s / vs
(9)
μs0
in which
μ s 0 and μ s are chemical potentials of the solvent into standard and defined state
respectively and vs its partial–molar volume.
It follows from the Gibbs–Durham equation for two–component solution containing ns
moles of the solvent and n moles of macromolecules
dμ s = −
where
n
dμ
ns
27
(10)
μ is the chemical potential of the macromolecules.
Since the polymeric chains unlike to the common molecules possess by free energy of the
conformation F (or by negative entropy of conformation which is a measure of polymeric
chains self–organization [13]), it should be included as an additional term in usual
determination of chemical potential of component of the solution. Hence, we have for the
macromolecules
μ = μ 0 + RT ln γc + F
(11)
μ 0 is standard chemical potential of macromolecules; γ is an activity coefficient or
here
coefficient of proportionality between the thermodynamic activity of macromolecules and
their molar–volumetric concentration c.
Generally, the activity coefficient γ depends on the composition of solution. In the
ranges of our narrow purposes of investigations of the macromolecules chemical potential
conformation term influence on the osmotic pressure of polymeric solutions we will be
neglect by the change of γ lying γ ≅ const in all range of the macromolecules
concentrations into solution. This permits to write
dμ = RTd ln c + dF
(12)
Expressions (9) – (12) are initial for analysis of osmotic pressure of macromolecules
solution into further presented partial variants.
3. DILUTED SOLUTIONS
Let determine the diluted solutions by two conditions
c ≤ c* ,
(13)
ns v s ≅ V
(14)
here:
c* = 1 / N A RF
3
(15)
is critical molar–volumetric concentration of macromolecules into solution corresponding to
the start of polymeric chains conformation volumes intertwining; V is general volume of the
solution.
28
Accordingly to [13] the conformation radius RF of non–deformated Flory ball is
described by the expressions (2) and (5) at d = 3. This dimensionality of real space will be
kept further.
Free energy F of the conformation in calculation per one mole of macromolecules in
general case of diluted solution is equal to [13]
F=
here
5
RTN 1 / 5 / λv
2
(16)
λv ≤ 1 is multiplicity of volumetric deformation of Flory ball. In diluted solutions this
multiplicity is function only on the length of a chain and distinction of free energies of the
states S1 and S2 of two neighbour monomeric chains. That is why in diluted solutions
dF = 0
(17)
It follows that, the determination (9) takes the standard for the diluted solutions form
c
n
V
0
π = RT ∫ d ln c
(18)
that result (n/V = c) in the Vant–Goff equation
π = RTc
(19)
Hence, in the field of diluted both ideal
(λv = 1) and real (λv < 1) solutions (c ≤ c* ) the
conformation component of the chemical potential of the macromolecules has not an
influence on the osmotic pressure, and it is described by Vant–Goff equation.
4. SEMI–DILUTED SOLUTIONS
In the given presented case the semi–diluted polymeric solutions determined by the
conditions
c ≥ c* ,
(20)
ns v s ≅ V
(21)
The last means that the volumetric part of macromolecules in solution is sufficiently
little.
29
As it follows from [14] in the field of the chains intertwining the molar free energy of the
conformation is linear function of relative concentration of macromolecules and is described
by the following expression in approximation by deformation of m–ball in real solution
F=
5
⎛c⎞
RTN 1 / 5 ⎜ * ⎟
2
⎝c ⎠
(22)
It follows that
dF =
5
c
RTN 1 / 5 d *
2
c
(23)
with taken into account (10), (12), (21) and (23) the determination (9) for osmotic pressure
assumes the form
c
⎡c n
5
n c⎤
d ln c + N 1 / 5 ∫ d * ⎥
2
V c ⎦⎥
c*
⎣⎢ 0 V
π = RT ⎢ ∫
(24)
We will obtain after the integration
⎡
⎛ c c* ⎞⎤
− ⎟⎟⎥ ,
*
c ⎠⎦
⎝c
5
4
π = RTc ⎢1 + N 1 / 5 ⎜⎜
⎣
c ≥ c*
(25)
The expression (25) is similar to the expression (4) but has more general character: it
gives clear and simple determination of virial coefficient B and automatically is transferred
into Vant–Goff equation accordingly to condition c = c*.
The second term into square brackets (25) points out the relative contribution of the
macromolecules conformation free energy into the osmotic pressure. This term is sufficiently
= 4 its part exceeds 80 %. With the c/c* and
significant: even at c / c − c / c ≈ 1 and N
N increasing this contribution becomes dominant.
Accordingly to (19) the osmotic compressibility ∂π / ∂c into diluted solutions does not
*
*
1/ 5
depend on the concentration of macromolecules (∂π / ∂c = RT ) ; on the contrary, in semi–
diluted solutions it becomes (as it follows from (25)) as linear function of relative
concentration:
c⎞
⎛ 5
∂π / ∂c = RT ⎜1 + N 1 / 5 * ⎟
c ⎠
⎝ 2
(26)
30
5. CONCENTRATED SOLUTIONS
Let determine the concentrated polymeric solutions by the conditions
c >> c*
(27)
ns v s < V
(28)
that assumes a great volumetric concentration of macromolecules into solution.
Introducing the volumetric part ϕ of macromolecules into solution by the ratio
ϕ = vc
(29)
in which v is partial–molar volume of macromolecules. Attributive expression (9) with taken
into account (10), (12) and (23) results in expression (30) by changing the c = ϕ / v ,
c* = ϕ * / v , ns vs = V ( 1 − ϕ ) :
ϕ
⎡ ϕ dϕ
5 N 1/ 5
ϕdϕ ⎤
+
π = RT ⎢ ∫
⎥
* ∫
⎢⎣ 0 v( 1 − ϕ ) 2 ϕ ϕ* v( 1 − ϕ ) ⎥⎦
(30)
In general case v is complicated and independent function on solution composition.
However, in narrow purposes of investigations the influence of macromolecules chemical
potential conformation component on osmotic pressure we use the approximation v = const .
Then after the integration of (30) we will obtain
π =−
RT
v
⎡
⎞⎤
5 N 1/ 5 ⎛ 1 − ϕ
⎜ ln
(
)
1
ln
ϕ
−
+
+ ϕ − ϕ * ⎟⎟⎥ ,
⎢
* ⎜
*
2 ϕ ⎝ 1−ϕ
⎠⎦
⎣
ϕ > ϕ*
(31)
It follows that the osmotic compressibility ∂π / ∂c = v∂π / ∂ϕ will be equal to
RT ⎛ 5 1 / 5 ϕ
∂π
⎜1 + N
=
ϕ*
∂c 1 − ϕ ⎜⎝ 2
⎞
⎟⎟ ,
⎠
ϕ > ϕ*
(32)
Expressions (31) and (32) are more general than the previous ones (25) and (26) and easy
transform in them accordingly to condition
Taking into account, that
ϕ * ≤ ϕ << 1 .
ϕ * is near to N–4/5 upon order of value, we can assume, that
N 1 / 5 / ϕ * >> 1 . Therefore, under condition ϕ >> ϕ * for concentrated solutions the first
additives in (31) and (32) can be neglected and we can obtain
π =−
5 RT N 1 / 5
[ln(1 − ϕ ) + ϕ ]
2 v ϕ*
31
(33)
∂π 5
N 1/ 5 ϕ
= RT *
∂c 2
ϕ 1−ϕ
(34)
This means, that in concentrated solutions π and ∂π / ∂c is wholly determined by the
conformation component of chemical potential of macromolecules.
Let write other form (33) assigning the condition
ϕ * ≤ ϕ << 1 . Then factorizing
ln(1 − ϕ ) in exponential series we will obtain
⎞
5 RT N 1 / 5 ⎛ ϕ 2 ϕ 3
⎜
π=
+
+ ...⎟⎟
* ⎜
2 v ϕ ⎝ 2
3
⎠
(35)
As we can see, the eq. (35) is analogue of the scaling expression (8) at evident
determination of const’ in the last one.
In that way, the thermodynamic approach with the use of conformational term of
chemical potential of macromolecules permitted to obtain the expressions for osmotic
pressure of semi–diluted and concentrated solutions in more general form than proposed ones
in the methods of self–consistent field and scaling. It was shown, that only the osmotic
pressure of semi–diluted solutions does not depend on free energy of the macromolecules
conformation whereas the contribution of the last one into the osmotic pressure of semi–
diluted and concentrated solutions is prelevant.
6. CONCLUSION
Let draw attention on the dependence of the osmotic pressure on the length of a chain. If
formally to lay that v = vm N , where vm is a partial–molar volume of the chain’s links, then
we will obtain
ϕ * = (vm / N A a 3 )N −4 / 5 . Therefore, the expression (33) can be written in the
form
π =−
5 RT N A a 3
[ln(1 − ϕ ) + ϕ ]
2 vm vm
which shows the independence of
(36)
π on N in obvious elevation.
However, for this it was necessary to turn into the parameter vm of the chain’s links, to
their tie–up, and the concentration of polymer to express by volumetric part, which is general
for the macromolecules and their links. The contrary situation can be observed into diluted
solutions: at using the molar–volumetric concentration of links, the Vant–Goff equation in the
32
form (3) indicates on the dependence of π on N, whereas at using the molar–volumetric
concentration of macromolecules the same Vant–Goff equation in the form (19), on the
contrary, indicates on the independence of π on N. Since the macromolecule (but not its
links) is a component of the solution, from the thermodynamic point of view, the expression
(19) is more correct form of the Vant–Goff equation writing.
Under this connection let mark that the position about an independence of the osmotic
pressure of polymeric solutions into concentrated field of the strongly intertwined chains used
in the scaling method is successful upon the result (8) in the presented concrete case, but can
not be by general principle spreading on the all thermodynamic visualizations of polymeric
solutions. For instance, free energy of the macromolecules conformation accordingly to (22)
is function not only on the concentration, but also on the length of a chain at any choice of the
method for the concentration expression.
That fact the scaling method and presented thermodynamic approach from seeming
opposite positions lead to practically the same result in the form (8) and (35) can be named as
“mysterious incident” if it were not two circumstances. First is exactly free energy of the
conformation makes the main contribution into the osmotic pressure of the semi–diluted and
concentrated solutions. The second is the peculiarity of the point c = c*.
As we can see from the expressions (19) and (25), the osmotic pressure of the solution in
the point c = c* has the same value π = RTc independently on the move c → c* from below
(c* > c → c*) or from above (c* < c → c*). On the contrary, the osmotic compressibility in the
point c = c* has two values: first is ∂π / ∂c = RT at approach zone c → c* from below, the
*
⎛
⎝
second accordingly to (26) ∂π / ∂c = RT ⎜1 +
5 1/ 5 ⎞
N ⎟ at approach zone c → c* from above.
2
⎠
The reason of this is the analogous behaviour of free energy of the conformation F and its
derivative ∂F / ∂c . In accordance with the (16) and (22) in the point c = c* the value
5
RTN 1/ 5 is uniquely independently on a fact from which side to approach into c*. On
2
the contrary, the derivative ∂F / ∂c in the point c = c* has two values: first is ∂F / ∂c = 0 at
5
1/ 5
*
move c → c* from below, the second is ∂F / ∂c = RTN / c at move c → c* from
2
above. Hence, in the point c = c* the derivative ∂F / ∂c has a jump, consequence of which is
also the jump of ∂π / ∂c .
F=
Since free energy of the conformation F = –TS, where S is the entropy of the
conformation, it follows, that at given external parameters P and T neither free energy of
conformation F nor it’s the first derivative upon temperature S do not change in the point c =
c*, testifying only the hump; but their derivatives upon the concentration test the jump.
On the basis of these features the point c = c* is the critical one for the change of phase of
the second kind for polymeric solutions. In view of this, the analogy between the magnetic
behaviour near the critical temperature of the change of phase and polymeric solution
behaviour near the critical concentration c = c* of the change of phase noting by Des
Cloizeaux [11] permits to use the scaling correlations, however does not determine the criteria
of the corresponding power functions [15] indexes estimation.
33
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
Flory P. J. Principles of Polymer Chemistry // New York: Cornell Univ. Press, 1953,
594 p.
Huggins M. L. Physical Chemistry of Polymers // New York: Interscience, 1958, 175 p.
De Genes Scaling ideas in Physics of Polymers // Moscow: Myr, 1982, 368 p.
Zimm B. H., Stockmayer W. H., Fixman M. Excluded Volume in Polymer Chains // J.
Chem. Phys., 1953, 21 (10), p. 1716–1723.
Zimm B. H., Stockmayer W. H. Dimensions of Chain Molecules Containing Branches
and Rings // J. Chem. Phys., 1949, 17 (3), p. 1301–1314.
Prigogine I. The Molecular Theory of Solutions // New York: Interscience, 1959, 479 p.
Patterson D. Role of Free Volume Changes in Polymer Solutions Thermodynamics // J.
Polym. Sci. C, 1968, 16, p. 3379–3389.
Fixman M. // J. Chem. Phys., 1960, 33 (2), p. 370–381.
Yamakawa H. // J. Chem. Phys., 1965, 43 (4), p. 1334–1344.
Grossberg A. Yu., Khokhlov A. R. Statistical Physics of Macromolecules // Moscow:
Nauka, 1989, 344 p.
Des Cloizeaux // J. Phys. (France), 1976, 37 (5), p. 431–434.
Okano K., Wada E., Taru Y., Hiramatsu H. // Rep. Prog. Polym. Sci. Japan, 17, 141
(1974).
Medvedevskikh Yu. G. // Condensed Matter Physics, 2001, v. 4, № 2 (26), p. p. 209,
219.
Medvedevskikh Yu. G. Conformation and deformation of linear macromolecules in
concentrated solutions and melts in the self–avoiding random walks statistics (see paper
in presented book)
Marck N. H., Parrinello M. Collective Effects in Solids and Liquids // Adam Hilder Ltd,
Bristol, 1982.
Chapter 3
GENERALIZATION OF DATA CONCERNING TO THE
COAL SWELLING IN ORGANIC SOLVENTS AND THEIR
EXTRACTION USING THE LINEAR
MULTIPARAMETRIC EQUATIONS
L. I. Bazylyak*1, D. V. Bryk*2, R. G. Makitra2,
R. Ye. Prystansky1 and G. E. Zaikov*3
1
Physical Chemistry of Combustible Minerals Department; L. M. Lytvynenko
Institute of Physical–Organic Chemistry and Carbon Chemistry; National
Academy of Sciences of Ukraine
2
Institute of Geology and Geochemistry of Combustible Minerals;
National Academy of Sciences of Ukraine
3
N. Emmanuel Institute of Biochemical Physics;
ABSTRACT
Approaches to the consideration of a coal swelling process, which were used up to
now and based on the theory of regular solutions, do not give the possibility to generalize
quantitatively the experimental data. Adequate relation between the physical–chemical
properties of the solvents and the degree of a coal swelling in them can be obtained only
with the use of linear multiparametric equations which take into account the effects of the
all processes proceeding in the system; besides, the basicity and a molar volume of the
liquids are determinative. Such approach is effective at the generalization of data
concerning to extraction of a coal.
Keywords: swelling.
*
L. I. Bazylyak, R. Ye. Prystansky: 3a Naukova Str., 79053, Lviv, UKRAINE; e–mail: [email protected]
D. V. Bryk, R. G. Makitra: 3a Naukova Str., 79053, Lviv, UKRAINE; e–mail: [email protected]
*
G. E. Zaikov: 4 Kosygin Str., 117977, Moscow, RUSSIA; e–mail: [email protected]
*
36
L. I. Bazylyak, D. V. Bryk, R. G. Makitra et al.
The action of organic solvents on natural polymers combustible minerals (coal and brown
coal or peat) is intensively studied for a long time due to following reasons. Firstly, this is one
of the successful method of studying the structure of combustible materials and the second is
their technological application for obtaining of a so–called montan–wax or low–molecular
liquid extracts which can be transformed into synthetic liquid fuel due to hydration process.
Moreover, an interaction of a coal with the solvents is a basis of the coals liquation processes
and coals transformation into liquid fuel.
The first stage of an interaction in the system “coal–solvent” is a swelling, or an
increasing in the volume, as a result of introducing the molecules of a liquid into interstices
and directly into the structure of a coal. Depending on the solvent nature and the coal nature,
the volume of a coal can increase even in some times, and, respectively the weight growth of
investigated sample can be achieved to 100 and more percentages.
A review of early works concerning to a coal swelling is represented in [1, 2]. Let us
notify, that else in the fifties the coals swelling process was considered as the first degree of
their extraction and was connected with physical–chemical interaction of these coals with the
solvents [3]. Such process was explained from two points of view, namely: either this process
was coursed by adsorption of the liquid into interstices or such process was connected with
the change of the cohesion energy of solid and liquid phases of a system. Sanada and co–
authors [4 – 6] were taken into account, that the coal is natural three–dimensional polymer
and in accordance with the Flory–Huggins’s theory a change of free energy at the coal
swelling is conventional sum of the energies of mixing the polymer and solvent and first of
all is determined by the disparity of solubility parameters of both components accordingly to
Hildebrand parameter δ:
ΔG = [ln(1 – Ø2) + χØ22 + Ø2],
(1)
where Ø2 is volumetrical part of netting structure (polymer) in swollen system; and parameter
χ indicating the interaction of a polymer with the solvent which is equal to
χ=
β + ( δ 1 − δ 2 )2 V1
RT
(2)
also contains the empirical term β, correction factor, which takes into account the number of
branching in the structure of polymer; δ1 and δ2 are Hildebrand’s parameters of solubility for
the solvent and polymer and are equal to [(ΔHevapor – RT) / Vm]1/2.
After insignificant transformations the Flory–Renner’s equation can be obtained. Such
equation helps to calculate the sizes of polymer link between the cross bonds Mc
ρ 2V1Ø21 / 3
,
Mc =
2
[ − ln( 1 − Ø2 ) − χØ2 − Ø2 ]
(3)
where ρ2 is the density of a polymer into solution; V1 is molar volume of the solvent.
Coefficient χ should be determined empirically for every solvent and, of course, from the
concentration dependence of the osmotic pressure and with taken into account a series of
Generalization of Data Concerning to the Coal Swelling…
37
assumptions. In the work Sanada [5] and subsequent works of other authors, the swelling
degree in the volumetric parts Q is represented as a function from the δ of solvents. These
data in most cases form the parabolic, “belfry”–like curve with a maximum for the solvents,
δ2 of which accordingly to a theory of regular solutions is equal to or is near to δ1 of polymer
(coal). In reality, it was maintained already in the work [5] that for the coal only
approximated dependencies are obtained – a number of experimental data concerning to Q are
visibly take one's leaved from the generalizing curve. It was determined in the work [4] at the
extraction by solvents in the Soxhlet’s apparatus of vitrain from Yubary field (the content of
carbon consists of 85,2 %), that the maximal yields of an extract are observed at their molar
volume about 10 cm3/mole (ethylendiamine, dimethylformamide, cyclohexanone 24 – 26 %,
acetophenone 35,6 %, pyridine 33,2 %). Such results were explained by the influence of the
value of cohesion energy. However, it exists a plenty of exclusions, for example for butanole
Vm = 9,5, for which the yield of the extract is only 0,8 %. The explanation of this deviation as
a result of the solvent association caused by the presence of hydrogen bond seems
unconvincing since under the experiments conditions (the extraction in the Soxhlet’s
apparatus, and that is under boiling temperature) the association will be insignificant. It was
discovered in the work [6], that the value Mc for japanese coal with the carbon content less
than 80 % is unreal low – only 10 (!), next this value is sharply increased and is achieved the
maximum Mc = 175 at 85 0C and after that is decreased. Authors starting from following
positions explained this fact: firstly, experimental determinations were carried out in pyridine,
in which specific interactions can take place and, the second this deviation can be explained
by the mistakes at the determination of χ coefficient.
The same approach was discussed in the work Kirov and co–authors [7] in detail on
example of swelling (and extraction) for three kinds of bituminous Australian coal. These
authors confirmed the main observations of Sanada – the swelling degree Q increases from ~
1,4 in hydrocarbons to ~ 2 in pyridine (δ – 11,0) and again decreases to ~ 1,5 in alcohols.
Calculated on this basis value δ of coal increases droningly with increasing the content of
carbon from 70 % till 87 % and in a case of more metamorphized coal is sharply decreased
again. Data concerning to the extraction of Greta coal are evidence of maximal yield of
extract (more than 20 %) under it treatment with ethylendiamine and dimethylformamide (δ –
11,5), however, authors admit a fact that this is a consequence of specific interactions, since
in alcohol from the δ of the same order the yield of the extract is only 1 – 2 %.
Authors concluded, that although the swelling degree is not directly connected with
molecular characteristics of absorbed liquids, however determining factor is their parameter
of solubility in spite of the fact that at detailed consideration of the dependencies Q = f(δ) (or
f(δ2)) there are a number of deviations (as same as in the work [5]) from the ideal curve for
many solvents. It is necessary to notify that although it is hard to estimate the verisimilitude
of determined in such a way molecular weights of structural links of a coal between the points
of cross bonds, however, in a case of synthetic polymers in a same way determined masses of
links visible don’t agree with the values obtained in accordance with others methods.
In spite of the indicated lacks, the described above approach is applied to later works
concerning to coal swelling and results interpretation. It is necessary to distinguish a plenty of
investigations devoted to swelling studies of coal № 6 from Illinois State (standard in USA
coal for the carbon–chemical investigations) [8 – 10]. General conclusions are in good
agreement with the results of the works [5, 7]. Comparison of swelling degree for different
coal in some solvents depending on the content of carbon has been done in the work [11].
38
Similar investigation for Siberia Kansk–Achynsk coal was carried out in the works [12, 13].
In both cases, as same as in a work [7], it was proved the dependence of swelling degree of
coal on the carbon content in it.
That is why logically to assume the possibility of specific interactions also during the
swelling process, since the values of parameters of the coal solubility δ2, which are
determining accordingly to the Flory–Renner’s equation are differed. It depends on fact if the
data for all solvents are taking into account in calculations or such calculations are performed
with the exclusion of results for solvents able to be as acceptors of hydrogen bonds (amines,
ketones). Different results have been obtained also under application of other methods for
calculations, especially of the Van–Krevelen’s method [14].
It is notified in the work [15], that the swelling of some coal does not agree with the
thesis of regular solutions theory; that is why, it is not allowed to calculate the parameter χ for
them. Authors explain this fact by the presence of oxygen atoms in the investigated coal. But
also the molecular weight of separate sections (clusters) between the points of crossing for
methylated or acetylated samples of this coal is equal only to 300 – 600 in accordance with
the calculations (that is unreal).
It is necessary to notify, that the critical analysis of the Flory theory application for the
determination of molecular mass and the crossing density of the coal structure has been done
in the Painter’s works [16]. Authors assert, that the possible formation of hydrogen bonds
between the hydroxy groups of low–metamorphized coal has an important role here; that is
why, even a lot of empirical amendments introduction into calculations leads to obtaining the
understated values of molecular masses of clusters.
Taking into account the above–mentioned lacks many authors concluded that the theory
of regular solutions is insufficient for adequate description of the coal swelling process (and
also for the extraction process) in different solvents since such theory does not take into
account the possible specific solvation of active structures of coal and first of all its
heteroatoms [17] especially by formation of hydrogen bonds. With the aim of taking into
account the possible acid–base interactions it was proposed by Marzec and co–authors [18,
19] to determine the swelling degree as a function of donor number of DN solvents or as a
function of their donor and acceptor numbers disparity accordingly to Gutmann. However,
corresponding analysis of data concerning to swelling the slessian bituminous coal showed
the following: although between the Q and DN is visible symbasis, however the deviations
from the straight line is less than for the function Q = f(δ); but, at the same time it is
complicated to confirm about the quantitative description of the process. The same conclusion
about only qualitative character of such dependence has been done by authors [13] on
example of swelling the brown Kansk–Achynsk coal and some kinds of Donbas coal.
Above–mentioned facts and disagreements lead to the conclusions [20] that the sorption
of solvents by coal is very complicated process, which covers also the changes under the
action of solvent into the coal structure and other possible phenomena. That is why,
application for a coal the theories developed for the description of thermodynamically
equilibrium process of swelling the simple synthetic polymers is unwarranted first of all due
to neglect the existing chemical (specific) solvation interactions. As it was confirmed in many
investigations, the swelling Flory–Huggins’s model based on the theory of regular solutions
is not sufficiently consistent with the real experimental data. It is caused by a range of
simplifying assumptions putted into the base of this model and, first of all, the presence of
full isoentalpic mixing (solution) of two phases that is in disagreement with the reality – even
39
in a case of the polymers which do not contain the donor–acceptor groups into the structure a
swelling and solution processes are accompanied with a great enthalpy effect; it is know, that
even non–specific solvation is often accompanied by the changes of free energy and enthalpy
of the system. And isoentalpy will be not remained in a case of the possible donor–acceptor
(acid–base) interaction, which is often observed in a case of synthetic polymers with the
content of heteroatoms (polyurethane, nitryle rubbers) and is observed in a case of coal as a
result of the presence in it such groups as –OH, –COOH, tertiary atom of nitrogen and ect.
Calculations on the basis of the theory of regular solutions for the coal swelling have mostly
unsatisfactory generalizing and predicted ability. Thus, our main task was to explain the value
of coal swelling as an effect of the sum influence of different properties of penetrating liquids
and also to obtain the quantitative picture that is possible starting from the principle of the
linearity of free energies.
The principle of the linearity of free energies (LFE) is applied in chemistry of solutions
over 30 years for quantitative description of the solvents influence on the behavior of
dissolved substances (spectral characteristics, constants of the reaction rate). In accordance
with this principle general change of free energy of the system consists of the separate inter–
independent terms and first of all consists of non–specific and specific solvation and also
needed energy for the formation of cavity in the structure of liquid phase with the aim of
allocation the exterior molecule introducing there. And only full sum of these all possible
energetic effects gives the final (equilibrium) energy of the system [21]:
ΔG = ∑ Δg i
(4)
With taken into account, that the constants of the reaction rates are determined via the
equilibrium constants of the activated reactive complex formation, and the last in part depend
on the solvation processes, it was proposed by Koppell and Palm [22] the following equation
in order to determine the influence of medium properties on the reaction rates of processes
proceeding in it:
lg K = a0 +
a1 (n 2 − 1) a2 (ε − 1)
+
+ a3 B + a4 ET
(n 2 + 2)
(2ε + 1)
(5)
This equation takes into account the influence of the polarization f(n2) and polarity f(ε) of
the solvents determining their ability to non–specific solvation and also their basicities B [22]
which are accordingly to Koppell–Palm’s quantitatively equal to OH–group displacement
absorption band in IR–spectrum of the phenol dissolved in given solvent, and electrophilicity
accordingly to Reichardt ET characterizing their ability to introduce into acid–base
interactions (specific solvation). Appropriateness of this equation for the generalization of
experimental data of the dependencies of reactions rates (and also spectral characteristics of
dissolved substances) on physical–chemical characteristics of the solvents has been proved by
a number of hundred examples.
It was determined by us at the attempts to describe the gasses dissolving processes into
liquids with the use of the equation (5) that to obtain of satisfactory results the Koppell–
Palm’s equation should be expanded by fifth term, which takes into account the density of the
40
energy of solvents cohesion proportional to the squared Hildebrand’s solubility parameter δ2.
Due to this fact necessary energy for the formation of cavity for the allocation of the molecule
introducing into liquid phase is taking into account:
lg K = a0 + a1 f (n 2 ) + a2 f (ε ) + a3 B + a4 ET + a5δ 2
(6)
Modified equation was turned out effective for the determination of the solvents
influence on the equilibrium of such processes as solubility in different media not only of
gases, but solids too, the distribution of substances between two phases, resembling
equilibrium processes. So, it will be logically to try to use the equation (6) for the swelling
processes. As a matter of fact, it was turned out, that with the use of this equation it is
possible to determine the quantitative connection between the properties of the solvents and
equilibrium swelling degree of a number of polymers, and also of a coal [23 – 25]. In order to
achieve the satisfactorily high values of the coefficients of multiple correlations R, it is
necessary to exclude from the calculations the data for some quantity (3 – 5) of the solvents.
It is hard to explain it. Besides, it was not quite clear the model of the interactions into the
system. In a case when the solvation processes are energetically advantageous (∆G < 0) and
that is why promote to the swelling process, that is to the solvent penetration into the structure
of polymer, then the role of δ2 factor is remained not clear. Such factor characterizes the
energy needed for the cavity formation into the structure of the liquid; at the same time,
unlike to the evaporation process, under the swelling of substances into liquid the following
process takes place: liquid solvent penetrates into the structure of solid polymeric phase
mostly as the whole.
At the beginning of ninetieth the works of Aminabhavi are appeared [26]. These worked
were concerned the polymeric membranes swelling into organic solvents and to diffusion rate
D of the liquids into their structure in which these values were considered as dependencies
from the molar volume VM of the liquids. Generalizations obtained in [26] are rather
unsatisfactory – approximately linear dependencies lgQ or lgD on VM are observed only in the
homologic ranges or in the case of similar solvents. But approach must be considered as
logical: it is clear, that in a case of bigger sizes of introducing molecule, the last with
difficulty will be penetrated into the structure of polymer including the adsorbent interstice.
Low generalizing ability of the dependencies presented in the work [26] can be explained by
fact that they do not take into account the solvation effects, which promote to liquids
penetration. That is why the equation (6) has been expanded by additional term, which takes
into account the influence of molar volume of the solvents:
lg Q = a0 + a1 f ( n 2 ) + a2 f ( ε ) + a3 B + a4 ET + a5δ 2 + a6VM
(7)
Such equation under the stipulation that Q is represented not in the volumetric parts
accordingly to the Flory–Huggins’s model but in accordance with the interpretation of
equilibrium processes in the chemical thermodynamics as a moles of the solvent absorbed by
one gram or by one cm3 of polymer was turn out effective under the generalization of data for
swelling degree of different synthetic polymers, for example, polyethylene, in different
organic solvents depending on their physical–chemical parameters [27]. That’s why, it was
necessary to check the possibility of application the equation (7) for the generalization of data
41
concerning to coal swelling since this equation takes into account the all important possible
energetic effects caused by possible donor–acceptor interaction of active groups of the coal
with non–inert solvents including the formation of hydrogen bonds; the effects of non–
specific coal solvation with solvents which are caused by a presence in it the cyclic aromatic
structures as a result of which the visible influence of the ability of some solvents for the
polarization can be expected; and also endothermic effects as a result of steric complications
of the solvents penetration (VM) and destruction of the liquid phase structure (δ2).
Data concerning to a swelling of the most popular coal (namely, coal Illinois № 6) have
been taken by us as a main object of our investigations. This coal is the standard object for the
carbon–chemical investigations in USA. These data were already analyzed earlier in works
[23 – 25] with the aim of their generalization accordingly to equation (6), but obtained results
were unsatisfactory. Evidently this was caused by two factors: i) the influence of the
molecules sizes of the solvents penetrating into the coal structure (their molar volume) was
not taken into account in these works; ii) analyzed starting values of the swelling degree Q
were given accordingly to original works [9 – 11] in ml (sometimes in g) of the solvent
absorbed by 1 ml or 1 g of coal since the Flory–Huggins’s model has been used by authors
(this model uses the volumes of two liquids which are mutually mixed). If to consider the coal
swelling process (and generally polymers swelling processes) as thermodynamically
equilibrium process then the free energy change at the penetration and at the absorption of a
solvent and, respectively, the equilibrium constant of this process, it is preferable to determine
the quantity of connected solvent in molar units.
In the presented paper we have checked the efficiency of the above–mentioned factors
considering studying the swelling process in organic solvents. Illinois coals are low–
metamorphized, bituminous and contain 20 – 31 % of volatile substances, are characterized
by ash content 8 – 12 % and sulphur content 4 – 7,8 %. Investigated in the work [8] sample
was characterized by following composition: C 79,8; H 5,11; N 1,8; Sorg. 2,0 and O 11,2 %.
The samples were pulverized from the soluble components with pyridine; after vacuum–
drying they were saturated by solvent’s steams till their full saturation at room temperatures
in the closed vessels. Authors give the ratio of the weights for swelled samples respectively to
the starting W. Generalization of studied data for 10 solvents in accordance with the fifth–
parameter equation (6) leads to the expression with unsatisfactory low value of correlation
coefficient R = 0,81 [23]. Exclusion from the consideration the most uncoordinated data for
dioxane gives the possibility to obtain the fifth–parameter equation with low, but acceptable
degree of connection R = 0,941. At the same time, consideration of the molar volume factor
and the change of weight parts on the molar ones essentially improve the correlation – for all
10 studied solvents R = 0,940, and after the exclusion the data concerning to cyclohexane for
the rest 9 solvents we obtain the equation with high connection degree R = 0,996 [28].
However, there are only two decisive parameters – the basicity which assists to swelling
process and the is molar volume, which opposites to this process; taking into account the
needed energy and the negotiation of the cohesion forces have only insignificant influence
and the exclusion of this parameter from the calculations practically does not worsen the
equation
lg Q = −1,96 + ( 0,665 ± 0 ,074 )10 −3 B − ( 4,12 ± 0,58 )10 −3VM ;
R = 0,984 and S = 0,030
(8)
42
Obtained equations have greater predicted ability comparatively to fifth–parameter
equation obtained in the work [23], which does not take into account the factor of molar
volume (for nine solvents R is equal to 0,940).
The influence of the factor of molar volume is confirmed by fact that between lgQ and
VM the neatly marked symbasis is observed, namely: with increasing of VM the value lgQ is
decreased. The action of other decisive factor – solvents basicity – is opposite, in other words
with the basicity increasing the symbate increasing of lgQ is observed. Evidently, this is
caused by the specific solvation of acid centers, which are in the macromolecule of coal and,
first of all, of hydroxy groups. Their presence can be assumed taking into account a great
number of the oxygen in the Illinois coal. Comparison of these two oppositely directed
dependencies leads to the conclusion, that they are mutually compensated. Although these
dependencies are only symbate, but the algebraic sum of the influence of these two factors is
practically linearly connected with the respective values lgQ [29]. The third factor is more
little density of the cohesion energy, which is proportional to needed energy for separation of
absorbed molecules from the structure of liquid phase; this factor respectively also decreases
the swelling value. However, the influence of this value is insignificant; this fact is confirmed
by negligible decreasing of the Q value at its exclusion. The possible processes of non–
specific and electrophilic solvation practically do not impact on the value Q.
Our considerations about significance of the separate properties of the solvents influence
on the swelling degree are confirmed by analogous analysis of data in others works. In the
work [10] authors also have been studied the swelling process of the coal Illinois № 6 in the
liquid phase. Swelling degree S has been studied by volumetrically as the ratio of volumes of
swelling sample to the starting one. Unlike to [8], it was investigated the process in a range of
amines including the primary ones, able to the formation of hydrogen bonds and also
alcohols. At the generalization of these data in accordance with the fifth–parameter equation
without taking into account of VM for the all 17 solvents it was obtained the equation with the
low value R = 0,861; but at the use of the sixth parameter equation (7) and after the exclusion
of data for isopropanole and dimethylaniline we achieve of high correlation
lg Q = −2,91 + ( 0 ,454 ± 1,40 ) f ( n 2 ) + ( 5,73 ± 1,22 ) f ( ε ) + ( 1,43 ± 0 ,37 )10 −3 B − ( 7 ,15 ± 5,26 )10 −3 ET −
( 0 ,722 ± 0,947 )δ 2 − ( 6 ,52 ± 4,54 )10 −3VM
N = 15 , R = 0,981 , S = 0,160
(9)
and after the exclusion of insignificant factors of polarizability and cohesion energy density:
lg Q = −2 ,96 + ( 5,67 ± 1,11 ) f ( ε ) + ( 1,5 ± 0 ,30 )10 −3 B − ( 1,47 ± 3,99 )10 −3 ET − ( 4 ,01 ± 2 ,07 )10 −3Vm
R = 0,980 and S = 0,149
(10)
However, the factors of electrophilic solvation and unexpected molar volume have the
little influence too. The dependence of lgQ on the solvent property can be satisfactory
described by the two–parametric equation too and
43
lg Q = −4,34 + ( 3,42 ± 0,69 ) f ( ε ) + ( 2,02 ± 0,27 )10 −3 B − ( 0,86 ± 2,55 )10 −3Vm
R = 0,968 and S = 0,172
(11)
In this case the basicity and the molar volume of the solvents are decisive factors, the
influence of which is oppositely directed. An appearance of the polarity as significant factor
is connected with the specific selection of high polar solvents (alcohols, amines).
Calculated in accordance with the equation (11) values lgQcalc. and their deviation from
the experimental values are represented in Table 1.
Accordingly to [9] the swelling process of the Illinois coal № 6 has been carried out
principally under other conditions, namely: the samples were previously extracted with
pyridine, dried coal was standed till the full saturation with vapors at 100 0C in closed
metallic ampoules (with the exception of phenol, investigating temperature of which is 182
0
C). Authors presented the results of investigations as the ratio of swelling W (in percentages)
that is the ratio of weights of swelling sample after 1 hour to the dried sample. These data
have been previously generalized in the work [24]. Low value R for the all 12 solvents equal
to 0,876 after exclusion from the consideration data concerning to the phenol and
tetrahydrophurane is increased till 0,972. Essentially better results were obtained with taken
into account the molar volume factor.
The data concerning to W taken from [9] and calculated on their basis swelling values in
moles Q and lgQ are presented in Table 2; the generalization of these data in accordance with
the sixth parameter equation (7) leads to higher degree of relationship R = 0,909, and the
exclusion from the consideration of one solvent (butylamine) gives the possibility to obtain
the equation with satisfactory degree of relationship R = 0,974; an additional exclusion of
dimethylformamide gives the equation (11) with R = 0,991.
lg Q = −2,61 + (3,50 ± 0,82) f ( n 2 ) + (2,30 ± 0,46) f (ε ) − (0,33 ± 0,14)10 −3 B − (2,37 ± 6,8)10−3 ET +
(0,70 ± 0,24)10 −3 δ 2 − (1,5 ± 2,1)10 −3VM
N = 10, R = 0,991 and S = 0,055
(12)
and after the exclusion of insignificant factors
lg Q = −2,51 + (2,66 ± 1,20) f ( n 2 ) + (1,80 ± 0,60) f (ε ) − (7,4 ± 5,0)10 −3 ET − (2,8 ± 2,9)10 −3VM
R = 0,964 and S = 0,086
(13)
With the molar volume of the solvents increasing the coal swelling degree is decreased;
the same is an effect of the ability to electrophilic solvation. Unlike to both previous cases,
the positive influence of the solvents basicity (namely their ability to form the donor–acceptor
bonds with acid groups of the coal) here is insignificant evidently as a consequence of
especial influence of the conditions of experiment carrying out. Under higher temperatures
the hydrogen bonds are easy decomposed. At the same time, the possible positive influence of
the factors of non–specific solvation f(n2) and f(ε) is observed. Calculated values lgQ and
their discrepancy with the experiment ΔlgQ are presented for the comparison in Table 2.
44
Table 1. Experimental [10] and calculated in accordance with the
equation (10) values of swelling degree of the coal Illinois № 6
№
Solvent
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2–Picoline
Pyridine
Butylamine
Propylamine
Aniline
2–Hexanone
Methylaniline
Propanol
Ethanol
Butanole
Methanol
Dimethylaniline*
Isopropanole*
Toluene
p–Xylene
m–Xylene
Benzene
S
2,76
2,75
2,64
2,45
1,99
1,98
1,44
1,36
1,34
1,34
1,23
1,10
1,06
1,06
1,06
1,05
1,04
Experiments
Qm103
17,84
21,72
16,57
17,62
10,86
8,120
4,052
4,820
5,824
3,715
5,690
0,789
0,784
0,562
0,487
0,407
0,447
lgQm
–1,749
–1,663
–1,781
–1,754
–1,964
–2,090
–2,392
–2,317
–2,235
–2,430
–2,245
–3,103
–3,106
–3,250
–3,312
–3,390
–3,350
Calculations
lgQm
ΔlgQm
–1,794
0,045
–1,808
0,145
–1,941
0,160
–1,655
–0,099
–2,205
0,241
–2,312
0,221
–2,037
–0,355
–2,240
–0,077
–2,194
–0,041
–2,242
–0,188
–2,204
–0,041
––
––
––
––
–3,311
0,061
–3,326
0,013
–3,293
–0,097
–3,362
0,012
Note: *data excluded from the calculations.
Both the equilibrium swelling degree and the kinetics of this process depend on the
character of the solvent. In the work [10] it has been studied the swelling rate of the coal
Illinois № 6 volumetrically in different solvents; on the starting stages it is ordered to the
pseudo–first order reactions kinetics as is observed in the case of polymers swelling too. It
helped to determine the respective constants rate of the process, which are presented in Table
3. In the work [25] we have generalized these data for 24 solvents with the use of fifth–
parameter equation (6). For the all maximal sequence of the data the value of correlation
multiple coefficient R was very low and equal to 0,694 and only after the exclusion from the
calculation the data for five solvents (that is practically 20 %) it could obtain the satisfactory
value of R = 0,957. Additional taking into account the influence of molar volume, that is
transition to sixth parameter equation, gives the possibility to obtain the expression with R =
0,883. And in order to obtain the satisfactory correlation it was enough to exclude from the
calculations data for only two solvents, namely 2–hexanone (methylbutyl ketone) and
triethylamine
lg k = 2,20 − ( 2,55 ± 3,84 ) f ( n 2 ) + ( 1,08 ± 4,26 ) f ( ε ) + ( 4,17 ± 1,12 )10 −3 B − ( 71,7 ± 62,5 )10 −3 ET −
( 0,92 ± 2,45 )δ 2 − ( 42,8 ± 9 ,1 )10−3VM
N = 22, R = 0,959 and S = 0,448
(14)
45
Table 2. Experimental [9] and calculated in accordance with the equation (12) values of
“swelling ratio” of soluble part of coal for the coal Illinois № 6
№
1
2
3
4
5
6
7
8
9
10
11
12
Solvent
Dimethylformamide
N–Methylpirrolodone
Dimethylsulphoxide
Ethylendiamine
Aniline
Butylamine*
Pyridine
Phenol
Pipyridine
Tetrahydrofuran
Toluene
Hexane
Experiments
W
Qm103
6,2
60,54
5,7
37,17
5,5
49,19
4,6
33,24
4,6
34,13
3,8
29,82
3,7
28,67
3,4
22,49
3,0
19,26
2,8
22,97
2,6
16,65
1,6
6,902
lgQm
–1,218
–1,430
–1,308
–1,478
–1,467
–1,525
–1,543
–1,648
–1,543
–1,639
–1,779
–2,161
Calculations
lgQm
––
–1,503
–1,407
–1,466
–1,513
––
–1,475
–1,512
–1,475
–1,615
–1,874
–2,134
ΔlgQm
––
0,073
0,099
–0,012
0,047
––
–0,068
–0,136
–0,068
–0,024
0,095
–0,027
The equation terms characterizing the influence of non–specific solvation and also
cohesion energy have a great standard deviations which are more than the absolute values of
the coefficients and that is why are evidently insignificant. Checking the value R decreasing
at the exclusion of these terms confirmed this assumption and helped to obtain the equation
with lesser quantity of significant terms. This equation also adequately characterizes the
influence of the solvents properties on the rate of their penetration into the coal structure;
besides, the decisive factor in this case as same as in a case of swelling value is the influence
of molar volume of the solvents, increasing of which leads to the process rate decreasing.
lg k = 1,12 + ( 4 ,85 ± 0 ,52 )10 −3 B − ( 66,0 ± 19 ,5 )10 −3 ET − ( 42,1 ± 6,2 )10 −3VM
R = 0,957 and S = 0,418
(15)
Significant factor as same as in a case of swelling degree is the solvents basicity. With
the solvents basicity increasing, the process rate is also increased. The less essential is a role
the solvents ability to electrophilic solvation; although this factor increases the process rate
but it exclusion from the consideration decreases R till 0,928. The value lgQ calculated in
accordance with the equation (15) is represented in Table 3.
Decisive role of the VM factor during the adsorption process of the solvents by coal is in
agreement with the determined in the work [25] proportionality for the alcohols between lgk
and steric factor Es of the Hammet–Taft’s equation.
46
Table 3. Experimental [10] and calculated accordingly to equation (14) values of the
logarithms of the constants rate of the coals Illinois № 6 swelling
№
Solvent
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Propylamine
Butylamine
Pyridine
2–Picoline
2–Hexanone∗
Methanol
Ethanol
Aniline
Propanol
Butanole
Isopropanole
Methylaniline
Butanole–2
Toluene
Isobutanol
Dimethylaniline
Benzene
Pentanol
p–Xylene
m– Xylene
o– Xylene
Ethyl benzene
Cumene
Triethylamine∗
Experiments
k105, s–1
1167,0
614,0
316,7
126,7
125,0
53,30
21,30
20,0
10,90
3,84
2,54
2,47
1,32
0,90
0,833
0,59
0,45
0,376
0,375
0,225
0,118
0,113
0,009
0,00038
lgk
–1,933
–2,212
–2,499
–2,897
–2,903
–3,273
–3,672
–3,699
–3,963
–4,416
–4,595
–4,607
–4,879
–5,046
–5,079
–5,229
–5,347
–5,425
–5,426
–5,648
–5,928
–5,947
–7,046
–8,420
Calculations
lgk
–1,679
–2,974
–2,655
–3,124
––
–3,183
–3,624
–3,962
–4,290
–4,926
–4,152
–4,063
–4,694
–5,334
–4,859
–4,578
–4,675
–5,510
–5,924
–5,919
–5,891
–6,032
–6,716
––
Δlgk
–0,254
0,763
0,155
0,226
––
–0,091
–0,048
0,263
0,328
0,511
–0,443
–0,545
–0,185
0,288
–0,220
–0,651
–0,671
0,085
0,498
0,271
–0,037
0,086
–0,330
––
So, the swelling characteristics of the Illinois coal are determined by total influence of
molar volume of liquids and their ability to specific solvation. The same conclusion has been
done by authors of the works [30, 31] explaining the adsorption growing by increasing the
donor number of the solvents via the formation of hydrogen bond by OH–groups of coal. But
these authors have not done respective quantitative generalization giving the possibility on the
basis of the linearity of free energies principle adequately to connect the properties of the
liquids with their ability to interact with a coal; it was confirmed that the approaches based on
the theory of regular solutions equitable only at the consideration of the swelling process in
the “inert” (so–called low–basic) solvents, mainly of low–polarity.
Correctness of the sixth parameter equation (7) and its simplified forms for the
generalization of the swelling data was proved for other coals including the Donbas coal [32]
at the parameters B and VM. If to apply the equation (7) to the coal extraction data, then the
factor of molar volume VM is insignificant, and the connection between quantities of extracted
substance (in g/mole of the solvent) and physical–chemical characteristics can be
satisfactorily described by fifth parameter equation (6) or by its simplified forms; in this case
possible acid–base interaction is the decisive factor, that is factor B [33 – 35]. This
confirmation is in good agreement with the above–said: bigger molecules harder introduce
47
into the coal structure and after equilibrium state their size does not play the role. Let us
notify, that the same approach has the positive results at the data generalization concerning to
the solubility of the synthetic low–molecular coal analogous – diphenylolpropane – in 20
solvents.
This approach is also applicable for the generalization of data concerning to the coal
extraction under sub–critical conditions, but the role of the specific solvation is also
insignificant, evidently as a result of its suppression at high temperatures.
So, it was discovered the lack of fit the description of the coal swelling process with the
use of one–parametric dependencies including those dependencies based on the theory of
regular solutions on the solubility parameter of liquids. It was shown, that the quantitative
connection between the swelling degree of coal and physical–mechanical properties of the
solvents is achieved only on the basis of principle of the linearity of free energy under
condition of taking into account the all solvation process. The basicity of the solvents and
their molar volume are the factors determining the swelling degree for low–metamorphized
coal.
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[14] Van Krevelen W. Сhemical structure and properties of coal // “Fuel” – 1965. – v. 44. –
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liquids // “Fuel” – 1983. – v. 62. – № 8. – p. p. 976 – 977.
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[32] Makitra R. G., Prystansky R. // “Khimiya tviordogo topliva” – 2003. – v. 4. – p. p. 24 –
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[33] Vasiutyn Ya. M., Makitra R. G., Pyrig Ya. M., Turovsky A. A. // “Khimiya tviordogo
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49
18.
[36] Makitra R. G., Bryk S. D., Palchykova O. Ya. Doslidzhennya vzajemodiji
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p. p. 126 – 130.
Chapter 4
NEW SILAZANE OLIGOMERS AND POLYMERS WITH
ORGANIC-INORGANIC MAIN CHAINS: SYNTHESIS,
PROPERTIES AND APPLICATION
N. Lekishvili*1, Sh. Samakashvili1, G. Lekishvili1 and G. Zaikov*2
1
I. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences,
Scientific Center for Nontraditional Materials; Tbilisi, Georgia
2
N.E. Emanuel Institute of Biochemical Physics of the Academy of Sciences
of Russia, Moscow
ABSTRACT
On the basis of the diallylsilazanes, α,ω-dihydrideoligoorganosiloxanes and 1,4-bis(dimethylhydridesilyl)benzene, new polyfunctional siliconorganic polymers have been
synthesized. General regularities and feasible mechanism of the reaction for obtaining diallylsilazanes have been studied. Based on data of elemental, IR and NMR 1H spectral
analysis, the composition and structure of synthesized polymers have been established.
The kinetics of polyhydrosailylation reactions has been studied. Quantum-chemical
calculations of the model system and data of NMR 1H spectra of the real products of the
polyaddition reaction have confirmed probability of passing polyhydrosilylation reaction
according to the aforementioned two concurrent directions obtaining both α and β
adducts. For the evaluation of relative activity for selected monomers the algebraicchemical approach has been used.
Using Differential Scanning Calorimetric and Roentgen-phase analyses methods it
has been established that synthesized polymers are amorphous systems. Thermal (phase)
transformation temperatures of synthesized polymers have been determined. Thermooxidation stability of the synthesized polymers has been studied. There was shown that
their thermooxidation stability exceeded the analogical characteristic of polyorganocarbosiloxanes. Using synthesized diallylsilazanes modification of the properties of some
important industrial polymer composites based on phenolformaldehide resins has been
carried out. Preliminary investigations showed that synthesized polymers in combination
*
*
N. Lekishvili: 1, Ilia Chavchavadze ave., 0128 Tbilisi, Georgia, [email protected]
G. Zaikov: 119991 Moscow, 5, N.N. Kosigin Street, Russian Federation; [email protected]
52
N. Lekishvili, Sh. Samakashvili, G. Lekishvili et al.
with phenolformaldehyde resins were successfully used as binding-components for
polymer/graphite and polymer/carbon black electro-conducting composites.
Keywords: diallylsilazane, dihydridsiloxane, polyhydrosilylation, properties, application.
INTRODUCTION
The synthesis of silicon-organic monomers and polymers (silazane, siloxane-arylene,
carbosilazane, epoxide, etc.) containing aromatic groups with unsaturated radicals of allyl and
vinyl types have been attracting particular attention [1-4]. The classical method of
polyhydrosilylation revealed new possibilities of obtaining polymers with such a structure.
The range of unsaturated monomers used for reaction of polyhydrosilylation increased [4-7].
The use of unsaturated monomers of new type, distinguished from the standard divinyl
monomers, required elaboration of a non-traditional approach to this reaction [7]. The other
hand, the synthesis of polymers with aforementioned structure is of interest for modification
of properties of some important industrial polymers, such as polycarbonate, phenolformaldehide resins, rubbers based on organic and siliconorganic elastomers, etc. [7]. They
also may be used in combination with some other organic and element-organic polymers (for
example, with polyepoxides) as the substrates for nanohybrides [8, 9].
EXPERIMENTAL
Synthesis methods: α,ω-oligodihydridedimethylsiloxanes were synthesized by the
methods described in ref [11]. 1,3-tetramethyldisiloxane was obtained by hydrolysis of
dimethylchlorinesilane [10]. 1,5-trimethyltriphenyltrisiloxane has been synthesized by
reduction of 1,5-dichlorine-1,3,5-trimethyltriphenyltrisiloxane with LiAlH4 [10]. 1,5-tetramethyl-3,3-diphenyltrisiloxane was obtained via interaction of (Me)2SiHCl with diphenylsilandiol [7].
Investigation methods: the IR spectra of all samples were obtained, from KBr pellets, on
SPECORD and UR-20 spectrophotometers, while NMR 1H spectra were obtained with AM360 instrument at the operating frequency of 360 MHz. All spectra were obtained using
CDCl3 as a solvent and an internal standard. Perkin-Elmer DSC-7 differential scanning
calorimeter was used to determine DTA and the thermal (phase) transition temperatures were
read at the maximum of the endothermic or exothermic peaks. Heating and cooling scanning
rates were 100C/min. The column set comprised 103 and 104 Å Ultrastyragel columns. Wideangle X-ray diffractograms were obtained by DRON-2 instrument. Cu Kα was measured
without a filter; the motor angular velocity was ω ≈ 20 / min
New Silazane Oligomers and Polymers with Organic-Inorganic Main Chains…
53
RESULTS AND DISCUSSION
We have studied polyhydrosilylation reactions of α,ω-oligodiorganodihydride siloxanes
and 1,4-bis(dihydridedimetylsilyl)benzene with dialylsilazanes (DAS) in the presence of
Speier’s catalyst (0.1 mole solution of H2PtCl6·6H2O in isopropanol) [3-7] in dry toluene and
in mass.
The initial diallylsilazanes were synthesized via interaction of industrial organocyclosilazanes (hexametylcyclotrisilazane, methylphenylcyclotrisilazane and methylvinylcyclotrisilazane) with orto-allylphenol (o-AP) and 4-allyl-2-methoxyphenol (Evg.), in the area of Argon
being free from oxygen and moisture [6]. The reactions proceeded easily in mass, at 333353K, according to the following scheme [6, 7]:
[CH3(R)SiNH]n+2HO-Ar-CH2-CH=CH2
to
>
− NH 3
,
where R = CH3, CH=CH2, C6H5, Ar = phenylene, methoxiphenylene, n=3.
Scheme 1.
The resultant products are slightly viscous, optically transparent (in visual area of the
spectra) liquids soluble in ordinary organic solvents (benzene, toluene, acetone, etc.) and
practically insoluble in water. The composition and structure of the obtained diallylsilazanes
were confirmed based on the data of elemental and IR spectral analysis [6, 7] The maximums
of the absorption, related to Si−NH−Si and Si−O−Si, Si−O−C groups (915-925 cm-1, 9901000 cm-1 and 1060-1080 cm-1), also the maximums of the absorption, related to Si−CH3,
CH2=CH, Si−C6H5 and benzene ring (1250 cm-1, 1430 cm-1, 1445 cm-1, 1620-1630 cm-1, 1600-1605
cm-1 correspondingly) were found in the IR spectra [6].
It should be noted that the method used for manufacturing diallylsilazanes is accessible
(easy of access) and has some of noteworthy positive technological features for a practical
viewpoint [6]:
•
•
•
The reaction is carried out without (in the absence) solvents and catalysts;
Removal of side products is not difficult;
Control of the process is simple due to determination of the gaseus ammonia.
Polyhydrosilylation reactions of 1,4-bis(dimethylhydridesillyl)benzene and α,ω-oligodiorganodihydredesiloxanes with sinthesized dilsilazanes are passing according to the following
general scheme:
54
CH 3
(CH 2) 3
R
(CH 2) 3
Si
R'
CH 3
Rx
Si
R'
n
where Rx= O, C6H4, O[Si(CH3 )2 O]m, (m=6,11), CH3(C6H5)SiO, Si(C6H5)2, R = R1= CH3;
R= CH3, R1 = CH=CH2, C6H5; R1 = CH3, C6H5; n>>1.
Scheme 2.
Preliminarily we had studied the following model system: (CH3)3SiOSi(CH3)2H + DAS.
Heating of the corresponding reaction mixture in the temperature range of 60-80 0C, in
the absence of the Speier’s catalyst, showed that the polymerization of DAS or other changes
of the structures of the initial compounds do not take place. There didn’t observe any changes
in the IR, NMR 1H and NMR 13C of initial compounds. Content of the double bond of the
allyl group and active Hydrogen did not change either.
The process was controlled by determination of active hydrogen in Si−H groups for
several times [2, 6]. The influence of the structure of dihydride monomers on the reaction
rate, yield and properties of obtained polymers has been studied (table 1, figure 1). Based on
kinetic curves (figure 1) of Si−H groups conversion, the reaction rate constants have been
determined (table 1). The total reaction order equals to 2.
The products of polyhydrosilylation reaction are optically transparent viscous liquids or
elastic gums soluble in ordinary organic solvents (toluene, CHCl3, etc.).
The composition and structure of produced polysilazanes were established based on the
data of the elemental, IR and NMR 1H spectral analyses. In IR spectra there were found the
55
maximums of absorption (915-925 cm-1, 990-1000 cm-1, 1020-1060 cm-1, 1250 cm-1, 1410
cm-1, 1430 cm-1, 1445 cm-1, 1600-1605 cm-1), related to Si−NH−Si, Si−O−Si, Si−O−Car ,
Si−CH2, Si−CH3, Si−C6H5, and benzene link, correspondingly (scheme 5). The data of
elemental analysis (for example, Si(I),%, calc./found.=17.01/16.08; Si(VIII),%,
calc./found.=17.84/17.09, etc., where the index numbers I and VIII the numbers of polymers
in the table 2) corresponded to the structures of the products, obtained in accordance with the
reaction scheme 2.
One can observe the singlet signals with chemical shifts within the range of δ ≈ 0.03 _
0.44 ppm for protons in methyl group of ≡Si−CH3 in NMR 1H spectra of the synthesized
polymers (there illustrated the data for IV, V and VI - table 2). One can also observe two
signals with the center of chemical shifts at1.28 ppm and 1.62 ppm, which correspond to
methylene protons in Si_CH2 groups, and multiplet signals with chemical shifts within the
range of δ ≈ 6.6 - 7.5 ppm corresponding to protons of phenyl groups in the NMR 1H spectra.
There were observed the signals with chemical shifts within the range of δ ≈ 5.1 _ 5.2 ppm
corresponding to protons in NH-groups in NMR 1H spectra. The triplet signals with center of
chemical shifts at 0.81 ppm correspond to methine protons in Si_ СH(CH3) _ groups [5].
Figure 1. Conversion of Si−H group in time for hydrosilylation reaction of dihydride siloxanes and 1,4bis(dimethylhydridesilyl)benzene with diallylsilazanes: 1.- VII; 2. - VI; 3.- III; 4.- II; 5.- V; 6.- IV (table 1).
The data given above (elemental and spectral analysis and solubility of the resultant
products) excludes homopolymerization of diallylsilazanes under the conditions of polyhydrosilylation reaction.
To evaluate relative reactivity of dihydridesiloxanes (determination of the rank of their
relative reactivity in polyhydrosilylation reaction), algebraic-chemical method, particularly
pseudo-ANB-matrices, has been used for the first time for this type reactions. This method is
56
a modified version of adjacency matrices [13]. In the context of the aforementioned approach,
taking into account the nature (structure) of organic radicals R and R1 at the silicon atoms of
the dihydridesiloxanes, it has been established that lg(ΔANB) is efficient topologic index for
fixing and investigating QSPR (quantitative structure-property relations) [13]. Corresponding
correlation equation has the following form: k=alg(ΔANB)+b , where k is a rate constant for
polyhydrosilyation reaction; lg(ΔANB) is a decimal logarithm of the determinant of pseudoANB-matrices; a and b – slope and intercept, which are calculated by method of leastsquares: a=6,792•10-3, b=3,083•10-3. The correlation coefficient r=0.9788 (figure 2).
H
Si
O
Si
H
IV
H
O
Si
Si
O
CH3
C6H5
CH3
CH3
CH3
CH3
Si
CH3
The polyaddition reaction
rate constants
k•10-3,
l•mol-1•sec-
12
96.6
0.17
---
333
10
85.5
0.10
2.29
333
12
97.0
0.21
2.78
12
96.4
0.13
4.33
CH3
C6H5
CH3
Si
333
CH3
II
H
ηsp**
CH3
CH3
III
The yield of products of
the reactions
dihydridsiloxsanes
and 1,4 bis- (dihydridedimethylsillyl)benzine
CH3
I
Reaction temperature,K
#
Duration of reaction, hrs
Table 1. Conditions of hydrosilylation reaction of 1,4-bis(dimethylhydridesillyl)benzine
and α,ω-oligodiorganodihydredesiloxanes with diallylsilazanes (DAS)*, the yield and
values of specific viscosities of synthesized polymers (in toluene)
O
Si
CH3
Si
O
6
H
H
333
CH3
Table 1. (Continued).
Si
H
V
CH3
CH3
CH3
Si
O
C6H5
CH3
H
VII
Si
11
The polyaddition reaction
rate constants
k•10-3,
l•mol-1•sec-
ηsp**
12
91.7
0.22
3.97
333
12
96.2
0.15
2.38
333
12
94.6
0.11
1.54
343
12
93.4
0.12
---
CH3
H
Si
O
Si
333
CH3
C6H5
C6H5
CH3
O
H
Si
O
CH3
Si
H
VI
Si
O
57
CH3
CH3
CH3
The yield of products of
the reactions
dihydridsiloxsanes
and 1,4 bis- (dihydridedimethylsillyl)benzine
#
Duration of reaction, hrs
Reaction temperature,K
H
C8H17
C8H17
CH3
C6H5
CH3
VIII
Si
H
CH3
_
_
O Si
C6H5
O Si
H
CH3
_
* CH2=CH CH2 Ar O[(CH3)2SiNH]2(CH3)2SiO_Ar_CH2_ CH=CH2; where Ar= C6H4 (VIII); Ar=
CH3OC6H4 (I-VII) (scheme 2); **) 1% solution in toluene.
According to the classic researches, polyhydrosilylation reaction of dihydridesiloxanes
with α,ω-divinyloligosiloxanes proceeds according to the general scheme given above
(scheme 2) [11]. At the same time, some other modern publications showed that both α and β
adducts are obtained (scheme 5) [2-6].
Quantum-chemical calculations of the model system (scheme 5) have confirmed the
probability of passing polyhydrosilylation reaction according to mentioned above two
concurrent directions.
58
k10-3 l.mol-1.c-1
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
4.75
4.8
4.85
4.9
4.95
5
5.1
5.05
Ig(ΔAND)
Figure 2. Dependence of value for hydrosilylation reaction rate constants on decimal logarithm of
determinant of pseudo-ANB-matrices in the series of α,ω-oligodiorganodihydridesiloxanes (table 1).
CH3
CH2
R
Si
CH2 + H
CH
OSi (CH3)3
CH3
CH3
I
CH2
CH2
R
CH2
Si
CH3
CH3
II
CH2
R
Si
CH3
CH3
CH3
R= CH3O
Si
CH3
Scheme 3.
OSi (CH3)3
CH
CH3
NH
Si
CH3
OSi (CH3)3
59
As a method of quantum-chemical calculation, we used AM1 method; MM2 method was
applied to perform optimization of geometry of adducts [7].
The calculation of the heat of formation (ΔHform) for the reaction model products showed
that formation of α-adduct (I) (ΔHIform = – 1067.77 kJ) is slightly more probable than that of
β-adduct (II) (for the product with the structure II, ΔHIIform= – 1055.67 kJ); both I and II
products are actually obtained [5]. One can observe the signals with chemical shifts at δ=0.81
and δ=1.62, which correspond to β (II) and α (I) adducts (scheme 4) in NMR 1H spectra of
real polysilazanes [5].
In case of the polyhydrosilylation reaction of dihydridesiloxanes with diallylsilazanes
(scheme 2) there may also proceed dehydrocondensation reaction (due to the interaction of
NH-groups of di- and intermediate oligosilazanes with Si–H groups of dihydridesiloxanes),
alongside with the main processes, via obtaining trisilylated nitrogen atom. To determine
which process (dehydrocondensation or polyaddition) is more probable, we have calculated
basic energetic parameters of model systems, for the products of polyhydrosilylation reaction.
As model systems there were selected structures described the actual reaction products [7]:
R'
R'
H3C
O
Si
H3C
N
Si
CH3
Si
C
H2
H
C
(III)
CH2
CH3
H3C
R
,
where R=OCH3, R′=CH3;
Scheme 4.
In spite of the fact that formation of model systems containing the trisilylated nitrogen
atom is thermodynamically possible (ΔHIIIform.= –928,76 kJ), separation of hydrogen did not
take place during the process of polyhydrosylation reaction [6]. At the same time, in IR
spectra of actual products of this reaction, the maximum of absorption related to trisilylated
nitrogen atoms (950-960cm-1) was not found [6, 7].
Evidently, it is favorable for dihydridesiloxanes to attract terminal allyl groups rather
than NH-group bonded to silicon atoms, surrounded with organic radicals under the
conditions of polyhydrosilylation reactions. That leads to formation of macromolecules with
linear structure (scheme 2) [6].
Using Roentgen-phase (RP) (figures 3) and Differential Scanning Calorimetric (DSC)
(figures 4) Analysis Methods, the synthesized polymers have been investigated. It has been
established (DSC and RPA methods) that they are amorphous substances. On the DSC-curves
(figure 4, a, b and c) endothermic peaks correspond to their glass transition temperature (Tg).
60
4.55 Å
7.15 Å
7.15 Å
7.08 Å
1
4.31 Å
4.13 Å
2
3
5
10
15
20
25
2Θ°
Figure 3. Difractograms of polymers: 1.-II; 2. IV; 3.-V (table 1).
a
HEAT FLOW (mw)
7.5
1
5
2.5
0
-140.0 -110.0 -80.0
-50.0 -20.0
10.0
Temperature
40.0
( 0C)
70.0
100.0 130.0 160.0
61
10
b
7.5
5
2.5
0
-140.0 -110.0
-80.0
-50.0
-20.0
10.0
40.0
70.0
100.0
130.0
160.0
Temperature ( 0 C)
10
HEAT FLOW (mw)
c
7.5
5
2.5
0
-140.0 -110.0
-80.0
-50.0
-20.0
10.0
Temperature
40.0
70.0
100.0
130.0
160.0
( 0 C)
Figure 4. DSC corves of polymers: II (a), VI (b), IV (c) (table 1).
Thermooxidation stability of synthesized polymers (DTA and TGA analyses methods,
figures 5) exceeds thermooxidation stability of polydimethylcarbosiloxanes containing
terminal functional groups [6]. This fact may be explained by formation of intermediate stable
cross-linked macromolecules by interaction of N–H group of polysilazanes with H2N–Si
groups of linear oligomers [12] at high temperature (210-2300C, in the open air) (figure 3a,
62
curves of DTA, exothermic pick at the 2200C); these oligomers maybe obtained via
hydrolysis of Si–NH–Si bonds by air moisture. Intensive thermooxidation destruction of the
synthesized polymers proceeds only within the temperature interval of 350-4500C. Based on
the TGA curve (figure 5), calculation of the activation energy (Ea) for the basic process of
thermooxidation destruction of synthesized polymers, has confirmed the above mentioned
supposition. So the value of calculated Ea (64 kJ/mol) exceeds correspond parameter (52-54
kJ/mol) for polydimethylcarbosiloxanes with terminal functional groups [14].
Figure 5. DTA (a) and TGA (b) corves for polymers X (table 1).
Produced diallyllsilazanes and polymers based on them were used for the modification of
the properties of some industrial polymer composites based on polymers with functional
groups.
Some satisfactory results were also obtained by modification of properties of phenolformaldehyde resin (PFR) composites with the synthesized diallylsilazanes (scheme 1). Thas,
addition of diallylsilazanes (1-3 mass %) to this composition has improved some of essential
characteristics of hardened PFR (table 3). It should be noted that other important physical and
mechanical properties of the composites have remained safe (table 3).
Besides the aforementioned, preliminary investigations showed that synthesized
oligomers and polymers, in combination with phenolformaldehyde resin, were successfully
used as binding component for polymer/graphite electro-conducting composites (ECC) [15,
16]. Obtained ECC were recommended for creation of electrode material for electrolytic
section and the chemical (fuel) sources of electrical energy (on the basis of analogous
material) [16].
63
Table 3. Some physical and mechanical properties of the modified
phenolformaldehide resin composite
#*
Electrical
conductivity,
ρ, om.cm
Strength on
pressure,
σ, MPa
Strength on
winding,
σ, MPa
I
II- 1%
III - 1%
III - 3%
53,28
49,23
49,63
49,50
21,22
21,22
27,16
56,59
19,80
12,00
18,50
16,90
Specific
percussive
viscosity,
kg. cm/cm2
2,76
2,40
2,45
2,27
IV - 3%
51,67
41,58
26,20
2,75
* I – without modifiers (scheme 1);
II – diallylsilazane based on 4-allyl-2-methoxyphenol:hexamethylcyclotrisilazane (2:1);
III – diallylsilazane based on 4-allyl-2-methoxyphenol:trimethyltriphenylcyclotrisilazane (2:1);
IV – diallylsilazane based on 4-allyl-2-methoxyphenol:hexamethylcyclotetrasilazane (2:1).
ACKNOWLEDGMENT
The authors thanks Dr. M. Katsitadze - for the synthesis of 1,3-dimethyl-1,3dioctyledisiloxane and 1,4-bis(dihydridedimetylhyl)benzene, also Prof. Dr. Aneli and Dr. D.
Gventsadze - for study of created electro-conducting polymer composites.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
Silanes and Other Coupling Agents. Edit.: K.I. Mittal. The Fourth International
Symposium on Silanes and Other Coupling Agents, MST Conferences, LLC in Orlando,
FL, Vol.3. June 11-13, 2003.
Kopylov V.M., Koviazina T.G., Buslaeva T.M., Sinicin N.M., Kireev V.V., Gorshkov
A.V.. Peculiarity of the Hydrosilylation Reaction of the Polyfunctional Methylvinyland Methylhydrosiloxanes. Zhurnal Obshchei Khimii. (Journal of General Chemistry),
57, 5 1117-1127 (1987) (Rus.);
Lekishvili N., Samakashvili Sh., Murachashvili D., Lekishvili G., Gverdtsiteli M..
Oligoepoxysiloxanes with side epoxy groups: synthesis and properties. Chemistry and
Industry. (Bulg.). Vol. 77 (2006) (In press).
Mukbaniani O.V. and Zaikov G.E. Cyclolinear Organosilicon Copolymers: Synthesis,
Properties, Application. Netherlands, Utrecht, VSP (2003).
Mukbaniani O., Tatrishvili T., Titvinidze G. Hydrosilylation Reaction of
Methylhydridesiloxane to n-Hexene-1. Georgian Chemical Journal. 3, 3 214-215
(2003) (Rus.).
Lekishvili N., Samakashvili Sh. Reactions of polyaddition of dihydride siloxanes to
diallylsilazanes: new approaches. Proceedings of Tbilisi State University, 360, 19-23
(2005) (Geo.).
64
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
Kopylov V.M., Sokolskaya I.I., Murachashvili D.U., Lekishvili N.G., Khubulava E.I.,
Zaikov G.E.. New Siliconorganic Modifiers of Rubbers Based on Carbochain
Elastomers. Konstruktsii iz Polimernikh Kompozitov, (Constructions from Polymer
Composites), 4, 37-48 (2003) (Rus.).
Brostow W. The Chain Relaxation Capability. Ch. 5. In performance of Plastics. Ed.
W. Brostow, Hanser, Munich-Cincinnati, 2000.
Witold Brostow, Wunpen Chonkaew, Haley Hagg and Oscar Olea. V Republican Conference, Chemistry. Abstracts. Georgia, Tbilisi, Georgian Chemical Society. P.41, 2830 October, 2004.
Andrianov K.A. Metodi Elementorganicheskogo Sinteza. Kremnii. (Methods of
Element Organic Synthesis. Silicon). Mockva, “NAUKA”. 1968 (Rus.).
Andrianov K.A., Gavrikova L.A., Rodionova E.F. Investigation of the polyaddition
reaction of α,ω-divinylalkyl(aryl)siloxane oligomers with α,ω-dihydroalkyl(aryl)siloxane oligomers. Visokomolekuliarnie soedinenya. (Polymer science) XIII(A), 4 937939 (1971) (Rus.).
Lekishvili N.G., Katsitadze M.G., Nakaidze L.I., Khananashvili L.M. Some Kinetically
Regularities of Polymerization Condensation Reaction of Organocyclosilazanes with
Spacial Groups at Silicon Atoms with Aromatic Dihydroxy compounds. Bulletin of the
Academy of Sciences of Georgia. Series of Chemistry. 152, 3 529-531 (1995) (Rus.).
Gverdtsiteli M., Gamziani G., Gverdtsiteli I. The Adjacency Matrices of Molecular
Graphs and their Modification. Tbilisi University Press. Tbilisi, 1996 (Geo.).
N. Lekishvili, M. Kezherashvili, Sh. Samakashvili. Silicon-organic Polymers with
Inorganic and Organic-Inorganic Main Chains, Containing Silicon-Nitrogen and
Silicon-Oxygen Bonds. Publish Company “UNIVERSALI”. Tbilisi, Georgia, 2006.
Aneli J., Khananashvili L., Zaikov G. Structuring and Conductivity of Polymer
Composites. Nova Science Publishers, Inc., N.-Y. 1998.
Lekishvili N., Gventsadze D., Aneli J., Samakashvili Sh., Khuchua T. Polymer
Materials with Specific Properties Based on Secondary Mineral Resources and
Petroleum Products. III All-Russian Conference “Physical chemistry of the Processing
of Polymers”. Chemical-Technological State University, Ivanovo (Russia), 2006.
Chapter 5
TO QUESTION ABOUT INFLUENCE
OF SOLVENT ON INTERACTION PROPANETHIOLE BY
CHLORINE DIOXIDE
R. G. Makitra, G. E. Zaikov* and I. P. Polyuzhyn
Division of physico-chemistry of fuels of Pisarzhevskij Institute physical chemistry
of Ukrainian National Academy of Science , 3A Naukova str., L'viv, Ukraine
The data for influence of solvents on oxidation propanthiole by chlorine dioxide are
satisfactorily generalized by means of five parameters equation according to principles of
Linear Free Energies Relationships (LFER). An essential role plays the density of media
cohesion energy, that bears out radical process nature.
Recently the data concerning to interaction of propanthiole with chlorine dioxide in 8
solvents have been published [1]. In this work it was shown, that the dependence of process
rate from solvents properties is satisfactory described for seven solvents, after the exclusion
of data for ethyl acetate, by the Koppel-Palm four parameters equation (coefficient of
multiple correlation R 0,96) at determining role of medium polarity (coefficient of pair
correlation between lg(k) and (ε - 1)/(2ε + 1) - r 0.90). Chemical mechanism of the reaction
including the formation of ion-radical RS+*Н and radical RS* has been proposed by authors
[1].
However, it is known, that in homolytical processes certaine influence on reaction rate
has also so-called "cage effect", which is described by density of medium cohesion energy.
That was confirmed by generalization of data concerning to influence of solvents upon
decomposition rate of benzoyl peroxide [2] or oxidizing processes [3, 4]. That is why the data
analysis from work [1] is seemed as expedient by means of five parameter equation:
*
G.E.Zaikov: N.M. Emanuel Institute of Biochemical physics; Russian Academy of Sciences, 4 Kosygin str.,
Moscow 119991, Russia
66
R. G. Makitra, G. E. Zaikov and I. P. Polyuzhyn
n2 −1
ε −1
+ a2 ⋅
+ a 3 ⋅ B + a 4 ⋅ ET + a 5 ⋅ δ 2
lg( k ) = a 0 + a1 ⋅ 2
2ε + 1
n +2
(1)
On comparison with known Koppel-Palm equation the equation (1) includes square of
Hildebrandt’s solubility parameter δ2 [5], P.219-225. This equation (1) allows with acceptable
precision degree to generalize all data from the work [1] (see Table) without necessity of
exclusion the data for ethylacetate:
lg(k)= 12.57 + (-12.76 ± 9.15)⋅f1(n2) + (23.03 ± 8.02)⋅f2(ε) + (3.72 ± 1.93)⋅10-3⋅B
+ (-0.67 ± 0.31)⋅ET + (18.04 ± 6.87)⋅10-3⋅δ2
s ± 0.408
N
8
R
0.9638
(2)
It is necessary to mark, that as difference to work [1] in presented research for description
of electrophilicity more preferable Reichardt parameter (value ET) [2] is applied but not
electrophilicity Е offered by Koppel-Palm. As analogy with [1] the exclusion from equation
(2) the data for one of solvents - acetone or ethylacetate allows to obtain an equation for lg(k)
with R > 0.99.
Analysis of meaning for separate parameters of the equation according to [6] by the way
of their in turn exclusion shows on only insignificant role of polarizability effects since for
the four parameters equation without f1(n2) the correlation coefficient is only insignificantly
lesser R 0.9536. The influence of nucleophilic solvation (factor near basicity B in the
equation) has relatively low meaning too as at its exclusion value R becomes as 0.9440. In the
same time exclusion from the equation any of three rest factors decreases the degree of
correlation to not allowed low value R as to 0.919; 0.939; 0.927 relatively. Here the medium
polarity has especially significant influence. It is unastonishingly, if one takes into account a
high degree of pair correlation between lg(k) and f2(ε) which is equal to 0.901.
Values lg(k) calculated by equation (2) are given also in table. In equation (2) significant
parameters of "solvation" such as f2(ε) and δ2 have sign "plus". That indicates on preferable
solvation of intermediate reactionary complex, which facilitates the reaction runing in result
of electrons division. That agrees confirmed with opinion of authors [1] about polar nature of
reactive complex. Evidently its formation is limiting stage, because antibatness is observed
between lg(k) and ΔG# with high correlation degree as value r is 0.990. Only medium ability
to electrophilic solvation ET has a sign "minus", evidently, in consequence of the positive
solvation of initial thiol. It is desirable but to note that significant correlation with r 0.916
exists between f2(ε) and ET. Besides, an essential influence is observed of medium cohesion
(δ2) since at exclusion of this factor the R value falls to 0.927. That bears out opinion
advanced by authors [1] about mainly radical nature of the process.
The energetic charactiristics of process such as Е#ACT., ΔН#, ΔG# and ΔS# also can be
generalized with acceptable precision by means of five parameters equations. As an example
in the table there are given the experimental activation energies (Е#ACT.) and its values
calculated by equation (3):
To Question about Influence of Solvent on Interaction Propanethiole…
67
E#АКТ = -51.85 + (-65.14±30.14)⋅f1(n2) + (-125.5±26.4)⋅f2(ε) + (24.90±6.35)⋅10-3⋅B + +
(3.70±1.02)⋅ET + (-52.87±22.63)⋅10-3⋅δ2
s ± 1.345
N
8
R
0.9571
(3)
Here as well as for lg(k), the exclusion of the most deviating data for one of solvents acetone for ΔG#, heptane or dioxane for Е#ACT and ΔН#, and benzene or heptane for ΔS#
allows to receive equations with R > 0.99. For majority of activation descriptors the
polarizability as f1(n2) is least meaningful factor exception ΔS# where is δ2 also, as and for
lg(k). However its exclusion decreases R from 0.95 to 0.93, that undesirable according to [6].
The exclusion of other parameters from equation is more noticeable.
Thus taking into account the cohesion energy density allows essentially to improve upon
results of correlation analysis on influence of medium properties on kinetics of oxidation of
propanethiole by chlorine dioxide. At the same time a significance of this factor is indirect
proof of radical stages in the process.
Table. Experimental on [1] and calculated values lg(k) for
kinetic of propanthiol oxidation by chlorine dioxide
Solvent
lg(k)
experimen
t
n-Heptane
1,4- Dioxane
Carbon tetrachloride
Benzene
Diethyl ether
Ethylacetate
Acetone
Acetonitrile
-2.777
-1.444
-1.411
-2.593
-0.086
-1.000
0.583
1.722
computatio
n by Eq.(2)
-2.773
-1.224
-1.847
-2.353
-0.266
-0.199
0.092
1.689
Е#ACT, ccal/mole
experiment
computation
by Eq. (3)
11.27
11.89
21.00
20.03
6.54
5.14
7.73
9.74
11.54
12.99
13.02
11.91
16.09
15.34
14.74
16.00
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
Yakupov M.Z., Lyapina N.K., Shereshovets V.V., Imashev U.B. // Kinetics and
catalysis (Rus). 2001. Vol.42. № 5. PP.673-676.
Makitra R.G., Pyrih Ya.N.., Havryliv E.M. Depon. In VINITI 1988 № 8418-В-88. Ref.
Zh. Khim. 1989. 5Б4128.
Kutcher R.V., Vasyutin Ya.M., Makitra R.G., Pyrih Ya.N. // Dokl. Acad. Sci. Ukr.SSR
Series "B". 1988. № 6. PP.47-51.
Pyrih Ya.N., Makitra R.G., Yatchyshyn Y.Y. // Kinetics and catalysis. (Rus). 1991.
Vol.32. № 5. PP.1040-1047.
Reichardt Ch. Solvents and Solvent Effects in Organic chemistry. Weinheim: Wiley
VCH, 2003. 630 p.
Recomendations for Reporting the Results of Correlation Analysis in Chemistry using
Regression Analysis // Quant. Struct. Acta Relat. 1985. Vol.4. № 1. P.29.
Chapter 6
MATHEMATICAL MODELLING OF THERMOMECHANICAL DESTRUCTION
OF POLYPROPYLENE
G. M. Danilova-Volkovskaya, E. A. Amineva1 and B. M. Yazyyev2
1
Rostov-on-Don Agricultural Machinery State Academy; 344023,
Strana Sovetov Street, 1, Rostov-on-Don.
e-mail: [email protected]
2
Ushakov Naval State Academy
353900, Lenin Avenue, 93, Novorossiysk
ABSTRACT
There has been provided mathematical description of the processes of thermonuclear
destruction in deformed polypropylene melts; the aim was to use the criterion of
destruction estimation in modelling and optimising the processing of polypropylene into
products.
Keywords: Thermo-mechanical destruction, polypropylene, molecular mass, effective
viscosity.
During processing polypropylene melts under the action of transverse strain there occur
strain-chemical conversions which can result in both decrease and increase in their molecular
masses; the mechanical effect on the rapidity and level of the occurring processes is
considerably more prominent than the mere contribution of thermal and thermal-oxidative
breakdown. These data necessitate studying the process of polymer destruction. For this
purpose it would be most effective to apply the criterion of assessment of the intensity with
which destructive processes happen in polymer melts.
If the destruction is observant from the initial value of molecular mass М0 to a certain
finite value М∞, then at point of time t the chain group with molecular mass М0 - Мt (where
Мt is the average value of molecular mass at a given point of time) is involved in the process.
It is natural to assume that the rate of destruction in a unit time is proportional to the whole
70
G. M. Danilova-Volkovskaya, E. A. Amineva and B. M. Yazyyev
number of breakdowns in macromolecules up to the destruction limit. These assumptions
enable us to propose an expression for calculating the rate of destruction process:
d (( M t − M ∞ ) / M t
= − Kdt
(M t − M ∞ ) / M ∞
,
The integration of this expression results in:
ln
Mt − M∞
= − Kt + e ,
M∞
(1)
Since at t=0 Мt = M0, then:
С = ln
Mt − M∞
M∞
,
(2)
If we substitute (1) with (2) after some transformations we get:
ln
Mt − M∞
= − Kt ,
M∞
From here:
М t = ( M 0 − M ∞ )e kt + M ∞ ,
As value М0 - М∞ is constant for the polymer of the given molecular mass, we can
designate it as A; after substitution we get:
ln
Mt − M∞
= − Kt
M0 − M∞
from here:
М t = A ⋅ e − kt + M ∞ ,
where K is the rate constant depending on the
chemical nature of a polymer and, in particular, on how close macromolecular chains are
packed.
Each criterion obtained from the given expressions represents a concept of one of the
interrelated consequences of thermo-mechanical destruction process: decrease in molecular
weight, the number of macromolecular breakdowns, and the approach to the possible level of
macromolecular destructions. The merit of the criteria is that their values do not depend on
the initial molecular weight [1-3].
Mathematical Modelling of Thermo-Mechanical Destruction of Polypropylene
71
Paper 20 dwells on the ideas allowing us to advance in the quantitative assessment of
thermo-mechanic destruction degree.
Taking these data as a basis we can propose an expression for calculating the degree of
thermo-mechanic destruction in the form of:
ϕ а1 =
1 η 0 − kt
⋅ ⋅e ,
а ηt
(3)
where a is the constant of proportionality which is equal to 3.105.
On the other hand:
ϕ а1 = (η а ,τ 1, 2 ,η 0 , it ) ,
(4)
where ηа is the effective viscosity of a material melt,
τ1,2 are transverse strains during processing.
Combining the defining parameters of equation (3) and modifying this equation into a
dimensionless form, it is possible to demonstrate that criterion φ1а, is the function of only two
parameters ηа and τ1,2.
Comparing (3) and (4) enables the following expression for the criterion of thermomechanic destruction degree to be proposed:
⎛ τ ⋅t ⎞
ϕ а1 = f ⎜⎜η 0 , 1, 2 ⎟⎟ ,
ηa ⎠
⎝
(5)
The direct application of this expression in order to estimate the degree of thermomechanic destruction in connection with polymer processing is hindered because the process
rate constant depends on the temperature and intensity of thermo-mechanical impact on a
material. Consequently, of significant interest is the issue of selecting an attribute for
characterizing the degree of destruction. Most researchers consider it worthwhile to simply
use viscosity variable (ηа) or characteristic viscosity variable.
Here is proposed the criterion for the rate of thermo-mechanical destruction in the
polymeric system Ψ11:
−τ 12 ⋅t
1 ⎡η 0 ηa ⎤
Ψ = ⋅⎢ е
⎥,
a ⎢⎣η a
⎥⎦
1
1
where τ12 are strain rate tangents.
(6)
72
G. M. Danilova-Volkovskaya, E. A. Amineva and B. M. Yazyyev
This relation is helpful because it provides an opportunity for the quantitative assessment
of polymer thermo-mechanical destruction rate in dependence with the thermo-mechanical
impact regime during processing.
Analyzing the data obtained when testing the samples of extrusion products made of
polypropylene, the conducted research on their molecular-weight properties, and the
calculated values of the criterion for the destruction processes rate, we concluded that the
processes of attachment and bifurcation correspond to the values of Ψ11 = 1, while the
processes of destruction correspond to Ψ11= - 1.
Assuming that the effective viscosity in a polypropylene melt is sensitive to changes in
molecular mass and in chain-length distribution and taking into consideration the specific
character of the thermo-mechanical impact developing during extrusion, it is proposed to
calculate the intensity of destruction processes from the latter expression. The advantage of
the criterion is that it does not require defining the molecular mass of a polymer.
Comparing the values of Ψ11, obtained at testing PP samples processed under various
technological regimes and calculated with the aid of a mathematical model allows us to
propose applying the criterion to the estimation of physical and chemical transformations
occurring in a polymer at modifying the parameters of thermo-mechanical impact.
Taking into consideration Ψ11 values, we have found the optimal regime when PP is
under extrusion processed into products with improved deformation-strength properties [4].
CONCLUSIONS
There has been provided mathematical description of the processes of thermonuclear
destruction in deformed polypropylene melts; the aim was to use the criterion of destruction
estimation in modelling and optimising the processing of polypropylene into products.
REFERENCES
[1]
[2]
[3]
[4]
Olroyd J.G. On the formulation of rheological equation of stat. - Trans. Roy. Soc., 1970,
A 200, N 1063, p. 523 -527.
De Witt T., Mezner .W. A rheological equation of state which predicts non-Newtonian
viscosity, normal stresses and dynamics module. J. Appl.Phys., 1985, v. 26, p. 889-892.
Baramboymb I.K. Mechanochemistry of high-molecular substances. – 3rd edition.
Moscow. The Chemistry publishing house, 1978, p. 34.
Danilova-Volkovskaya G.M. The effect of processing parameters and modifiers on the
properties of polypropylene and PP-based composite materials. — Doctoral Thesis,
(technical sciences). 2005, p. 273.
Chapter 7
ENERGY CRITERIONS OF PHOTOSYNTHESIS
G. А. Коrablev*1 and G. Е. Zaikov*2
1
Basic research-educational center of chemical physics and mesoscopy,
Udmurt research center, Ural Division, RAS, Izhevsk
2
Institute of biochemical physics after N.M. Emanuel, RAS, 119991,
4 Kosygina St., Russia, Moscow
ABSTRACT
The application of methodology of spatial-energy interactions (P-parameter) to main
stages of photosynthesis is given. Their energy characteristics are calculated. The values
obtained correspond to the reference and experimental data.
Keywords: Spatial-energy parameter, free radicals, structural interactions, photosynthesis.
DESIGNATIONS
m1 and m2
ΔU1 and ΔU2
ΔU
Z*
n*
Wi
ri
ni
SEI
Р0
РE
*
masses of material points (kg);
potential energies of material points (J);
their resulting (mutual) potential energy of interaction (J);
nucleus effective charge (Cl);
effective main quantum number;
bond energy of electrons on i-orbital (eV);
orbital radius of i-orbital (Å);
number of electrons on this orbital;
spatial-energy interactions;
spatial-energy parameter (eVÅ);
effective Р-parameter (eV);
G.А. Коrablev: E-mail: [email protected]
74
R
Hv
N1, N2, …
N
РС
α
ρ
PS
АТP
RuDF
PGA
NADP
PGA
Е
ЕС
(eV).
dimensional characteristic of atom or chemical bond (Å);
light quantum energy (J, eV);
number of homogeneous atoms;
average repetition factor in the formula (10);
structural Р-parameter of complex structure (eV);
coefficient of structural interactions, isomorphism (%);
degree of structural interaction (%);
photosystem (PSI and PSII);
adenosine triphosphate;
ribulose-diphosphate;
3 phospho-glycerin acid;
nicotine-amide-adenine-dinucleotide-phosphate;
phosphor-glycerin aldehyde;
energy of bond or molecule reduction (eV);
resulting energy of bond or reduction for radical groups
INTRODUCTION
Photosynthesis – process of converting electromagnetic energy of the sun rays into the
energy of chemical bonds of vital organic substances … [1].
It is the only natural process through which the organic world obtains the reserve of free
energy and which provides all bio-organisms with chemical energy. From the moment
photosynthesis was discovered by D.M. Priestly (1771-1850), the researches passed several
important stages. The first works connected with photosynthesis energy refer to 1850-1900
(R. Mayer, D.G. Stocks, J. Sax). The application of physiological concepts – in 1900-1950
(М.S. Tsvet, А.А. Richter, W. Arnold). Further development of bio-physicochemical aspects
of synthesis till now resulted in its modern model and clarified the way of carbon during
photosynthesis (M. Calvin), concept of two photosystems (R. Emerson), structure of reaction
center (I. Deizinhoffer, H. Michel, R. Huber), etc.
The basis of photosynthesis – consecutive chain of redox reactions, during which
electrons are transferred from donor-reducer to acceptor-oxidizer with the formation of
reduced compounds (carbohydrates) and oxygen isolation.
It is known that excitation energy for complex organic molecules of chlorophyll type
lasts for 10-8-10-9 sec and can be stored only for insignificant fractions of a second. But during
photosynthesis the energy of absorbed light quantum is stored for a long period (from several
minutes to millions of years). The energy is stored here in molecular as chemical bonds rich
with energy in complex organic structures. Therefore photosynthesis energy can be presented
based on the analysis of changes in energies of chemical bonds of molecular structures in
dynamics of all main types of photosynthesis.
This is the aim to use the methodology of spatial-energy interactions (P-parameter) in this
paper.
*
G.Е. Zaikov: E-mail: [email protected]
75
SPATIAL-ENERGY PARAMETER (Р-PARAMETER)
Structural and interatomic interactions are sure to have electron nature. Thus the
registration of the extent to which electrons fill the atom valence states is the basis of the
method of valence bonds in chemistry and is numerically expressed through coulomb
electrostatic interaction.
Also important are exchange-promotional structural interactions that determine
isomorphism, solubility of components in solid, liquid and molecular media [2].
During the interactions of oppositely charged heterogeneous systems the volume energy
of interacting structures is compensated to a certain extent thus leading to the decrease in the
resultant volume energy.
The analysis of different physical and chemical processes allows assuming that in many
cases the principle of adding reciprocals of volume energies or kinetic parameters of
interacting structures is executed.
Some examples: ambipolar diffusion, total rate of topochemical reaction, change in the
light velocity when transiting from vacuum into the given medium, resultant constant of
chemical reaction rate (initial product – intermediary activated complex – final product).
Lagrange equation for relative movement of isolated system of two interacting material
points with masses m1 and m2 in coordinate х can be presented as follows:
1
ΔU
≈
1
ΔU 1
+
1
ΔU 2
(1)
where ∆U1 and ∆U2 – potential energies of material points in elementary section of
interactions, ΔU - resulting (mutual) potential energy of these interactions.
The atom system is formed from oppositely charged masses of nucleus and electrons. In
this system energy characteristics of subsystems are the orbital energy of electrons (Wi) and
effective energy of nucleus that takes into consideration the screening effects (by Clementi).
Therefore, assuming that the resultant interaction energy of the system orbital-nucleus
(responsible for interatomic interactions) can be calculated based on the principle of adding
reciprocals of some initial energy components, we substantiate the introduction of Pparameter [2] as an averaged energy characteristic of valence orbitals in accordance with the
following equations:
1
1
+
=
1
q r Wn Р
2
i
i
Р
E
=
Р
r
0
i
i
(2)
E
(3)
76
Р
E
1
Р
=
0
(3а)
R
=
1
2
P0
q
q=
Z*
n*
+
1
(Wrn) i
(4)
(5)
Here: Wi – bond energy of electrons [3]; ri – orbital radius of i–orbital [4]; ni – number of
electrons of the given orbital, Z* and n* – effective charge of nucleus and effective main
quantum number [5], R – numerical characteristic of atom (bond).
The Р0 value will be called a spatial-energy parameter, and the РE value – effective Р–
parameter. Effective РE–parameter has a physical sense of some averaged energy of valence
electrons in atom and is measured in energy units, e.g. in electron-volts (eV).
The values of Р0- and РE-parameters of some elements calculated based on equations (25) are given in table 1.
Table 1. Р-parameters of atoms calculated via the bond energy of electrons
1
Valence
electrons
2
W
(eV)
3
ri
(Å)
4
q2 0
(eVÅ)
5
Р0
(eVÅ)
6
Н
1S1
13.595
0.5295
14.394
4.7985
2P1
11.792
0.596
35.395
5.8680
2P2
11.792
0.596
35.395
10.061
Atom
С
N
2Р1г
2P3г
2S1
2S2
2S1+2P3г
2S1+2P1г
2S2+2P2
2P1
2P2
2P3
2P4г
2P5г
2S1
2S2
2S2+2P3
19.201
0.620
37.240
15.445
0.4875
52.912
25.724
25.724
0.521
0.521
53.283
53.283
4.4044
13.213
9.0209
14.524
22.234
13.425
24.585
6.5916
11.723
15.830
19.193
21.966
10.709
17.833
33.663
R
(Å)
7
0.5295
0.46
0.28
R-I=1.36
0.77
0.69
0.77
0.69
Р0/R
(eV)
8
9.0624
10.432
17.137
3.525
7.6208
8.5043
13.066
14.581
0.77
0.77
0.77
0.77
0.77
0.70
0.70
0.70
0.55
0.55
0.70
0.70
0.70
11.715
18.862
28.875
17.435
31.929
9.4166
16.747
22.614
34.896
39.938
15.299
25.476
48.09
77
Table 1. (Continued)
Atom
Valence
electrons
2P1
2P1
2P1
2P2
W
(eV)
17.195
ri
(Å)
0.4135
q2 0
(eVÅ)
71.383
Р0
(eVÅ)
4.663
17.195
0.4135
71.383
11.858
2P4
17.195
0.4135
71.383
20.338
2S1
2S2
2S2+2P4
33.859
33.859
0.450
0.450
72.620
72.620
12.594
21.466
41.804
5.3212
1.690
17.406
5.929
8.8456
O
Ca
S
Se
Р
Mg
4S1
4S2
4S2
4S2
3P1
3P2
3P4
3S1
3S2
3S2+3P4
4P1
4P2
4P2
4P2
4P4
4P4
4S1
4S2
4S2+4P4
4S2+4P4
3P1
3P1
3P3
3P3
3S2
3S2+3P3
3S1
3S2
Mn
4S1
4S2
3d1
4S1+3d1
4S2+3d2
4S2+3d5
Na
3S1
Cl
3P1
11.901
11.901
11.904
23.933
23.933
0.808
0.808
0.808
0.723
0.723
48.108
48.108
48.108
64.852
64.852
6.0143
13.740
21.375
13.659
22.565
43.940
8.5811
15.070
15.070
15.070
24.213
10.963
0.909
61.803
22.787
0.775
85.678
10.659
0.9175
38.199
14.642
25.010
49.214
49.214
7.7864
10.659
0.9175
38.199
16.594
18.951
0.803
50.922
6.8859
1.279
17.501
19.050
35.644
5.8568
8.7787
6.7451
1.278
25.118
17.384
0.3885
177.33
4.9552
1.713
10.058
6.4180
10.223
6.5058
12.924
22.774
38.590
4.6034
13.780
0.7235
59.849
8.5461
R
(Å)
0.66
RI=1.36
RI=1.40
0.66
0.59
RI=1.36
RI=1.40
0.66
0.59
0.66
0.66
0.66
0.59
1.97
1.97
R2+=1.00
R2+=1.26
1.04
1.04
1.04
1.04
Р0/R
(eV)
9.7979
4.755
4.6188
17.967
20.048
8.7191
8.470
30.815
34.471
19.082
32.524
63.339
70.854
3.0096
4.4902
8.8456
7.0203
7.7061
13.215
20.553
13.134
1.04
1.17
1.17
1.6
1.14
1.17
1.6
1.17
1.17
1.17
1.6
1.10
R3-=1.86
1.10
R3-=1.86
1.10
1.10
1.60
1.60
R2+=1.02
42.250
7.3343
12.880
9.4188
13.219
20.710
15.133
12.515
21.376
42.066
30.759
7.0785
РЭ=4.1862
15.085
8.9215
17.318
32.403
3.6618
5.4867
8.6066
1.30
1.30
1.30
1.30
1.30
1.30
1.89
R+I=1.18
R+I=0.98
1.00
R-I=1.81
4.9369
7.8638
5.0043
9.9414
17.518
29.684
2.4357
3.901
4.6973
8.5461
4.7216
78
Atom
Fe
К
Valence
electrons
4S1
3d1
4S1+3d1
4S2+3d1
4S1
W
(eV)
7.0256
17.603
4.0130
ri
(Å)
1.227
0.364
2.612
q2 0
(eVÅ)
26.572
199.95
10.993
4S2(*)
Р0
(eVÅ)
6.5089
6.2084
12.717
16.664
4.8490
7.2115
R
(Å)
1.26
Р0/R
(eV)
4.8325
1.26
1.26
2.36
R+I=1.45
2.36
R+I=1.45
10.093
13.226
2.0547
3.344
3.0557
4.9734
Table 2. Structural РС-parameters calculated via the bond energy of electrons
Radicals, fragments of
molecules
P i'
ОН
Н2О
СН2
СН3
СН
Н3О
С2Н5
СН2
СН3
СН3
СН
СН
СО
С=О
С=О
С-О2
С-О2
СО-ОН
CH-OH
CO-H
P "i (eV)
PC
17.967
9.7979
9.7979
17.967
10.432
9.0624
10.432
17.138
6.5999
4.7080
5.0525
8.7712
O (2P2)
O (2P1)
O (2P1)
O (2P2)
2·9.0624
2·10.432
2·17.138
28.875
31.929
28.875
31.929
28.875
28.875
31.929
31.929
3·17.138
2·31.929
31.929
28.875
31.929
28.875
31.929
31.929
14.581
17.435
28.875
31.929
12.315
11.152
8.4416
17.967
17.967
17.967
2·17.138
2·17.138
2·9.0624
3·17.138
3·9.0624
17.138
9.0624
17.138
17.967
5·17.138
2·9.0624
3·17.138
3·9.0624
10.432
10.432
20.048
20.048
20.048
2·20.048
2·20.048
8.7712
8.7712
9.0624
9.0226
9.6537
11.788
15.674
16.531
11.125
19.696
14.003
10.755
7.059
11.152
13.314
36.590
11.562
18.491
14.684
7.6634
7.8630
12.315
8.4416
9.3252
16.786
17.774
5.1226
4.9159
4.3705
O (2P2)
O (2P2)
O (2P2)
С (2S12P3г)
С (2S22P2)
С (2S12P3г)
С (2S22P2)
С (2S12P3г)
С (2S12P3г)
С (2S22P2)
С (2S22P2)
O (2P2)
С (2S22P2)
С (2S22P2)
С (2S22P3г)
С (2S22P2)
С (2S22P3г)
С (2S22P2)
С (2S22P2)
С (2P2)
С (2S12P1г)
С (2S12P3г)
С (2S22P2)
С (2S22P2)
С (2S22P2)
С (2P2)
(eV)
(eV)
Orbitals
Modifying the rules of adding reciprocals of energy characteristics of subsystems as
applied to complex structures we can obtain [6] the equation for calculating РС-parameters of
complex structure:
1
Р
⎛ 1 ⎞ ⎛ 1 ⎞
⎟ +⎜
⎟
⎝ NP E ⎠ ⎝ NP E ⎠
=⎜
С
1
+ ...
79
(6)
2
where N1 and N2 – number of homogeneous atoms in subsystems.
The calculation results of some complex structures based on equation (6) are given in
table 2.
The calculations for 21 elements showed that the values of РE-parameters are similar to
corresponding values of total energy of valence electrons according to the statistic model of
atom.
Simple dependence between PE-parameter and electron density at the distance ri can be
obtained (according to the statistic model of atom):
β
2/3
i
= A ⋅ P 0 = A Р E , where А-constant
r
(7)
i
When the solution is formed in the places of atom-components contact, the unified electron
density has to be established. The dissolving process is accompanied by the redistribution of
this density between valence areas of both particles and transition of some electrons from
external spheres to the neighboring ones.
It is obvious that if electron densities in free atom-components of the solution at the
distances of orbital radius ri are similar, the transition processes between boundary atoms of
particles are minimal thus favoring the solution formation.
Thus the task of evaluating the solubility in many cases comes to comparative evaluation
of electron density of valence electrons in free atoms (on averaged orbitals) participating in
the solution formation.
In this regard the maximum total solubility evaluated through the coefficient of structural
interaction and isomorphism α are determined by the state of minimal value that represent
relative difference of effective energies of external orbital:
α=
P'o / ri '− P''o / ri ''
100% ;
( P'o / ri '+ P''o / ri '') / 2
' − "
α = РС РС 200%
' + Р"
РС
С
(8)
(9)
Multiple calculations and comparisons with the experiment allowed arranging the unified
averaged figure-nomogram of degree of structural interaction and solubility (ρ) dependence
upon coefficient α [2].
80
The following spatial-energy principles defining the character of structural spatial-energy
interactions were determined:
1. Complete (total-lot) isomorphic interaction takes place at relative difference of Pparameters of valence orbitals of interchanging atoms (within 4-6%).
2. Р-parameter of the smallest value defines the orbital that is mainly responsible for
isomorphism.
3. Qualitatively the isomorphism character is defined by geometrical similarity of
orbital shapes responsible for isomorphism. At the same time, the more similar are
the extensions, trajectories and inclination angles of such orbitals, the more perfect is
isomorphism.
According to the degree of isomorphic similarity of interchanging structures they can be
classified into three types (I, II, III) given for some cases in table 3.
PHOTOSYNTHESIS. INITIAL STAGE
Magnesium atom that is four-coordinated with nitrogen atoms is included into
chlorophyll in the central cavity of the whole structure. The porphinated chlorophyll ring is
located in aqueous medium. Each central Mg atom forming chelate compound has two bonds
by donor-acceptor mechanism and two covalence bonds. Two molecules of bacteriochlorophyll are located close to each other (about 3 Å) and form competent-structure – dimer
chlorophyll. In the dynamics of structural permutations all four bonds of each Mg atom
become equivalent [7]. All this allows assuming that total effective РE-parameter of Mg will
be approximately two times greater than from 2S2-orbital (5.4867х2=10.973 eV).
At the first stage of photosynthesis in the system of PS-2 dimensional characteristics of
hydrogen atom can change in structured water molecules under the radiation with energy hν
from boron radius (0.529 Å) to atomic (“metal”) – 0.46 Å, this corresponds to the obtaining
of РE-parameter equal 10.432 eV by hydrogen that is similar to РE-parameter of 2Mg. It
should be pointed out that general change in the scale of photosynthesis potentials PS-2
approximately equals 1.5 eV, and the difference between the data of Р-parameters of
hydrogen atoms equals 1.37 eV.
The rest of hydrogen atoms with “boron” РE-parameter equaled to 9.0624 eV have
similar values with РE-parameters of 2Р1-orbitals of nitrogen atoms surrounding magnesium.
Other data are not less important: initial value of РE-parameter of 2S2-orbital of
magnesium atom gives from РE-parameter (table 3) of radical (О-Н) α=8.24 % and ρ ≈ 77-82
%. This ρ value can increase to even 100 % under the light action due to minor changes in
dimensional characteristics of atoms-components. Absolute difference of these Р-parameters
equals 0.43 eV, thus corresponding to the changes in the scale of potentials during the
synthesis of АТP.
Total spatial-energy action upon the bond Н-О-Н of magnesium and nitrogen atoms
(table 3) results in the possibility of breaking this bond with the isolation of free hydrogen
and oxygen atoms.
Table 3. Photosynthesis structural interactions
Atoms .molecules.
radicals
O-P
O-P
Mg2+-H
H2O-CH2
C-O
CO-OH
CO-H2O
CH2-CO2
2Mg-H
Mn-H
Mn-O
Mn-O
N-H
Mn-OH
Mg-(O-H)
K+-H
Fe-S
Na+-H
1 component
Orbitals
2Р2
2Р1
3S2
1S1-2Р2
2S1-2Р1
2Р2-2Р2
2S12Р1г-2Р2
2S22Р2-1S1
3S2 (3S2)*
4S13d1
4S13d1
4S23d2
2Р1
4S1
2S2
4S1
4S23d1
3S1
РE. РС (eV)
8.470*
4.6188*
8.6066
11.788
17.435
8.4416
9.3252
16.531
10.973
9.9414
9.9414
17.518
9.4166
4.3969
5.4867
3.344
13.226
3.901
2 component
Orbitals
3Р3
3Р1
1S1
2S12P3г-1S1
2Р2
2Р2 -1S1
1S1-2Р2
2S12P3г-2Р2
1S1
1S1
2P1
2P2
1S1
2P1-2S1
2P1-2S1
1S1
2P2
1S1
РE. РС (eV)
8.9215*
4.1862*
9.0624
11.125
17.967
8.7712
9.0226
16.785
10.432
10.432
9.7979
17.967
9.0624
4.7080
5.0575
3.525
13.215
3.525
α (%)
ρ (mol%)
SEI types
5.19
9.83
5.16
5.79
3.01
7.51
2.21
1.53
5.05
4.82
1.45
2.53
3.83
4.75
8.24
5.27
0.08
10.1
100
60-65
100
100
100
90-95
100
100
100
100
100
100
100
100
77-82
100
100
55-60
I
I
I
II
I
II
II, III
III
I
I
II
II
II
II, III
II
I
II
I
82
This initial process finishes with the participation of manganese-containing system
connected with proteins of reaction center PS-2. Structural reconstruction can take place in
manganese cluster (two-nucleus or four-nucleus) under the action of radiation [8, 9] from
univalent state (4.9369 eV – this is similar to initial values of Mg РE-parameter) to bivalent
(9.9414 eV) and further – to quadrivalent state (17.518 eV).
All this provides enzymatic action of Mn upon the bond Н-О-Н, both upon oxygen and
hydrogen atoms, and hydroxyl group in general. This is confirmed by the approximate
equality of РE-parameters of bi- and quadrivalent Mn with РE-parameters of 2Р1 and 2Р2orbitals of oxygen atom (table 3). Thus, all the above interactions and structural re-groupings
inducted with light result in the formation of oxidized chlorophyll based on the following
reaction [10]:
Н2О+2hν→
1
О2+2е-+2Н+
2
with the isolation of two electrons and two protons. These electrons, broken off from the
water, through the chain of “dark” reactions go further to PS-1 that utilizes them in the next
photosynthesis stages to reduce NADP+ to NADPN that is carried out also with the help of
proton transfer system.
For double bond of 2Р1-orbital the carbon atom has РE-parameter – (8.5043 eV) – similar
to РE-parameter of hydrogen atom (table 1). Therefore one of the freed hydrogen atoms join
the double bond С=С available in NADPN with the formation of single bond with carbon
atom [9].
PHOSPHORYLATION
It is considered [7,11] that directed transition of protons serves as energy source during
phosphorylation. Between the numbers of transported protons and electrons certain
stoichiometric relations are revealed. Thus, in the course of electron transfer (along the whole
transport system) ATP molecules are formed.
Apparently, ATP phosphorylation energy can also be estimated through the system of
electron transfer.
In particular, electron transfer results in that phosphoric acid molecules present in АТP,
NADP and NADPN contain oxygen atoms in the form of О-. Spatial-energy interactions
(including isomorphic) are objectively expressed both at similar and opposite electrostatic
charge of atoms-components. Such interactions can also take place between two
heterogeneous atoms, if only their РE-parameters are roughly equal, and geometric shapes of
orbitals are similar or alike.
The radiation energy hν in PS-1 promotes, apparently, the changes in dimensional
characteristics of phosphorous and oxygen atoms from covalent to anion ones. Therefore, Р0parameters of free phosphorus and oxygen atoms are distributed at the distance of their anion
radii 1.86 Å and 1.40 Å, respectively. This similarity of values of their РE-parameters: α=5.19
% for 2Р3-orbitals of phosphorous with 2Р2-orbitals of oxygen (table 3).
Such approximate equality of РE-parameters and geometric similarity of shapes of
orbitals of atoms-components shows that actual degree of their interaction ρ=100 %, thus
83
providing the energy of formation of macroenergy bond Р-О. Then bond energy of
phosphorous and oxygen atoms from two different molecules of phosphoric acid necessary
for structural formation during phosphorylation can be considered phosphorylation energy.
To calculate bond energies or energies of molecule reduction during photosynthesis (Е)
the technique previously tested [6] for 68 binary and more complicated compounds following
the equation was applied:
1
1
=
=
Е Рс ⎛
1
+
1
N⎞ ⎛ N⎞
⎜ РE ⎟ ⎜ РE ⎟
⎝ K⎠ ⎝ K⎠
1
(10)
2
where N – bond average repetition factor, К – hybridization coefficient that usually equals the
number of atom valence electrons registered.
The half of internuclear distance (for binary bond) of similar atoms or atomic, covalence
or ionic radii (depending upon bond type) can be used as a dimensional characteristic of
atoms.
The calculations involving anionic distances of atomic orbitals for Р and О atoms were
made: 3Р1 (phosphorous)-2Р1 (oxygen) and for 3Р3 (phosphorous)-2Р2 (oxygen). The values
of Е obtained appeared to be slightly greater than experimental and reference data (table 4).
But actual power physiological processes during photosynthesis have the efficiency below the
theoretical, being in some cases about 83% [7].
It is probable that electrostatic component of resulting interactions on anion-anion
distances is registered in such a way. In fact, the calculated value 0.83Е practically
corresponds to the experimental bond energy values during phosphorylation (first line in table
4) and free energy for АТP in chloroplasts (second line in table 4).
The calculations of bond energy based on the same technique but on covalence distances
of atoms for free molecule Р…О (sesquialteral bond) and for molecule Р=О in Р4О10 (double
bond) are given in table 4 for comparison.
Sesquialteral bond was evaluated introducing the coefficient N=1.5 using the average
value of oxygen РE-parameter for single and double bonds.
It is interesting to point out that calculations of Е based on covalence distances
correspond to experimental data without introducing the coefficient 0.83.
ASSIMILATION OF СО2
Binding of СО2 takes place in aqueous medium by the carboxylation reaction of ribulosediphosphate (RuDP) with the formation of 3-phospho-glycerine acid (PGA) – table 5. Water
molecule and radical С=О at the distances of molecular interaction have quite similar values
of РE-parameters for forming the general structural grouping of dimeric composite type. Total
РE-parameter of water molecule and radical С=О nearly equals РE-parameter of СО2 and
therefore the molecules of СО2 and Н2О join RuBP with the formation of two radicals СООН
в PGA (table 5). In ferment RuDP- carboxylase, Mg atoms and О- ions (5.4867 eV and 4.755
eV) play an active role, their РE-parameters similar to РE-parameter of radical СООН.
Table 4. Bond and reduction energies of molecules during photosynthesis (eV)
Atoms, structures,
orbitals
1 component
2 component
РE (eV)
2
4.1862
4.1862
8.9215
N/K
3
1/5
1/5
1/5
РE (eV)
4
4.6188
4.755
8.470
N/K
5
1/6
1/6
1/6
Р---О
3S23P3-2S22P4
32.403
1.5/5
70.854
63.339
Р=О
3Р3-2P2
С-Н
2Р2-1S1
Н2О
1S1-2S2
-O-O2P1-2P1
O=O
2P2-2P2
CO2
2P2-2P2
=C=O
2S22P2-2P2
C-O
2P2-2P2
(C=O)-H
(2S22P2-2P2)-1S1
-O-H
2P2-1S1
CO-OH
(2S22P2-2P2)-(2P21S1)
CH2O
2S22P2-1S1-2P2
15.085
2/3
13.066
1
Р-О 3Р1-2Р1
Р-О 3Р2-2Р2
3 component
РE (eV)
6
N/K
7
Calculation
Е
8
0.400
0.405
0.77
0.83Е
9
0.33
0.34
0.64
Е by
[7.8.14]
Notes
-
10
0.340.35
0.670.59
6.14
Free PO molecule
-
6.504
In Р4О10 molecule
3.797
-
3.772
-
2.570
-
2.476
-
-
4.90
-
5.11
2/4
--
-
5.012
-
5.11
2•20.048
2/6
-
-
4.717
-
4.56
2/4
20.048
2/2
-
-
8.8874
-
13.066
1/2
17.967
1/2
-
-
3.782
-
3.688
31.929
2/4
20.048
2/2
9.0624
1/1
4.487
-
4.553
17.967
17.967
8.8874
1/2
1/2
1/1
17.137
9?0624
5.894
1/1
1/1
1/1
-
-
-
-.4.390
-
-
5.894
4.511
3.544
-
-
31.929
1.33/4
2.90624
1/1
20.048
2/2
5.025
-
4.965.07
_
_
-
-
1.5/6
1.5/6
-
-
20.042
2/2
-
-
6.277
6.024
<
6.15>
6.697
1/2
9.0624
1/1
-
-
2•9.0624
1/1
17.967
1/6
-
9.7979
1/1
9.7979
1/1
20.048
2/4
20.048
14.581
2/4
31.929
11
Phosphorylation
ÄG of ATP
Decomposition of
one molecule
Reduction
Free energy of the
formation of one
mole
Table 5. Spatial-energy characteristics of СО2 assimilation (eV)
Reaction
blocks
PE
RuDF
Mg, RuDFcarboxylase
¾ C = O + H2O
8.4416
+ CO2
9.0226;
17.774;
NADPN,
PGA ATP, O2COOH
2X5.1226 ;
PGA
ATP Mg
2COH + O2
. . .
2x4.3705; 17.967x2 ;
EC
8.8874
2.570
EC1 =1.401
Calculation:
EC2-EC1 =0.37;
By [7]: 1 ATP molecule
4.717
3,544
3,544
4.487
5.012
EC3 =2.367
EC2 =1.770
9060
17.967x2
(7.333)
(8.741)
E
CH2O + O2 + . . .
5.025
5.012
EC4 =2.509
EC3-EC1 ~ 0.97
EC3-EC2 ~ 0.60
3 ATP molecule (1.06 eV)
2 ATP molecule
Notes:
РE – initial values of РE-parameters, for Мg (5.4867), Mg2+ (8.6066), for О- (4.755; 4.6188)
Е – bond or reduction energy
ЕС – resulting bond or reduction energy for groups of radicals or fragments: 1/ЕС=1/Е1+1/Е2+…
86
A great difference in the number of atoms of interacting structures proves that
carboxylase can play only a fermentative role, “tuned” to obtain this final product (СООН).
The further complicated way of СО2 assimilation to form СН2О flows through series of
intermediate compounds and reactions (Calvin cycle). Let us show some results of
calculations of total spatial-energy assimilation processes of СО2. When СО2 is reduced to the
level of its structural formation in СН2О, the chemical bonds are reconstructed on all stages
of the cycle. Therefore, the additional activation energy from ATP and NADPN is required.
It is also obvious that power consumption should be rationally calculated taking into
account the reconstruction processes of chemical bonds, i.e. via the values of bond energy –
for binary structures, and reduction energy – for more complex molecules and radicals (Е).
Thus we calculated the value E based on equation (10) for several compounds and
radicals during photosynthesis – tables 4 and 5. For radical – С =О the calculations were
made in two possible variants of activity of valence orbitals of carbon atoms. The compliance
of calculated Е values with reference data [12,13] was in the range of 5% for all bonds of
covalence type without introducing the coefficient 0.83.
The main part of light energy is stored by a plant on the reduction stage to PGA. At the
same time, 4.56 eV (per molecule) are spent – [12.13]. Our calculations give the reduction
energy of radical СОН equal to 4.487 eV. Free energy for the formation of one mole of СН2О
based on reference data [7,12, etc] is 4.96-5.07 eV. The calculations following the method of
Р-parameter evaluate this energy as 5.025 eV.
Н
In molecule О=С–Н the average repetition factor for carbon atom bond was taken as
equal to (2+1+1)/3=1.33.
Applying the approved approach to calculate the resulting bond energy (or the reduction
energy) of structural subsystems for each stage, the values of these energies were calculated
(table 5) – ЕС. It is known [7] that the cycle moving energy to PGA can be 1.06 eV due to
three ATP molecules (per one СО2 molecule), one ATP molecule is consumed in the cycle to
PGA.
Following our data, the cycle moving energy (ΔЕС) equals the difference of ЕС values for
the corresponding stages:
1) stage СО2 – FGAК: ΔЕС=1.770-1.401=0.369 eV
Phosphorylation energy of one ATP molecule = 0.34-0.35 eV
2) stage СО2 – FGA: ΔЕС=2.367-1.401=0.966 eV
Phosphorylation energy of three ATP molecules: 0.34х3=1.02 eV
Thus Р-parameter gives the satisfactory characteristics of energetics of the СО2
assimilation cycle main stages. Photorespiration reaction is as if “competitive” to the СО2
assimilation reaction. Also here it is possible to reveal similar values of РE-parameters of
interacting radicals С=О and НСОН with РE-parameters of oxygen atoms. As in assimilation
reaction the ferment RuDP- carboxylase “is tuned” for the formation of final product СООН.
Other ferments can participate in photosynthesis and photorespiration, for example, the
substitution of Mg atoms for Fe atoms results in the formation of cytochromes, in which РEparameter of two-valence iron (РE=10.093 eV) is an active spatial-energy component of
photosynthesis structural interactions. Therefore, iron-sulfur proteins – ferrdoxins executing
87
various transport functions connected with ATP synthesis are initial and secondary acceptors
of electrons in the system PSI.
CONCLUSION
In this approach we give quantitative and semi-quantitative evaluation of spatial-energy
interactions at main stages of complicated biophysical process of photosynthesis based on the
utilization of initial atomic characteristics. The analysis of results after the application of Рparameter methodology shows that they correspond to reference data both in the direction and
energetics of these processes.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
Big medical encyclopedia. М.Т.26.1985.560 p.
Korablev G.A. Spatial-Energy Principles of Complex Structures Formation.
Netherlands. Brill Academic Publishers and VSP. 2005, 426p. (Monograph).
Fischer C.F. Average-Energy of Configuration Hartree-Fock Results for the Atoms
Helium to Radon.//Atomic Data.-1972. -№ 4. -p. 301-399.
Waber J.T.. Cromer D.T. Orbital Radii of Atoms and Ions//J. Chem. Phys -1965. -V 42.
-№12. -p. 4116-4123.
Clementi E.. Raimondi D.L. Atomic Screening constants from S.C.F. Functions.
1.//J.Chem. Phys.-1963. -v.38. -№11. -p. 2686-2689.
Korablev G.A.. Zaikov G.E. Energy of chemical bond and spatial-energy principles of
hybridization of atom orbitalls.//J. of Applied Polymer Science. USA. 2006.
V.101.n3.P.2101-2107.
Photosynthesis/Edited by Govingi. М.:Mir, V.1-1987, 728p; V.2-1987, 460p.
P. Clayton. Photosynthesis. Physical mechanisms and chemical models. М.:Mir-1984,
350p.
S.A. Schukarev. Inorganic chemistry. V.2-1974, 382p.
D. Hall, K. Rao. Photosynthesis. М.:Mir, 1983.
J. Edwards, D. Walker. Photosynthesis of С3 and С4-plants: Mechanisms and
regulation. М.: 1986.
Encyclopedia in physics. М.: 1966, V.5, 576p.
Kamen M.D. Primary processes in photosynthesis. L. 1963.
Break-off energy of chemical bonds. Potentials of ionization and affinity to electron /
Edited by V.I. Kondratjev. М.:Nauka, 1974, 351p.
Chapter 8
SPATIAL-ENERGY INTERACTIONS
OF FREE RADICALS
G. А. Коrablev*1 and G. Е. Zaikov*2
1
2
Institute of biochemical physics after N.M. Emanuel, RAS, 119991,
4 Kosygina St.; Russia, Moscow
ABSTRACT
Spatial-energy characteristics of many molecules and free radicals are obtained. The
possibilities of applying the P-parameter methodology to structural interactions with free
radicals and photosynthesis energetics evaluation are discussed. The satisfactory
compliance of calculations with experimental and reference data on main photosynthesis
stages is shown.
Keywords: Spatial-energy parameter, free radicals, structural interactions, photosynthesis.
DESIGNATIONS
m1 and m2
а
Δх
ΔU1 and ΔU2
ΔU
Z*
n*
*
*
masses of material points (kg);
their acceleration (m/s2);
coordinate (m);
potential energies of material points (J);
their resulting (mutual) potential energy of interaction (J);
nucleus effective charge (Cl);
effective main quantum number;
G.А. Коrablev: E-mail: [email protected]
G.Е. Zaikov: E-mail: [email protected]
90
Wi
ri
ni
SEI
Р0
РE
R
N1, N2, …
РС
Ψ
α
ρ
bond energy of electrons on i-orbital (eV);
orbital radius of i-orbital (Å);
number of electrons on this orbital;
spatial-energy interactions;
spatial-energy parameter (eVÅ);
effective Р-parameter (eV);
dimensional characteristic of atom or chemical bond (Å);
number of homogeneous atoms;
Р-parameter of complex structure (eV);
Ψ-function;
coefficient of structural interactions, isomorphism (%);
degree of structural interaction (%).
INTRODUCTION
Free radicals are the atom groups or molecule fragments having unpaired electrons. Most
of them are unstable with high reactivity. Interacting between themselves and with other
molecules they produce new compounds that continue chemical reactions based on chain
principle – similar to neutrons in chain nuclear reactions. In many cases such processes are
the main reason of pathologic condition of living systems [1].
Therefore the problem of searching “retardants” for these chain reactions of free radicals
is critical. For instance, it is known that sulfur-containing amino acid (cysteine) “attracts”
unpaired electrons of protein [2,3]. Similar properties are reported about selenium, the
element of the same subgroup VI-а of the System as sulfur [4].
It is found out that the number of unpaired electrons in dry bio-objects (after their
production) decreases when introducing nitric oxide or increasing the moisture content.
On the contrary, the role of oxygen atoms (also the element of VI-а subgroup of the
System) is often expressed as the role of an accelerator of irreversible reactions of free
radicals. Free radicals (including oxygen) demonstrate specific influence in complicated biophysicochemical processes of photosynthesis. Fundamental regularities of reactions with free
radicals were found by I.I. Semenov and his disciples. Important contribution to solving the
problem of free radical participation in biological processes was made by N.M. Emmanuel,
А.G. Gurvich, B.N. Tarusov, L.А. Bluemenfeld, G.М. Frank, W. Gordy, B. Commoner, M.J.
Calvin and others. It seems interesting to find a functional dependence and directedness of
free-radical processes with initial energy and dimensional characteristics of their atomscomponents.
In this paper we are attempting to explain such processes applying the methodology of
spatial-energy notions (P-parameter).
91
METHODOLOGY SUBSTANTIATION
Comparing multiple regularities of physical and chemical processes we can assume that
in many cases the principle of adding reciprocals of volume energies or kinetic parameters of
interacting structures is implemented.
Some examples: ambipolar diffusion, total rate of topochemical reaction, change in the
light velocity when transiting from vacuum into the given medium, resulting constant of
chemical reaction rate (initial product – intermediary activated complex – final product).
Lagrange equation for relative movement of isolated system of two interacting material
points with masses m1 and m2 in coordinate х with acceleration α can be presented as follows:
1
≈ − ΔU
1 /( m 1 aΔx) + 1 /( m 2 aΔx)
1
or:
ΔU
≈
1
ΔU 1
+
1
ΔU 2
(1)
where ∆U1 and ∆U2 – potential energies of material points in elementary section of
interactions, ΔU - resulting (mutual) potential energy of these interactions.
The atom system is formed from oppositely charged masses of nucleus and electrons. In
this system energy characteristics of subsystems are the orbital energy of electrons (Wi) and
effective energy of nucleus that takes into consideration the screening effects (by Clementi).
Therefore, assuming that the resultant interaction energy of the system orbital-nucleus
(responsible for interatomic interactions) can be calculated based on the principle of adding
reciprocals of some initial energy components, we substantiate the introduction of Pparameter [5] as an averaged energy characteristic of valence orbitals in accordance with the
following equations:
1
1
+
=
1
q r Wn Р
2
i
i
Р
E
Р
r
=
i
0
(2)
E
(3)
i
1
=
1
2
P0
q
q=
Z*
n*
+
1
(Wrn) i
(4)
(5)
92
Here: Wi – bond energy of electrons [6]; ri – orbital radius of i–orbital [7]; ni – number of
electrons of the given orbital, Z* and n* – effective charge of nucleus and effective main
quantum number [8].
The Р0 value will be called a spatial-energy parameter, and the РE value – effective Р–
parameter. Effective РE–parameter has a physical sense of some averaged energy of valence
electrons in atom and is measured in energy units, e.g. in electron-volts (eV).
Based on the results [5] the values of РE-parameters numerically equal (within 2%) total
energy of valence electrons (U) by the atom statistic model. Using the well-known ratio
between electron density (β) and inneratomic potential by the atom statistic model, we can
obtain the direct dependence of РE-parameter upon the electron density at the distance ri from
the nucleus:
β
2
i
3
= A P0 =
r
AP
E
where А – constant
i
Validity of this equation was confirmed when calculating the electron density using
Clementi’s wave functions and comparing it with electron density value calculated via РEparameter value.
Besides the modules of maximum values of ψ-function radial part were compared with
Р0-parameter values, and the line dependence between these values was found. Using some
properties of wave function for P-parameter, the wave equation of P-parameter was obtained.
Based on calculations and comparisons two principles of adding spatial-energy criterions
depending upon wave properties of P-parameter and systemic character of interactions and
charges of particles were substantiated:
1. Interaction of oppositely-charged (heterogeneous) systems consisting of I, II, III, ...
atom sorts is satisfactorily described by the principle of adding corresponding energy
reciprocals by equations (2-5) (this corresponds to the minimum of weakening oscillations
taking place in antiphase);
2. During the interaction of similarly-charged (homogeneous) subsystems the principle of
algebraic adding of their P-parameters is realized based on the following equations:
m
Σ Р0= P'0+ P'0' +...+ P0m
i =1
(6)
∑ РE =
∑ Р0
R
(7)
where R –dimensional characteristic of atom (or chemical bond).
This principle corresponds to the maximum of oscillation intensification taking place in
the phase. Modifying the rule of adding energy reciprocals of subsystems as applied to
complex structures we can obtain the equation for calculating РС-parameter of complex
structure:
1 ⎛ 1 ⎞ ⎛ 1 ⎞
⎟ +⎜
⎟ + ...
=⎜
Pc ⎜⎝ NPE ⎟⎠1 ⎜⎝ NPE ⎟⎠ 2
93
(8)
where N1 and N2 – number of homogeneous atoms in subsystems.
During the formation of solution and other structural interactions the same electron
density must be formed in the areas of contact of atoms-components. This process is
accompanied by the redistribution of electron density between valence zones of both particles
and transition of a part of electrons from some outer spheres into neighboring ones.
Apparently, spanning electrons of atoms do not participate in such an exchange.
Apparently, with the closeness of electron densities in free atoms-components, the
transition processes between boundary atoms of particles will be minimum, thus favoring the
formation of new structure. So, the evaluation of the degree of structural interactions in many
cases comes to the comparative evaluation of electron density of valence electrons in free
atoms (on averaged orbitals) participating in the process.
The less is the difference (Р'0/r'i – P"0/r"i), the more favorable is the formation of a new
structure or solid solution from energy point.
In this connection the maximum total solubility evaluated through the coefficient of
structural interaction α is defined by the condition of minimum value of α that represents a
relative value of effective energies of outer orbitals of interacting subsystems:
P 'o / ri '− P ''o / ri ''
α=
100%
( P 'o / ri '+ P ''o / ri '') / 2
' − Р"
РС
С 200%
(9a) α =
' + Р"
РС
С
(9)
The nomogram of dependence of structural interaction degree (ρ) upon the coefficient α,
unified for a broad range of structures was designed based on all the data obtained. Figure 1
shows the nomogram obtained using РE-parameters calculated via the bond energy of
electrons (wi) for structural interactions of isomorphic type.
Following this methodology the mutual solubility of atoms-components was evaluated in
many (over a thousand) simple and complex systems. The calculation results agree with
reference and experimental data.
Isomorphism as a phenomenon is used to be applied to crystalline structures. Apparently,
analogous processes can also take place between molecular compounds where their role and
significance are no less than of purely coulomb interactions.
In complex organic structures the main role can be performed by separate “blocks” or
fragments. Therefore the task is to identify these fragments and evaluate their spatial-energy
parameters. According to wave properties of Р-parameter, total Р-parameter of each fragment
has to found based on the principle of adding reciprocals of initial P-parameters of all the
atoms. The resultant Р-parameter of fragment block or all the structure is calculated following
the rule of algebraic adding of P-parameters of fragments constituting them.
The role of fragments can be performed by valence-active radicals, e.g. СН, СН2, (ОН)-,
NO, NO2, (SO4)2-, etc. In complex structures this carbon atom usually has not one, but two or
three side bonds. The priority significance when calculating based on the principle of adding
94
reciprocals of P-parameters have those bonds, for which the condition of interference
minimum is better executed. Therefore first the fragments of bond С-Н (for СН, СН2, СН3
…) are calculated, and then separately the fragments N-R, where R-binding radicals (e.g. –
for the bond C-N).
Figure 1. Nomogram.
Apparently, spatial-energy interactions (SEI) based on equalization of electron densities
of valence orbitals of atoms-components have in nature the same universal significance as
purely electrostatic coulomb interactions, but they supplement each other. Isomorphism
known from the time of E. Micherlikh (1820) and D.I. Mendeleev (1856) is only a particular
manifestation of this overall natural phenomenon. The quantitative side of evaluating
isomorphic replacements of components, both in complex and simple systems, can be
rationally placed in the frameworks of P-parameter methodology. The problem of evaluating
the degree of structural SEI for molecular and organic structures is more complicated. The
methodology for calculating P-parameters of molecules, structures and their fragments are
successfully implemented [5]. But such structures and their fragments are not often
completely isomorphous to each other. Nevertheless SEI proceeds between them, its degree
can be evaluated only semi-quantitatively or qualitatively. All systems can be split into three
types based on their isomorphous similarity:
I Systems mainly isomorphous to each other – the systems with almost the same number
of heterogeneous atoms and summarily similar geometric shapes of interacting orbitals.
II Systems with limited isomorphous similarity – the systems that:
1. either differ in the number of heterogeneous atoms but have summarily similar
geometric shapes of interacting orbitals;
95
2. or definitely differ by geometric shape of orbitals but have the same number of
interacting dissimilar atoms.
III Systems without isomorphous similarity – the systems that considerably differ both in
number of dissimilar atoms and geometric shape of their orbitals.
Then, taking into account some experimental data, all types of SEI can be approximately
classified as follows:
Systems I
1. α < (0-6)%; ρ = 100 %.
Complete 100% isomorphism, complete isomorphous replacement of atoms-components;
2. 6 % < α < (25-30)%; ρ = 98 – (0-3) %.
Either broad or limited isomorphism as shown in nomogram 1;
3. α > (25-30) %; no SEI
Systems II
1. α < (0-6)%;
a. а) Reconstruction of chemical bonds, can be accompanied with the formation of a
new compound;
b. b) Breaking of chemical bonds can be accompanied with the separation of a fragment
from the initial structure, but without joining or replacing.
2. 6 % < α < (25-30)%;
A limited internal reconstruction of chemical bonds without the formation of a new
compound and replacements is possible.
3. α > (20-30) %; no SEI
Systems III
1. α < (0-6)%;
a. а) Limited change in the type of chemical bonds of the given fragment, internal
regrouping, without breaking from the main part of the molecule and replacements is
possible;
b. b) Some dimensional characteristics of the bond can change;
2. 6 % < α < (25-30)%;
A very limited internal regrouping of atoms;
3. α > (25-30) %; no SEI.
Nomogram № 1 is made for isomorphous interactions, i.e. for such structures or
subsystems with the same number of dissimilar atoms and approximate geometric
resemblance of interacting atomic orbitals.
96
In all other cases the calculated values of α and ρ refer only to the given type of
interactions, nomogram of which is not yet existing, and all the comparisons are merely
assumptions of qualitative or semi-quantitative character.
But if taking into account the universality of spatial-energy interactions in nature, this
evaluation can be significant for analyzing structural rearrangements in complex biophysicochemical processes (this will be further shown on the example of photosynthesis).
Enzymatic systems can greatly contribute to the correlation of the degree of structural
correlations. In this model the enzyme role is as follows: active parts of its structure
(fragments, atoms, ions) the РE-parameter value equal to the РE-parameter of the reaction
final product. I.e. the enzyme is structurally “tuned” via ПЭВ to obtaining the reaction final
product, but will not join it due to imperfect isomorphism of its structure (in accordance with
III).
CALCULATIONS AND COMPARISONS
Based on equations (2-5) with initial data calculated with quantum-mechanical
techniques [6-8], the values of Р0-parameters of the majority of elements being tabulated
constant values for each valence atom orbital were calculated. Mainly covalent radii were
applied as a dimensional characteristic for calculating РE-parameter – by main type of
chemical bond of interactions considered (table 1). For hydrogen atom also the value of Bohr
radius and value of atomic (“metal”) radius were applied.
In some cases the calculations of P-parameters are given considering the possibility of
hybridization of atom orbitals (marked with “Г”) – following the methodology discussed
before [9]. Besides we took into account the bond repetition factor for carbon and oxygen
atoms. In the course of calculations for potassium atom – element of group IV of large period
in the System the possibility of the influence of internal d-orbitals was considered. For several
elements the values of РE-parameters were calculated using ionic radii whose values are given
in column 7. All the values of atomic, covalent and ionic radii are basically taken by BelovBokiy, but crystalline ionic radii – by Batsanov [10].
Table 1. Р-parameters of atoms calculated via bond energy of electrons
Atom
1
Н
Valence
electrons
2
1S
1
W
(eV)
3
13.595
ri
(Å)
4
0.5295
q2 0
(eVÅ)
5
14.394
Р0
(eVÅ)
6
4.7985
R
(Å)
7
0.5295
0.46
0.28
R-I=1.36
Р0/R
(eV)
8
9.0624
10.432
17.137
3.525
97
Atom
С
N
1
Valence
electrons
W
(eV)
ri
(Å)
q2 0
(eVÅ)
Р0
(eVÅ)
R
(Å)
Р0/R
(eV)
2P1
11.792
0.596
35.395
5.8680
2P2
11.792
0.596
35.395
10.061
0.77
0.69
0.77
0.69
7.6208
8.5043
13.066
14.581
0.77
0.77
0.77
0.77
0.77
0.70
0.70
0.70
0.55
0.55
0.70
0.70
0.70
7
0.66
RI=1.36
RI=1.40
0.66
0.59
RI=1.36
RI=1.40
0.66
0.59
0.66
0.66
0.66
0.59
1.97
1.97
R2+=1.00
R2+=1.26
1.04
1.04
1.04
1.04
11.715
18.862
28.875
17.435
31.929
9.4166
16.747
22.614
34.896
39.938
15.299
25.476
48.09
8
9.7979
4.755
4.6188
17.967
20.048
8.7191
8.470
30.815
34.471
19.082
32.524
63.339
70.854
3.0096
4.4902
8.8456
7.0203
7.7061
13.215
20.553
13.134
1.04
1.17
1.17
1.6
1.14
1.17
1.6
1.17
1.17
1.17
1.6
42.250
7.3343
12.880
9.4188
13.219
20.710
15.133
12.515
21.376
42.066
30.759
2Р1г
2P3г
2S1
2S2
2S1+2P3г
2S1+2P1г
2S2+2P2
2P1
2P2
2P3
2P4г
2P5г
2S1
2S2
2S2+2P3
2
2P1
2P1
2P1
2P2
19.201
0.620
37.240
15.445
0.4875
52.912
25.724
25.724
0.521
0.521
53.283
53.283
3
17.195
4
0.4135
5
71.383
4.4044
13.213
9.0209
14.524
22.234
13.425
24.585
6.5916
11.723
15.830
19.193
21.966
10.709
17.833
33.663
6
4.663
17.195
0.4135
71.383
11.858
2P4
17.195
0.4135
71.383
20.338
2S1
2S2
2S2+2P4
33.859
33.859
0.450
0.450
72.620
72.620
12.594
21.466
41.804
5.3212
1.690
17.406
5.929
8.8456
O
Ca
S
Se
4S1
4S2
4S2
4S2
3P1
3P2
3P4
3S1
3S2
3S2+3P4
4P1
4P2
4P2
4P2
4P4
4P4
4S1
4S2
4S2+4P4
4S2+4P4
11.901
11.901
11.904
23.933
23.933
0.808
0.808
0.808
0.723
0.723
48.108
48.108
48.108
64.852
64.852
10.963
0.909
61.803
22.787
0.775
85.678
6.0143
13.740
21.375
13.659
22.565
43.940
8.5811
15.070
15.070
15.070
24.213
14.642
25.010
49.214
49.214
98
Atom
Р
Mg
Mn
Valence
electrons
W
(eV)
ri
(Å)
q2 0
(eVÅ)
Р0
(eVÅ)
R
(Å)
Р0/R
(eV)
3P1
3P1
3P3
3P3
3S2
3S2+3P3
3S1
3S2
10.659
0.9175
38.199
7.7864
10.659
0.9175
38.199
16.594
18.951
0.803
50.922
6.8859
1.279
17.501
19.050
35.644
5.8568
8.7787
4S1
4S2
3d1
4S1+3d1
4S2+3d2
4S2+3d5
3S1
6.7451
1.278
25.118
17.384
0.3885
177.33
4.9552
1.713
10.058
4.6034
3P1
13.780
0.7235
59.849
8.5461
2
4S1
3d1
4S1+3d1
4S2+3d1
4S1
3
7.0256
17.603
4
1.227
0.364
5
26.572
199.95
6
6.5089
6.2084
12.717
16.664
4.8490
1.10
R3-=1.86
1.10
R3-=1.86
1.10
1.10
1.60
1.60
R2+=1.02
1.30
1.30
1.30
1.30
1.30
1.30
1.89
R+I=1.18
R+I=0.98
1.00
R-I=1.81
7
1.26
7.0785
РE=4.1862
15.085
8.9215
17.318
32.403
3.6618
5.4867
8.6066
4.9369
7.8638
5.0043
9.9414
17.518
29.684
2.4357
3.901
4.6973
8.5461
4.7216
8
4.8325
1.26
1.26
2.36
R+I=1.45
2.36
R+I=1.45
10.093
13.226
2.0547
3.344
3.0557
4.9734
6.4180
10.223
6.5058
12.924
22.774
38.590
Na
Cl
1
Fe
К
4S2(*)
4.0130
2.612
10.993
7.2115
Table 2 contains the computational results of structural РС-parameters of free radicals by
the equation (8). The calculations are made for those radicals forming protein and aminoacid
molecules (СН, СН2, СН3, NH2, etc), as well as for free radicals being formed during
radiolysis and dissociation of water molecules (Н, ОН, Н3О, НО2).
The comparison of РС-parameter values of free radicals obtained with carbon, sulfur,
selenium and oxygen atoms was carried out in supposition of paired interactions by all
possible variants – based on the equation (9). It should be specifically stressed that here we
have the calculations of РE-parameters and structural interactions of practically all possible
values of initial dimensional characteristics of atoms. In the norm of stable bonds without
external interactions covalent bonds are the most probable in organic molecular structures.
The other options of SEI given in tables 1-3 correspond to such possible structural regrouping
when due to some reasons their dimensional characteristics vary from covalent to atomic or
even ionic. The results of such calculations of coefficient α and degree of structural
interactions (ρ) are given in table 3, when analyzing it the following conclusions and
comparisons can be made:
1. Valence orbitals of sulfur and selenium atoms have quite similar values of Pparameters as well as the degrees of structural interactions (ρ). On the contrary, РE-parameters
99
of oxygen atoms sufficiently differ from such values thus resulting, in many cases, in the
opposite results in chemical activity of its atoms.
2. Degree of structural interactions of sulfur and selenium atoms with radicals СН3,
NH2,H3O equals 100%. But with radicals СН and СН2 it equals zero or is insignificant – in
the range of 0 – 47%. It should be mentioned that structural interactions of the same elements
with basic carbon chain of polymeric biomolecules cannot result in their breaking-in since the
corresponding values of α for the interactions of Se-C and S-C exceeds 30%, thus ρ=0 in
these cases.
Atoms of S and Se can sufficiently structurally influence fragments of СН3 that are
frequently located on the ends of hydrocarbon chains or in the form of free radicals. The data
given confirm high reactivity of sulfur and selenium atoms as retardants of chain reactions of
free radicals as elements “drawing back” unpaired valence electrons of free radicals, but at
the same time preserving the basic structure of hydrocarbon chain.
3. Interactions of oxygen atoms result in α > 30% and ρ=0 with structures NH2, H3O and
– with radicals СН and СН3 based on С atom (2S22P2). But for radical СН2 on the same base
of carbon ρ=75-80 %, and for radical СН3 based on С atom (2S12P3г) – α=2,87 % and ρ=100
%.
It is also important to add that in contrast to S and Se, atomic structures of oxygen and
carbon have great values of РE-parameters and produce SEI at ρ=100 %.
All this means that 1) degree and character of structural SEI of oxygen are ambiguous
and considerably differ from the elements of selenium and sulfur; 2) oxygen atoms have
potential possibilities for decomposing some molecular structures of bio-objects initiating the
further free-radical process.
4. Water molecules (Н2О) produce ρ=100% with free radicals СН2, Н and ОН, this
proves the possibility of decreasing the number unpaired electrons in dry bio-objects with
their humidity decrease.
In this approach the mechanism of radical Н3О formation during water dissociation can
be apparently explained according to SEI (table 3). Hydrogen being released during
dissociation by equation Н2О Н+ + ОН¯ further completely interacts with water molecules (as
they have ρ=100%): Н+ + Н2О Н3О+.
Table 2. Structural РС-parameters calculated via bond energy of electrons
molecules
ОН
Н2О
СН2
СН3
Pi'
(eV)
17.967
9.7979
9.7979
17.967
2·9.0624
2·10.432
2·17.138
28.875
31.929
28.875
31.929
28.875
P "i (eV)
PC
10.432
9.0624
10.432
17.138
17.967
17.967
17.967
2·17.138
2·17.138
2·9.0624
3·17.138
3·9.0624
6.5999
4.7080
5.0525
8.7712
9.0226
9.6537
11.788
15.674
16.531
11.125
19.696
14.003
(eV)
Orbitals
O (2P2)
O (2P1)
O (2P1)
O (2P2)
O (2P2)
O (2P2)
O (2P2)
С (2S12P3г)
С (2S22P2)
С (2S12P3г)
С (2S22P2)
С (2S12P3г)
100
molecules
СН
NH
NH2
Н3О
Н2О–Н
НО2
С2Н5
NO
СН2
СН3
СН3
СН
СН
СО
С=О
С=О
СО-Н2
С-О2
С-О2
СО-ОН
NO
CH-OH
CO-H
Se-H
S-H
Se-H
S-H
СО-СН3
SO2
SeO2
Pi'
(eV)
28.875
31.929
31.929
22.296
22.296
22.296
22.296
3·17.138
9.0226
17.138
2·31.929
22.296
31.929
28.875
31.929
28.875
31.929
31.929
14.581
17.435
12.315
28.875
31.929
12.315
22.614
11.152
8.4416
12.880
13.215
12.880
13.215
12.315
20.533
20.710
P "i (eV)
PC
17.138
9.0624
17.138
9.064
17.138
2·9.0624
2·17.138
17.967
9.0624
2·17.967
5·17.138
17.967
2·9.0624
3·17.138
3·9.0624
10.432
10.432
20.048
20.048
20.048
2·9.0624
2·20.048
2·20.048
8.7712
17.967
8.7712
9.0624
9.0624
9.0624
17.137
17.137
8.7712
2·20.048
2·20.048
10.755
7.059
11.152
6.4370
12.019
9.9980
13.509
13.314
4.5212
11.604
36.590
9.9495
11.562
18.491
14.684
7.6634
7.8630
12.315
8.4416
9.3252
7.3330
16.786
17.774
5.1226
10.012
4.9159
4.3705
5.3194
5.3758
7.3533
7.4615
5.1226
13.579
13.656
(eV)
Orbitals
С (2S12P3г)
С (2S22P2)
С (2S22P2)
N(2P3)
N(2P3)
N(2P3)
N(2P3)
O (2P2)
O (2P2)
O (2P2)
С (2S22P2)
N(2P3)
С (2S22P2)
С (2S22P3г)
С (2S22P2)
С (2S22P3г)
С (2S22P2)
С (2S22P2)
С (2P2)
С (2S12P1г)
С (2S22P2)
С (2S12P3г)
С (2S22P2)
С (2S22P2)
N(2P3)
С (2S22P2)
С (2P2)
Se (4P2)
S (3P2)
Se (4P2)
S (3P2)
С (2S22P2)
S (3P2)
Se (4P4)
GENERAL CONCLUSIONS
1. Oxygen and its systemic fragments initiate free-radical processes normally producing
the rational balance with all forms of active protection of macromolecules from
them; in particular, atoms of sulfur and selenium can be applied for that.
2. Spatial-energy characteristics of different valency for sulfur and selenium define the
possibility of formation of such structures with these elements that possess
multipronged physical and chemical properties from poisons to oxidants.
3. Methodology of spatial-energy parameter helps not only to explain experimentally
determined dependencies of interactions of these elements with free radicals, but also
provides practical solution for searching new reagents with given properties.
101
Table 3. Evaluation of the degree of structural interactions (ρ)
Atoms,
molecules,
radicals
1
Se–CH3
S–CH3
О–CH3
Se–C
О-С
О-С
S–C
O-H
O-H2
O-H
H2O-H
H2O-OH
OH-H
Se-CH3
Se–H3O
S–H3O
O–H3O
O-CH2
O-CH
Se-NH2
S-NH2
O-NH2
O-CH3
S-CH3
O-S
О–CH2
Se–CН
S–CН
Se–CН2
S–CН2
Se–CН2
S–CН2
Se–CН
S–CН
1 component
Orbitals
РE , РС
(eV)
2
3
4Р4
20.710
3Р4
20.553
2Р4
30.815
4Р4
20.710
2Р4
30.815
2Р2
17.967
3Р4
20.533
2Р2
17.967
2Р2
17.967
2Р1
9.7979
1S1-2Р2
9.0226
2Р2-1S1
8.7712
4Р2
13.219
4Р2
12.880
4Р2
12.880
3Р2
13.215
2Р2
17.967
2Р2
17.967
2Р1
9.7979
4Р2
12.880
3Р2
13.215
2Р2
17.967
2Р2
17.967
3Р2
13.215
2Р2
20.048
2Р2
17.967
4Р4
20.710
3Р4
20.553
4Р4
20.710
3Р4
20.553
4Р2
12.880
3Р2
13.215
4Р2
12.880
3Р2
13.115
2 component
Orbitals
РE , Р С
(eV)
4
5
2S22P2-1S1
19.696
2S22P2
19.696
2S22P2
19.696
2S22P2
31.929
2S22P2
31.929
2S12P1 г
17.435
2S22P2
31.929
1S1
17.138
1S1
9.0624
1S1
9.0624
1S1
9.0624
1S1
9.0624
2S12P3 г-1S1
14.003
1S1-2P2
13.314
1S1-2P2
13.314
1S1-2P2
13.314
1S1-2P2
13.314
2S22P2-1S1
16.531
2S22P2-1S1
7.059
2P3-1S1
13.625
2P3
13.625
2P3
13.625
2S12P3
18.491
2S1P3 г-1S1
14.003
3Р4
20.533
2S12P3г-1S1
11.125
2S22P2-1S1
11.152
2S22P2
11.152
2S22P2
16.531
2S22P2
16.531
2S22P2
11.562
2S22P2
11.562
2S22P2
11.152
2S22P2
11.152
α (%)
6
5.02
4.16
44
42.6
3.55
3.01
43.4
4.72
0.88
7.80
0.40
2.83
3.27
5.76
2.56
0.75
29.7
8.33
32.15
5.62
3.06
27.5
2.87
5.76
2.39
34
60
59.3
22.4
21.7
10.8
13.3
14.4
16.9
ρ
(mol%)
7
100
100
0
0
100
100
0
100
100
84-88
100
100
100
100
100
100
0
75-80
0
100
100
0
100
100
100
0
0
0
2-5
2.5-5.5
7
47-52
30-35
23-28
Assumed
SEI type
8
III, 1
III, 1
III, 3
I, 3
I, 1
I, 1
I, 1
II, 1
II, 1
II, 1
II, 1
II, 1
II, 1
III, 1
III, 1
III, 1
III, 3
III, 2
III, 3, II, 3
III, 1
III, 1
III, 3
III, 1
III, 1
I, 1
II, 3, III, 3
III, 3
III, 3
III, 3
III, 3
III, 2
III, 2
III, 2
III, 2
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[3]
[4]
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Korablev G.A. Spatial-Energy Principles of Complex Structures Formation,
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Helium to Radon.//Atomic Data,-1972, -№ 4, -p. 301-399.
[7] Waber J.T., Cromer D.T. Orbital Radii of Atoms and Ions//J. Chem. Phys -1965, -V 42,
-№12, -p. 4116-4123.
[8] Clementi E., Raimondi D.L. Atomic Screening constants from S.C.F. Functions,
1.//J.Chem. Phys.-1963, -v.38, -№11, -p. 2686-2689.
[9] Korablev G.A., Zaikov G.E. Energy of chemical bond and spatial-energy principles of
hybridization
of
atom
orbitalls.//J.
of
Applied
Polymer
Science.
V.101,n.3,Aug.5,2006,p.2101-2107.
[10] S.S. Batsanov. Structural chemistry. Facts and dependencies. М.:MSU-2000,292p.
Chapter 9
POLY (VINYL ALCOHOL)[PVA]-BASED POLYMER
MEMBRANES: SYNTHESIS AND APPLICATIONS
Silvia Patachia,a Artur J. M. Valente,b
Adina Papanceaa and Victor M. M. Lobob
a
Department of Chemistry, “Transilvania” University of Brasov,
29 Eroilor Street, 500036 Brasov, Romania.
b
Department of Chemistry, University of Coimbra,
3004-535 Coimbra, Portugal
1. INTRODUCTION
Poly(vinyl alcohol) (PVA) is a polymer of great interest because of its many desirable
characteristics specifically for various pharmaceutical, biomedical, and separation
applications. PVA has a relatively simple chemical structure with a pendant hydroxyl group
(figure 1a). The monomer, vinyl alcohol, does not exist in a stable form, rearranging to its
tautomer, acetaldehyde. Therefore, PVA is produced by the polymerization of vinyl acetate to
poly(vinyl acetate) (PVAc) followed by the hydrolysis to PVA (figure 2). Once the hydrolysis
reaction is not complete, there are PVA with different degrees of hydrolysis (figure 1b). For
practical purposes, PVA is always a co-polymer of vinyl alcohol and vinyl acetate [1].
H2C
CH
OH
a.
Figure 1. Continued.
n+m
104
Silvia Patachia, Artur J. M. Valente, Adina Papancea et al.
H2C
CH
OH
CH2
CH
O
n
C
O
CH3
m
b.
Figure 1. Molecular strucuture of PVA fully hydrolyzed (a) and partially hydrolyzed (b).
n H2C
initiator
CH
*
CH2
CH
*
O
OCOCH3
Vinyl acetate
COCH3
n
Poly(vinyl acetate)
a.
*
CH2
CH
*
+ n CH3OH
O
COCH3
n
NaOH
*
CH2
CH
*
OH
n
Poly(vinyl alcohol)
Methanol
+
Poly(vinyl acetate)
n CH3OCOCH3
Methyl acetate
b.
Figure 2. Polymerization of vinyl acetate (a) and hydrolysis of PVAc to PVA (b).
PVA must be cross-linked in order to be useful for a wide variety of applications. A
hydrogel can be described as a hydrophilic, cross-linked polymer, which can sorbe a great
amount of water by swelling, without being soluble in water. Other specific features of
hydrogels are their soft elastic properties, and their good mechanical stability, independent of
the shape (rods, membranes, microspheres, etc.).
PVA can be prepared by chemical or physical cross-linking; general methods for
chemical cross-linking are the use of chemical cross-linkers or the use of electron beams or γ-
Poly(Vinyl Alcohol)[PVA]-Based Polymer Membranes…
105
radiation, whilst the most common method to produce physical cross-linking PVA is the socalled “freezing-thawing” process.
PVA can be cross-linked [2] using cross-linking agents such as glutaraldehyde,
acetaldehyde, etc. When these cross-linking processes are used in the presence of sulfuric
acid, acetic acid, or methanol, acetal bridges form between the pendant hydroxyl groups of
the PVA chains. As with any cross-linking compound, however, residual amounts are present
in the PVA gel matrix; furthermore, other compounds such as initiators and stabilisers will
reamin after synthesis. To use these gels for pharmaceutical or biomedical applications, we
will have to extract all residues from the gel matrix. This is an extremely undesirable timeconsuming extraction process; also, if the process is not 100 % efficient and the residue is not
completely removed, the gel will not be acceptable for biomedical or pharmaceutical
applications.
Other methods of chemical cross-linking include the use of electron beam or γirradiation. These methods have advantages over the use of chemical cross-linking agents as
they do not leave behind toxic, elutable compounds. The minimum gelation dose of γ-rays
(from 60Co sources) depends on the degree of polymerisation and the concentration of
polymer in solution [3]. The effect of irradiation dose on the physical properties of PVA
fibers, hydrogels and films irradiated in water is reported in [4-6].
The third mechanism of hydrogel preparation involves “physical” crosslinking due to
crystallite formation [7]. This method addresses toxicity issues because it does not require the
presence of a cross-linking agent (figure 3). Such physically cross-linked gels also exhibit
higher mechanical strength than PVA gels crosslinked by chemical or irradiative techniques
because the mechanical load can be distributed along the crystallites of the three-dimensional
structure [1]. Some characteristics of these “physically” crosslinked PVA gels include a high
degree of swelling in water, a rubbery and elastic nature, and high mechanical strength. In
addition, the properties of the gel may depend on the molecular weight of the polymer, the
concentration of the aqueous PVA solution, the temperature and time of freezing and
thawing, and the number of freezing/thawing cycles [8-10].
Figure 3. Schematic representation of PVA gels formed by freezing/thawing process.
106
PVA hydrogels have been used for numerous biomedical and pharmaceutical
applications. PVA hydrogels are non-toxic, non-carcinogenic, show bioadhesive
characteristics, and they are easily processed. The safety of PVA is based on the fact that the
acute oral toxicity of PVA is very low, with LD50s (the amount of a material, given all at
once, which causes the death – lethal dose - of 50 % of a group of test animals) in the range of
15-20 g/kg; when orally administered PVA is very poorly absorbed from the gastrointestinal
tract; PVA does not accumulate in the body when administered orally; PVA is not mutagenic
or clastogenic; and the no-observed adverse-effect level (NOAEL) of orally administered
PVA in male and female rats were 5000 mg/kg body weight/day in the 90-day dietary study
and 5000 mg/kg body weight/day in the two-generation reproduction study, which was the
highest dose tested [11].
Furthermore, PVA gels exhibit a high degree of swelling in water and a rubbery and
elastic nature. For all these features PVA is an excellent biomaterial. In fact, PVA is capable
of simulating natural tissue and can be readily accepted into the body. PVA gels have been
used for contact lenses, the lining for artificial organs, and drug-delivery applications.
Recently, intelligent hydrogels have been used to produce micro- and nano-fabricated devices
that seek to develop a platform of well controlled functions in the micro- and nano-level. For
example, polymer surfaces in contact with biological fluids, cells, or cellular components can
be tailored to provide specific recognition properties or to resist binding depending on the
intended applications. Another recent application of PVA is related with the development of
biomimetic methods to build biohybrid systems or even biomimetic materials for drug
delivery, drug targeting, and tissue engineering devices. Besides all these applications, PVA
is an important gel in different enginnering and industrial fields. For example, in the U.S.A.,
the majority of PVA is used in the textile industry as a sizing and finishing agent. PVA can
also be incorporated into a water-soluble fabric in the manufacture of degradable protective
apparel, laundry bags for hospitals rags, sponges, sheets, covers, as well as physiological
hygiene products. PVA is also widely used in the manufacture of paper products. As with
textiles, PVA is applied as a sizing and coating agent. It provides stiffness to these products
making it useful in tube winding, carton sealing and board lamination. PVA is used as a
thickening agent for latex paint and common house hold white glue or in other adhesive
mixtures such as remoistenable labels and seals, as well as gypsum-based cements such that
used for ceramic tiles. PVA is relatively insoluble in organic solvents and its solubility in
aqueous solutions is adaptable to its necessary application [11].
The US Food and Drug Administration (FDA) allows PVA for use as an indirect food
additive in products which are in contact with food [11]. For example, under 21 CFR 73.1,
PVA is approved as a diluent in color additive mixtures for coloring shell eggs and under 21
CFR 349.12, PVA is approved as an ophthalmic demulcent at 0.1–4.0 %.
Other applications of PVA are in areas of water and wastewater treatment (extraction,
ultra-filtration, ion-exchange materials, etc.), catalysis, separation, etc.
As an industrial and commercial product, PVA is valued for its solubility and
biodegradability, which contributes to its very low environmental impact. Several
microorganisms ubiquitous in artificial and natural environments — such as septic systems,
landfills, compost and soil — have been identified and they are able to degrade PVA through
enzymatic processes.
Membranes have gained an important place in chemical technology and are used in a
broad range of applications. The key property that is exploited is the ability of a membrane to
107
control the permeation rate of a chemical species through the membrane. In controlled drug
delivery, the goal is to moderate the permeation rate of a drug from a reservoir to the body. In
separation applications, the goal is to allow one component of a mixture to permeate the
membrane freely, while hindering permeation of other components.
The objective of this chapter is to give an overview of the developments in synthesis and
applications of PVA-based membranes in the last years.
2. SEPARATIONS BY MEMBRANAR PROCESSES
2.1. Pervaporation Processes
Pervaporation, in its simplest form, is an energy efficient combination of membrane
permeation and evaporation. Pervaporation involves the separation of two or more
components across a membrane by differing rates of diffusion through a thin polymer and an
evaporative phase change comparable to a simple flash step. A concentrate and vapour
pressure gradient is used to allow one component to preferentially permeate across the
membrane. A vacuum applied to the permeate side is coupled with the immediate
condensation of the permeated vapors. Pervaporation is typically suited to separating a minor
component of a liquid mixture, thus high selectivity through the membrane is essential.
Despite concentrated efforts to innovate polymer type and tailor polymer structure to
improve separation properties, current polymeric membrane materials commonly suffer from
the inherent drawback of tradeoff effect between permeability and selectivity, which means
that membranes more permeable are generally less selective and vice versa.
Pervaporation (PV) is considered to be a promising alternative to conventional energy
intensive technologies like extractive or azeotropic distillation in liquid mixtures’ separation
for being economical, safe and ecofriendly. PV can be considered the so-called ‘clean
technology’, especially well-suited for the treatment of volatile organic compounds. The
separation of compounds using pervaporation methods can be classified into three major
fields viz. (i) dehydration of aqueous–organic mixtures [12], (ii) removal of trace volatile
organic compounds from aqueous solution [13] and (iii) separation of organic–organic
solvent mixtures [14]. The hydrophilic membranes were the first ones to have found an
industrial application for organic solvent dehydration by PV [15]. Very recently, B. Smita et
al. [16] reported that some restrictions for a variety of membranes for their application are
still encountered, suggesting potential routes to overcome these drawbacks as, for example,
the development of appropriate membrane material (flux and selectivity of a membrane are
deciding factors in pervaporation mass transport; therefore, development of a new polymer
material is a key research area in membrane technology. The aim in the development of new
pervaporation membranes is either to increase the flux, keeping the selectivity constant or
aiming for higher selectivities at constant flux, or both. In order to achieve such goals, the use
of PVA as component of copolymers, blends, or composites membranes for pervaporation has
been used.
108
2.1.1. Pervaporation of Phenol/Water
Using pervaporation through PVA membranes, J. W. Rhim et al. [17] have studied the
separation of water-phenol mixtures.
The pervaporation separation of water-phenol mixtures was carried out using poly(vinyl
alcohol) (PVA) cross-linked membranes with low molecular weight poly(acrylic acid) (PAA),
at 30, 40, and 50 °C. They have used pervaporation because the separation rate is higher (for
liquid organic mixtures) in pervaporation than in reverse osmosis.
A separation factor of the mixture, α, is calculated using
α = ( Ywater / Yphenol ) / (Xwater / Xphenol )
where X is the weight fraction of permeate and Y, the weight fraction of feed.
A very high separation factor has been obtained in phenol dehydration by using
pervaporation process and PVA/PAA as membranes. The membrane composition and the
process characteristics are presented in table 1.
Table 1. Characteristics of the separation process by pervaporation
function of the membrane composition and structure, composition of feed
mixture and temperature [18]
Membrane
composition PVA/PAA
80/20
Composition of liquid
mixture
phenol/water
80/20
Permeation rate /
/ (g m-2 h-1)
T / ºC
Separation
factor
50
30
3580*
* Ref. 17.
Conclusion: the separation factor increases by increasing the cross-linker, and decreases
by increasing the temperature.
2.1.2. Isopropanol/Water Separation
The selective separation of water from aqueous solutions of isopropanol or the
dehydration of isopropanol can be carried out with different membranes, which contain polar
groups, either in the backbone or as pendent moieties. For the dehydration of such a mixture,
poly(vinyl alcohol) (PVA) and PVA-based membranes have been used extensively. PVA is
the primary material from which the commercial membranes are fabricated and has been
studied intensively for pervaporation because of its excellent film forming, high
hydrophilicity due to –OH groups as pendant moieties, and chemical-resistant properties. On
the contrary, PVA has poor stability at higher water concentrations, and hence selectivity
decreases remarkably.
The use of conjugated polymer as membranes to separate various liquid mixtures has
been reported in the literature [19,20]. From those, polyaniline (PANi) is one of the most
interesting and studied conjugated polymers. Polyaniline is usually prepared by direct
oxidative polymerization of aniline in the presence of a chemical oxidant, or by
electrochemical polymerization on different electrode materials [21,22]. The possible
interconversions between different oxidation states and protonated and depronated states [23],
figure 4, make this material remarkable for different purposes. Under most conditions, PANi
109
acts as a passive material, but electrolysis or exposure to acidic aqueous solutions gives rise to
conductive materials. In fact, the susceptibility of PANi protonation-deprotonation is an
important property once it makes possible to control the electrical conductivity of polyaniline,
being possible to obtain changes of more than two orders of magnitude in the electrical
conductivity [24]. Both synthesis and characterization of PANi have been reviewed by
different authors [21-23]. These reviews deal with chemical, electrochemical and gas-phase
preparations, polymerization mechanisms, physicochemical and electrochemical properties,
redox mechanisms, theoretical studies, and applications of the polymer.
Interest in polyaniline (PANi), as a material for membrane separations, stems for its high
selectivity toward liquids since most liquids are in the size regime of 0.2–1 nm. Another
advantage is that PANi has the ability to be tailored after its synthesis through
doping/undoping processes. Since there is a tremendous driving force for adding protonic
dopants to the imine nitrogens in the PANi backbone [20], the polymer chains are readily
pushed apart by the incoming dopants. Thus, doping would induce morphological changes in
the polymer resulting in varying permselectivities. Besides such morphological changes, the
undoped and doped forms of PANi exhibit different characteristics. For instance, the undoped
form of PANI is hydrophobic, while the doped form is hydrophilic [25,26]. Hence, doped
PANi preferentially permeates water over the organics, such as isopropanol. The abovementioned advantages are considered to search for novel membranes containing PANi
nanoparticles dispersed in the PVA matrix. The synthesis of a novel hybrid nanocomposite
membrane by in situ polymerization of aniline in the PVA matrix in acidic media is described
in the Ref. 27. Aniline monomer was introduced into the PVA matrix and by carrying in situ
polymerization outside the mesopores of the polymer matrix, a nanocomposite structure was
formed. The organic phase extends along the channels to the openings in the nanocomposite
structure due to strong interactions between the nanoparticle formed and the continuously
polymerized PANi nanoparticles. This hybrid polymer shows lower swelling degree and
higher water selectivity (about five-folds) compared to the plain poly(vinyl alcohol).
M. Sairam et al. [28], taking on the basis of the cited PANi nanoparticles dispersed in the
PVA matrix, suggests the incorporation of TiO2 filler-coated with polyaniline (emeraldine
state) salt nanoparticles in PVA. PVA contains a large number of hydroxyl groups which can
effectively inhibit the aggregation of TiO2 nanoparticles by the organic surface modification
and help to keep the TiO2 particles well dispersed in the aqueous PVA solution at the nanoscale for dehydration of iso-propanol. In order to control the dispersion of TiO2 fillers and to
adjust the permselectivity, the PV membranes formed have been crosslinked chemically with
glutaraldehyde. With this modification of TiO2 nanoparticles, it is expected that strong
interfacial bond, viz., Ti–O–C be formed on the surface of TiO2 nanoparticle, anchors PVA
molecules to the surface of TiO2 nanoparticles such that surfaces of TiO2 nanoparticles will
be wrapped with the layer of PVA polymer. It is known [29] that there are number of Ti–OH
groups that will cover the surface regions of TiO2 nanoparticles. When PVA chain segments
are adsorbed onto the surface of TiO2 nanoparticle, Ti–OH groups on the surface of TiO2
nanoparticles will react with the hydroxyl groups linking to the PVA chains. Dehydration and
condensation reactions can occur between both the hydroxyl groups.
N
N
N
N
(PNA)
4H+ + 2eHN
HN
X-
XNH
NH
acid
(H+X-)
(EM)
oxidation
base
(NaOH)
reduction
HN
HN
HN
N
(LM)
NH
NH
reduction
NH
N
N
solvent
(NMP)
1st acid-base cycle
N
as-cast EM film
NH
(NA)
N
Figure 4. Interconversions among the various intrinsic oxidation states and protonated/deprotonated states in polyaniline.
111
Another approach to enhance separation performance of membrane for dehydration of
isopropanol is the modification of PVA membranes in gaseous plasma [30]. The modification
of membrane properties in nitrogen plasma environment lead to increase in selectivity by
about 1477 at 25 °C; such increase in the selectivity is justified by an increase of crosslinking on membrane surface provoked by plasma treatment.
The same authors reported the possibilities of using a membrane made by PVA modified
by LiCl, whose surface has been modified by exposure to low-pressure nitrogen plasma [31].
The best results have been obtained for 0.05 wt% of LiCl in PVA membrane at 25 ºC
(selectivity 14 and flux 250 g m-2h-1).
Hybrid membranes composed of poly(vinyl alcohol) (PVA) and tetraethylorthosilicate
(TEOS), synthetised via hydrolysis and a co-condensation reaction for the pervaporation
separation of water-isopropanol mixtures has also been reported [32]. These hybrid
membranes show a significant improvement in the membrane performance for water–
isopropanol mixture separation. The separation factor increased drastically upon increasing
the crosslinking (TEOS) density due to a reduction of free volume and increased chain
stiffness. However, the separation factor decreased drastically when PVA was crosslinked
with the highest amount of TEOS (mass ratio of TEOS to PVA is 2:1). The highest separation
selectivity is found to be 900 for PVA:TEOS (1.5:1 w/w) at 30°C. For all membranes, the
selectivity decreased drastically up to 20 mass % of water in the feed and then remained
almost constant beyond 20 mass %, signifying that the separation selectivity is much
influenced at lower composition of water in the feed.
Recently, a new effective membrane for different organic solvents dehydration by
pervaporation has been reported. Novel hydrophylic polymer membranes based on
crosslinked poly(allylamine hydrochloride) (PAA.HCl)-PVA have been developed [33]. The
crosslinking agent was GA. The role of the PVA into the membrane is to increase its
flexibility and the stability. But the increasing of the PVA ratio, determines the decreasing of
the water selective amine hydrochloride functional groups amount and as consequence, the
rate of water intake by the membrane decreases. So, for different specific applications the
optimization of the PAA.HCl/PVA ratio in the formulation is essential. Also, the amount of
GA and curing temperature has to be optimized to obtain the desired membrane properties.
The characteristics of the iso-propanol (IPA) dehydration process, by using the pervaporation
technique, are presented in the table 2.
Table 2. The characteristics of the iso-propanol (IPA) dehydration process,
by using pervaporation technique, through (PAA.HCl)-PVA membrane
Composition of the
membrane
PAA.HCl/PVA/GA
60/35/5
* Ref. 33.
mixture
IPA-water
(wt%)
85/15
Water flux /
/ (kgm-2h-1)
T / ºC
Separation
factor
3.14
70
2930
112
Silvia Patachia, Artur J.M. Valente, Adina Papancea et al.
2.1.3. Pervaporation Ethanol/Water
Alcohol is a clean energy source that can be produced by the fermentation of biomass.
However, it needs to be highly concentrated. In general, aqueous alcohol solutions are
concentrated by distillation, but an azeotrope (96.5 wt% ethanol) prevents further separated
by distillation. Pervaporation, a membrane separation technique, can be used for separation of
these azeotropes: pervaporation is a promising membrane technique for the separation of
organic liquid mixtures such as azeotropic mixtures [34] or close-boiling point mixtures.
The synthesis of novel organic-inorganic hybrid membranes via hybridization between
organic and inorganic materials using the sol-gel reaction is reported elsewhere [35]. It is
well-known that poly(vinyl alcohol) (PVA) membranes are highly water permselective for
aqueous ethanol solutions during PV. However, the swelling of the PVA membrane in an
aqueous ethanol solution results in both an increase in solubility and diffusivity of ethanol,
and consequently lowers the water permselectivity [36]. The control of membrane swelling
has been attempted by cross-linking, surface modification, and annealing methods. However,
it is difficult to effectively control the swelling of the membrane. An attempt to improve and
to control the swelling is done by using mixtures of PVA and tetraethoxysilane (TEOS), as an
inorganic component, in order to obtain PVA/TEOS hybrid membranes prepared by sol-gel
reaction. The addition of TEOS into the PVA membrane decreases the swelling of the
membrane and improves the water permselectivity of the PVA/TEOS hybrid membrane. T.
Uragami et al. also studied the effect of the annealing process to PVA/TEOS hybrid
membranes. They found that the separation factor H2O/EtOH increases from 329 to 893 (with
the same permeation rate) when PVA/TEOS (TEOS content 25 %) membranes are submitted
from an annealing process at 160 ºC during 8 hours to 130 ºC during 24 hours.
In a previous section, the effect of plasma on PVA surface for pervaporation processes
was also mentioned. In fact, plasma treatment is a surface-modification method to control the
hydrophilicity–hydrophobicity balance of polymer materials in order to optimize their
properties in various domains, such as adhesion, biocompatibility and membrane-separation
techniques. Non-porous PVA membranes were prepared by the cast-evaporating method and
covered with an allyl alcohol or acrylic acid plasma-polymerized layer; the effect of plasma
treatment on the increase of PVA membrane surface hydrophobicity was checked [37].The
allyl alcohol plasma layer was weakly crosslinked, in contrast to the acrylic acid layer. The
best results for the dehydration of ethanol were obtained using allyl alcohol treatment. The
selectivity of treated membrane (H2O wt% in the pervaporate in the range 83–92 and a water
selectivity, αH2O , of 250 at 25 ºC) is higher than that of the non-treated one (αH2O = 19) as
well as that of the acrylic acid treated membrane (αH2O = 22).
PVA dense membranes treated by acrylic acid (Acr.Ac) plasma were obtained by A.
Essamri et al. [38]. These membranes were used for dehydration of the EtOH-H2O mixtures
by pervaporation. The behaviour of these films on ethanol-water pervaporation has increased
performances after plasma treatment.
This means an increase of the flux (J) and water selectivity (β) for the modified
membrane – due to the surface properties modification by plasma treatment – comparing to
the untreated membrane.
Conclusion: using plasma treatment, a good ratio between flux and selectivity could be
obtained.
Also, different other techniques for obtaining PVA/PAcr.Ac blends were reported [3956]:
Poly (Vinyl Alcohol)[PVA]-Based Polymer Membranes…
113
1. mixing of PVA and PAcr.Ac. aqueous solutions, solvent evaporation and thermal
treatment of the resulted film;
2. mixing of PVA and PAcr.Ac. aqueous solutions with curing agents solutions, solvent
casting and thermal treatment of the resulted film;
3. repetitive cycles of freezing and thawing of the aqueous solutions of polymer
mixture, in the presence or the absence of the curing initiators;
4. UV irradiation either of the aqueous solutions of polymers mixtures in the presence
of photoinitiators and curing agents, or of the PVA hydrogels swelled with acrylic
acid;
5. acrylic acid polymerization in the matrix of PVA, in the presence of curing agents
and initiators;
6. sedimentation polymerization of acrylic acid in the presence of PVA solution,
crosslinking agent and initiator;
7. swelling of PAcr.Ac dried hydrogels with an aqueous solution of PVA and
application of the freezing and thawing technique.
Changes in blends’ properties were obtained through different ways: by changing the
polymer mixing ratios; by using a small amount of acids that are catalysts for esterification
reactions; by changing the crosslinking degree of the polymers.
PVA and PAcr.Ac. are compatible polymers on the whole range of composition [40-45].
These blends are homogeneous and the films are transparent evidencing a good clarity
[43,57] or semitransparency [43]. However a heterogeneous IPN [45] was obtained by acrylic
acid polymerization in a PVA matrix.
The blends could exhibit different morphologies: continuous or microporous [46].
The blend crystalinity degree decreases with increasing the PAcr.Ac content up to 50
wt%, from 26 % to 2 %, and then remains constant [42].
The blends are water insoluble [47]. They can swell in different solvents: water, acetone,
aqueous solutions of acids and alkalis [47].
The swelling ratios increase with increasing the PAcr.Ac content in IPNs [45,48].
It was pointed out that the swelling degree evidenced a strongly decrease as the PAcr.Ac
content in membrane decreases to 20% [49].
The technique of obtaining blends influences their swelling ratios by inducing different
crosslinking degrees. For example, increasing the number of freezing-thawing cycles leads to
a swelling ratio significant decrease [50].
In general, the swelling ratios increase with the increasing the temperature up to 40 ºC
[45]. The dependence of swelling ratios on temperature shows a different function of the
blend composition.
So, interpenetrating polymer networks (IPNs) with a weight ratio of vinyl alcohol residue
in PVA to acrylic acid monomer 4:6 exhibit positive swelling changes with temperature but
IPNs 6:4 evidence negative swelling ones [48].
pH strongly influences the swelling behavior of the blends. For example, the difference
of the swelling ratio of IPN 4:6 between pH=4 and pH=7 is 2.0 [48].
Membranes of PVA/PAcr.Ac blends evidence a selective permeability against different
components of a liquid mixture. So, they may be used for the ethanol dehydration by
pervaporation technique.
Table 3 presents a summary of the published results.
114
These blends show good mechanical properties. The presence of PVA in the blend
improves the mechanical properties. Hydrogels have a significant mechanical strength and
elasticity [42]. The tensile strengths are larger than those of crosslinked PVA membranes and
show a maximum value at about 0.7 wt% glutaric dialdehyde (GA) [46].
Full-IPNs have higher compressional strength (2929 g load for 50 % compression) than
the corresponding semi-IPNs (1883 g load for 50 % compression) [42].
These membranes can swell in water and different aqueous solutions evidencing the
following aspects:
•
•
•
the presence of PAAm affects in a positive way the swelling;
the swelling in water increases with temperature (positive thermosensitivity);
-swelling in the water/ethanol mixture increases linearly with the water content.
Because of membrane preferential swelling in different aqueous solutions, it may be
recommended for use in separation processes by pervaporation.
The PVA/PAAm IPN membranes were found to have pervaporation separation factors
ranging from 45 to 4100 and permeation rates of about 0.06-0.1 kg m-2 h-1, for 95 % ethanol
aqueous solution, at 75 ºC [46]. For a concentration of 10 wt% ethanol, the permeation rates
were as large as 9 kg m-2 h-1 and the separation factors were about 20 [46].
Recently, a new effective membrane for dehydration of different organic solvents by
pervaporation has been reported. Novel hydrophylic polymer membranes based on
crosslinked poly(allylamine hydrochloride) (PAA.HCl)-PVA have been developed [33]. The
crosslinking agent was glutaraldehyde (GA). The role of PVA into the membrane is to
increase its flexibility and the stability. But the increasing of PVA percentage, determines the
decreasing of the water selective aminehydrochloride functional groups amount and as
consequence, the rate of water intake by the membrane decreases. So, for different specific
applications, the optimization of the PAA.HCl/PVA ratio in the formulation is essential. Also,
the amount of GA and curing temperature has to be optimized to obtain the desired membrane
properties. The characteristics of the ethanol dehydration process, by the pervaporation
technique, are presented in table 4.
Polymers, such as polysaccharides (cellulose and chitosan (CS)) show a stronger affinity
to water; hence their copolymers, blends or composites have been widely investigated for
pervaporative (PV) separation of EtOH/H2O mixtures [58-60]. Chitosan is generally preferred
due to its high abundance, natural occurrence, hydrophilicity, chemical resistance, adequate
mechanical strength, good membrane forming properties and ease of processing. PV
performance of EtOH/H2O mixtures through the surface crosslinked CS composite
membranes exhibit a high selectivity value but a low permeation flux [61]. The PV
membranes of derivatives of CS obtained by chemical modification have also been widely
studied [62,63].
115
function of the membrane composition and structure, composition of
feed mixture and temperature [18,43,46]
Composition
of the
membrane
PVA/PAcr.Ac
50/50
IPN
30/70
IPN
50/50
IPN
70/30
IPN
90/10
IPN
80/20
Composition
of liquid
mixture
ethanol-water
95.6/4.4
10/90
85/15
10/90
85/15
10/90
85/15
10/90
85/15
95.6/4.4
90/10
80/20
50/50
95/5
Permeation rate /
/ (g m-2 h-1)
T/
ºC
Separation
factor
260
50
5000
750
3800
360
2700
110
2000
90
9
30
27
60
65
125
120
550
50
50
12
0.8
15
0.85
15
1.0
18
3.0
39
14000
5800
9000
2800
1500
50
50
50
60
75
60
75
60
75
75
60
Permeate
activation
energy Ea /
(kJ mol-1)
-
30.5
30.9
38.9
-
260
150
Table 4. Dehydration of ethanol, using membranes PAA.HCl
(60 wt%)–PVA (35 wt%–GA (5 wt%) (aprox. 60μm thick) [33]
Feed concentration / (wt%)
T / ºC
Water flux / (kg m-2 h-1)
Selectivity
85
70
2.00
450
95
70
0.47
3953
B.-B. Li et al. [64] have studied the separation of EtOH-H2O solutions by pervaporation
(PV) using chitosan (CS), poly (vinyl alcohol)-poly(acrylonitrile) (PVA–PAN) and chitosanpoly(vinyl alcohol)/poly(acrylonitrile) (CS–PVA/PAN) composite membranes. It was found
that the separation factor of the CS–PVA/PAN composite membrane increased with an
increase of PVA concentration in the CS–PVA polymer from 0 to 40 wt%. With an increase
in the membrane thickness from 12 to 18 µm, the separation factor of the CS–PVA/PAN
composite membrane increased and the permeation flux decreased. With an increase of
ethanol–water solution temperature, the separation factor of the CS membrane decreased and
the permeation flux of the CS membrane increased while the separation factor and the
permeation flux of PVA/PAN and CS–PVA/PAN composite membranes increased.
116
Sodium alginate (SA), which is one of the polysaccharides extracted from seaweed, has
shown excellent water solubility [65], but the mechanical weakness of SA membranes has
been a drawback as a pervaporation membrane material. The use of SA–PVA blended
membranes prepared by physical mixing of components, in different ratios, for pervaporation
dehydration is reported elsewhere [66,67]. Taking on the basis of SA-PVA membranes,
Dong et al. [68] studied the PVA–SA hollow-fiber composite membranes for organic
dehydration by pervaporation. In particular, a polysulfone hollow-fiber membrane is coated
by a PVA-SA blended solution. The founded optimal process of preparing membranes is as
follows: 80 wt% PVA and 20 wt % SA are blended, and the casting solution of the PVA–SA
blend with a concentration of 2 wt % is obtained by dissolving the blend in water; then the
blend solution is cast onto the PS hollow-fiber membrane, and the composite membrane is
crosslinked with 1.5 wt% maleic acid and 0.05 wt% H2SO4 in ethanol solvent for 8 h. For
isoproanol, n-butanol, tert-butanol and ethanol aqueous solutions, as the alcohol concentration
is 90 wt% at 45 ºC, higher separation factors and permeation fluxes of crosslinked PVA–SA
blended membranes are obtained: 1727, 414 g m-2 h-1; 606, 585 g m-2 h-1; 725, 370 g m-2 h-1
and 384, 384 g m-2 h-1, respectively. This shows that these blended membranes have the
potential to be used in industry.
2.1.7. Acetic Acid/Water Separation by Pervaporation
Poly(vinyl alcohol) and polyacrylamide (PAAM) blends, obtained by the different
methods described above, can also be used for acetic acid dehydration, due to its capacity to
swell in mixtures of acetic acid/water.
Swelling in water/acetic acid mixture shows a maximum of swelling shifting to higher
temperatures when higher acetic acid concentrations increase (from 20 ºC for 50 % acetic
acid to 40 ºC for 70 %).
Water is preferentially sorbed by membranes, but much less from water-acetic acid
mixtures than from ethanol/water mixtures [46].
Table 5 presents the characteristics of the pervaporation process.
according to membrane composition and structure, composition of feed
mixture and temperature [18,52]
Compositi-on of
the membrane
PVA/PAcr.Ac
mixture
Permeation rate /
/ (g m-2 h-1)
T / ºC
Separation
factor
75/25
Acetic acidwater
5.6
30
795
90/10
A recent paper [69] presents a new type of PVA hybrid membrane prepared by hydrolysis
followed by condensation of a PVA and a tetraethylorthosilicate (TEOS) mixture, which
shows a significant performace in water-acetic acid mixture separation. The highest
separation selectivity (1116) with a flux of 3.33×10-2 kg m-2 h-1 at 30 ºC for 10% mass of
water in the feed has ben obtained by using the membrane containing 1:2 mass ratio of PVA
and TEOS. The performance of these membranes was explained on the basis of a reduction of
free volume and a decrease of the hydrophylic character owning to the formation of
117
covalently bonded crosslinks. Significant lower apparent activation energy values have been
obtained for water permeation comparatively to these of acetic acid permeation. The close
values obtained for activation energy for total permeation and water permeation signify that
the coupled transport is minimal due to the selective nature of membranes. The equal
magnitude of activation energy for water permeation and activation energy for water diffusion
indicates that both diffusion and permeation contribute almost equally to the PV process. The
Langmuir mode of sorption dominates the process for all types of studied membranes.
Another recent work presents the possibility to use a membrane made by PVA-gacrylonitrile (AN) to separate acetic acid/water mixtures by pervaporation [70]. The best
separation factor (14.6) has been obtained by using PVA-g-AN (52 %) membrane, at 30ºC,
90 % acetic acid in the feed. The permeation rate was 0.09 kg m-2 h-1.
2.1.5. Separation Caprolactam (CPL)/Water Mixtures by Pervaporation
Caprolactam (CPL) is the monomer of Nylon-6, extensively used in high quality Nylon-6
fibers and resin obtaining. Worldwild capacities reached above 4.5 million metric tones in
2005. A CPL dehydration study has been performed by pervaporation, using PVA crosslinked
membranes (with GA as crosslinker agent and heat treatment of the membrane) [71]. In spite
of the excellent dehydration performance for CPL/water mixtures exhibited by PVA
crosslinked membranes (total permeation flux by 800 g m-2 h-1 and separation factor by 575,
for PVA membrane crosslinked with 0.5 wt% GA, at 323 K and 50 wt% CPL in the feed), the
authors recommended the use of a composite membrane with an active layer made by PVA,
due to the poor durability and mechanical strength of the studied membrane.
2.1.6. Separation of Fluoroethanol/Water Mixtures by Pervaporation
2,2,2,-trifluoroalcohol (TFEA) is used for obtaining 2,2,2-trifluoroethyl methacrylate
(TFEMA), necessary for preparation of functional water repellent paints and optical fiber
coating agents. TFEMA can be manufactured by esterification of TFEA and methacrylic acid
(MA) in the presence of an acid catalyst, at 70 ºC. To obtain a higher conversion rate it is
necessary to remove the water from the system, avoiding the formation of the thermodynamic
equillibrium composition.
To attain this goal, a pervaporation technique has been proposed, using a PVA composite
membrane, made by casting of a mixture of PVA aqueous solution and a GA one on a
polyethersulfone (PES) porous support, solvent evaporation and thermic curing [72].
Excellent dehydration performance has been obtained (separation factor 320 and permeation
flux 1.5 kg m-2 h-1, for 90 wt% TFEA in the feed and 80 ºC).
2.1.7. Separation of Methacrylic Acid/Water Mixtures by Pervaporation
A PVA composite membrane, made by casting of a mixture of PVA aqueous solution and
a GA one on a polyethersulfone (PES) porous support, solvent evaporation and thermic
curing, has been used to attain this aim [72]. Excellent dehydration performance has been
obtained (separation factor 740 and permeation flux 2.3 kg m-2 h-1, for 90 wt% TFEA in the
feed, and 80 ºC).
2.1.8. Water Desalination
PVA/Poly(ethylene glycol) (PEG) membranes crosslinked by aldehydes and sodium salts
were used in water desalination by pervaporation. The desalination of 8 % NaCl solution by
118
pervaporation at 55 ºC and 5.00 kPa (downstream pressure) resulted in a single stage salt
rejection of 99% and the water flux of 14 kg h-1 [73].
2.1.9. Dehydration of Methanol by Pervaporation
Another important application of membrane-based pervaporation is a well-established
and commercially exploited method for the dehydration of organic solvents; in particular the
dehydration of alcohols is done with the help of high permselective (hydrophilic) poly(vinyl
alcohol)/polyacrylonitrile (PVA/PAN) thin film composite membranes, under the trade name
of “GFT- Gesellshaft Fur Trenntechnik” membranes. One of the key successes of PV is that,
if suitable membranes can be produced with a high permeability and a good selectivity to
water, it is possible to achieve an excellent separation, particularly at the azeotropic
composition. However, more number of novel polymeric membranes are needed for a
successful operation of the process in view of the fact that PV is environmentally cleaner than
the conventional distillation; moreover, this process is energy intensive. Consequently the
success of any membrane depends on a high flux, a good separation factor (selectivity) and a
long-term stability as well as a favourable mechanical strength to withstand the cyclic modes
of PV operating conditions, as described before.
Also, membranes from blends of PVA/Poly(acrylic acid) [PAcr.Ac.] show a selective
permeability against different components of a liquid mixture. This property of membranes
makes them useful for the separation of components from liquid mixtures by the
pervaporation method, i.e., for methanol dehydration.
Recently, a novel hydrophylic polymer membrane based on poly(allylamine
hydrochloride) (PAA.HCl)/PVA, crosslinked with GA, has been also tested for methanol
dehydration by pervaporation technique [33]. Even if the reported results show a small
selectivity of the last type of membrane, the blend’s composition, the curing degree and the
process conditions (temperature, feed concentration, etc.) could be used to obtain a better
separation of methanol.
Table 6 presents a summary of the published results.
mixture and temperature [18]
Composition of
the membrane
mixture
PVA/PAcr.Ac:
80/20
Methanolwater
PAA.HCl/PVA/
GA
60/35/5
Methanolwater
(%wt.)
70/30
90/10
95/5
86.5/1
3.5
Permeation
rate /
/ (g m-2 h-1)
70
340
109
33
1800
T / ºC
Separation
factor
Ref.
50
70
70
70
60
55
28
465
2650
23
42
33
2.1.10. Dehydration of Acetone by Pervaporation
Novel hydrophilic polymer membranes based on crosslinked poly(allylamine
hydrochloride) (PAA.HCl)-PVA have been developed in order to dehydrate different organic
compounds by pervaporation [33]. The characteristics of the acetone dehydration process,
119
using a pervaporation technique, are presented in the table 7. The high selectivity of the
membrane should be noted. The selectivity and flux characteristics of these membranes are
excellent compared with most of the known membranes.
Table 7. Dehydration of acetone, using membranes PAA.HCl
(60%wt.)-PVA (35%wt.-GA(5%wt.) (aprox. 60μm thick) [33]
Feed concentration / (% wt.)
86
T / ºC
50
Water flux / (kg m-2 h-1)
1.80
Selectivity
2270
2.1.11. Pervaporation of Ethanol/Toluene
PVA-PAcr.Ac. membranes have been tested also for ethanol separation from
ethanol/toluene mixture, by using pervaporation technique. The reported data concerning the
separation process characteristics are presented in table 8.
mixture and temperature [18, 40]
Composition of
the membrane
PVA/PAcr.Ac
10/90
Composition of liquid mixture
Ethanol/toluene
Permeation rate /
/ (g m-2 h-1)
T / ºC
Separation
factor
25-480
30
300-80
10-90% ethanol
2.1.12. Pervaporation of Ethanol/Benzene
PVA-PAcr.Ac.blends membranes are suitable also for separation of components in
ethanol/benzene mixtures. Reported data are presented in table 9.
2.1.13. Pervaporation of Methanol/Toluene
Methanol/toluene mixtures could be separated by pervaporation technique using
PVA/PAcr.Ac. blend membranes. Reported data are presented in table 10.
Composition of the
membrane
PVA/PAcr.Ac
Composition of
liquid mixture
ethanol/benzene
Permeation rate/
/ (g m-2 h-1)
T / ºC
Separation
factor
Permeate activation
energy Ea / (kJ mol-1)
20/80
10/90
30
50
110
19.2
SIPN
90/10
560
30/70
10/90
12
SIPN
90/10
460
30/70
10/90
6
SIPN
90/10
360
3.5
50
650
27.6
1.9
50
1100
53
31.4
120
Composition of
the membrane
PVA/PAcr.Ac
10/90
Composition of
liquid mixture
methanol/toluene
10/90
30/70
Permeation rate/
/ (g m-2 h-1)
T / ºC
Separation
factor
120
265
30
30
460
50
2.1.14. Separation Methyltertbutyl Ether (MTBE)/Methanol
Mixtures by Pervaporation
MTBE is a well known enhancer of the number of octanes in gasoline and as excellent
oxygentated fuel additives that decrease carbon monoxide emissions. Therefore, MTBE has
been one of the fastest growing chemicals of the past decade. MTBE is produced by reacting
methanol with isobutylene from mixed-C4 stream liquid phase over a strong acid ionexchange resin as catalyst. An excess of methanol is used in order to improve the reaction
conversion. This excess has to be separated from the final product. The pervaporation
technique, more energy efficient and with lower cost process, has been proposed as
alternative to distillation [74].
A membrane prepared by PVA blending with PAcr.Ac. in aqueous solution, casting,
solvent evaporation and then crosslinking by heat treatment (at 150 ºC), has been used.
The obtained results show that the prepared membranes are methanol selective, but the
performance of these membranes (separation factor=30, for PVA/Pacr.Ac.=80/20, 5 wt%
methanol in the feed, 25 ºC) is lower than those reported by J.W. Rhim and Y.K. Kim [75]
(separation factor 1250 for PVA/Pacr.Ac.=75/25, 20 wt% methanol in the feed, 30 ºC).
The authors suggested that a combination of pervaporation with a conventional
separation technique such as a hybrid distillation-pervaporation system could be useful
economically to break the azeotropy.
2.1.15. Pervaporation of Benzene/Cyclohexane
The separation of benzene/cyclohexane mixtures is one of the most important and most
difficult processes. Cyclohexane is produced by catalytic hydrogenation of benzene. The
unreacted benzene in the effluent stream must be removed for pure cyclohexane recovery.
Separation of benzene and cyclohexane is difficult because they have close boiling points
(difference only 0.6 K) and close molecular sizes [76]. It is generally thought that separating
benzene/cyclohexane mixtures is mainly governed by solubility selectivity due to the
interaction between benzene molecule and membrane. Hence, increasing benzene solubility in
the membrane is essential to obtain high permselectivity toward benzene. Poly(vinyl alcohol)
(PVA) is polar and hydrophilic, and is an ideal membrane material to separate
benzene/cyclohexane mixtures [77]. The selection of PVA is also due to its economical cost,
commercial availability and good membrane-forming properties. F. Peng et al. report [78] the
synthesis of poly(vinyl alcohol) membranes incorporating crystalline flake graphite (CG-PVA
membranes). These blends take advantage of structure of graphite being similar to that of
benzene favouring, in this way, the adsorption and packing of benzene on graphite surface
and, consequently, increase the selectivity. A CG-PVA membrane exhibits a higher
121
separation factor of 100.1 with a flux of 90.7 g m-2 h-1 at 323 K for benzene/cyclohexane
(50/50, w/w) mixtures, showing that the incorporation of graphite into the PVA matrix
interfered the polymer chain packing and enhanced effectively fractional free volume, and
thus favourable for components diffusing through the membrane. Another interesting
approach reported by the some authors [79] is to perform pervaporation of
benzene/cyclohexane by using β-cyclodextrin (β-CD)-filled cross-linked poly(vinyl alcohol)
(PVA) membranes (β-CD/PVA/GA). In the present case, the very important properties of the
β-CD are used to increase the perselectivity toward benzene. The permeation flux of βCD/PVA/GA membranes increased when the β-CD content was 0–8 wt%, but permeation
flux decreased slightly when the β-CD content was 8–20 wt%. The separation factor towards
benzene increased when β-CD content was in the range 0–10 wt% and decreased slightly
when the β-CD content was 10–20 wt%. Compared with the β-CDfree PVA/GA membrane,
the separation factor of the β-CD/PVA/GA membrane for benzene to cyclohexane
considerably increased from 16.7 to 27.0, and the permeation flux of benzene increased from
23.1 to 30.9 g m-2 h-1 for benzene/cyclohexane (50/50, wt) mixtures at 323 K.
To solve the tradeoff between permeability and selectivity of polymeric membranes,
organic-inorganic hybrid membranes composed of poly(vinyl alcohol) (PVA) and -glycidyl
oxypropyl trimethoxysilane (GPTMS) were prepared by an in situ sol-gel approach for
pervaporative separation of benzene/ cyclohexane mixtures [80]. The permeation flux of
benzene increased from 20.3 g m-2 h-1 for pure PVA membrane to 137.1 g m-2 h-1 for PVAGPTMS membrane with 28 wt % GPTMS content, while the separation factor increased from
9.6 to 46.9, simultaneously. The enhanced and unusual pervaporation properties were
attributed to the increase in the size and number of both network pores and aggregate pores,
and the elongation of the length of the diffusion path in PVA-GPTMS hybrid membranes.
Another hybrid membrane was prepared by filling carbon graphite (CG) into poly (vinyl
alcohol) (PVA) and chitosan (CS) blending mixture [81]. This blend membrane shows
homogenous distribution of graphite particles, considerable alteration of hydrogen bonding
interaction, remarkable decrease of crystallinity degree, dramatic enhancement of mechanical
properties and significant increase of free volume in CG-PVA/CS, which may contribute for
improving the separation performance of the membranes by the synergistic effect of blending
and filling. Comparing the performance of this blend with that used for PVA and
PVA/chitosan membranes, for C6H6/C6H12 separation, that new hybrid membrane exhibits a
highest separation factor of 59.8 with a permeation flux of 124.2 g m-2 h-1 at 323 K, 1 kPa.
2.1.17. Separation Cyclohexene/Cyclohexan Mixtures by Pervaporation
Solid PVA-Co2+ composite asymetric membranes have been prepared starting from PVA
and two different salts: Co(NO3)2 and Co(CH3COO)2, respectively, in order to separate
cyclohexene/cyclohexan mixtures. A facititated transport mechanism has been evidenced, due
to the capacity of Co2+ ions to coordinate the olefin molecules [82]. The authors reported
stronger complexation of Co2+ ions with cyclohexene in the case of PVA/ Co(CH3COO)2
mixtures then in the case of PVA/ Co(NO3)2 mixtures. It was found that for a concentration
ratio of ([Co2+]/[OH]) by 0.75 mol/mol, the permeation flux of PVA membrane containing
Co2+ increases 2-3 times and the separation factor increses 50 times compared with pure PVA
membrane.
122
2.1.17. Fusel Oil Components Separation
One of the main products of sugar manufacturing is molasses, which contains
approximately 50% sucrose and 50% other components (water, various other organic
components and inorganic salts). Because of its high sucrose content, a substantial portion of
the molasses is used for the production of ethyl alcohol through fermentation. The byproducts of the fermentation broths, more volatile than the alcohol, are mainly aldehydes with
acetaldehyde being the principal component. The aldehyde is removed, as a distillation head
product. The other by-product of the distillation step, the bottom product, is fusel oil. It is
composed of several alcohols, primarily C3, C4 and C5 aliphatic alcohols. The separation of
its components, using pervaporation technique and PVA/PAcr.Ac. blend as membrane has
been reported [55]. The characteristics of the pervaporation process are presented in table 11.
Composition of
the membrane
PVA/PAcr.Ac
90/10
Composition of
liquid mixture:
fusel oil
Permeation rate/
/ (g m-2 h-1)
T / ºC
Separation
factor
5000
60
10
Alcohols
mixture
with 10-30 % of
water
Permeate
activation energy
Ea / (kJ mol-1)
49.4-41.7 (water)
60.8-55.7 (EtOH)
2.2. Separation by Evapomeation
Evapomeation is a new membrane-separation technique for liquids mixtures, which
eliminates some disadvantages of the pervaporation technique such as the decreasing of
membrane permselectivity, due to its swelling by the direct contact with the feed solution. In
evapomeation technique the membrane is not in direct contact with the feed solution, only
with the solution’s vapors. In this way the swelling of the membrane could be suppressed and
consequently, the permeation rates in evapomeation are smaller than those in pervaporation,
but the separation factor is greater [83].
The differences between the pervaporation and evapomeation processes may be seen in
figure 5.
123
Figure 5. Schematic presentation of the pervaporation and evapomeation processes.
2.2.1. Isomers Separation by Evapomeation
Separation of n-propanol from a mixture of n-propanol (n-PrOH) and i-propanol (iPrOH)
Taking into account the capacity of cyclodextrins (CD-s) to entrap a large number of
organic and inorganic molecules, due to their hydrophobic cavity, β-CD has been introduced
into PVA in order to obtain a good separation of isomer mixtures.
Two methods for obtaining PVA/(β-cyclodextrins) (β-CD) blends have been reported:
I.
membranes were prepared by casting the solution (4%) of PVA (PD=1650;
saponification degree = 99.7 %) and β-CD in DMSO at 25 ºC and solvent
evaporation at 80 ºC [83,84];
II. by casting the aqueous solution of PVA (Mn=125,000), β-CD and 0.1%
glutaraldehyde and water evaporation at room temperature in a vacuum oven for 24 h
[85].
PVA and β-CD evidenced a good compatibility and produce transparent blend films [84].
The blend membranes are permselective for different organic isomers. So, these could be
used for the separation of n-propanol from a mixture of n-propanol (n-PrOH) and i-propanol
(i-PrOH) [84] and the separation of p-xylene from a p-xylene and o-xylene mixture [35]. It
was evidenced that, in both cases, the separation was better by applying the evapomeation
technique than that of the pervaporation.
It was observed that the n-PrOH concentration in the permeate through the CD/PVA
membrane by pervaporation was approximately same as that in the feed solution, namely, the
PrOH isomers could hardly be separated through these membranes by pervaporation. The nPrOH concentration in the permeate obtained by evapomeation was higher than that in the
124
feed solution, evidencing a higher permeation of the CD/PVA membrane for n-PrOH
compared to i-PrOH.
The same situation was evidenced in the case of xylene isomers separation. The
evapomeation is more efficient than that of pervaporation [83].
The n-PrOH concentration in the permeate and the normalized permeation rate increased
with the increasing CD content in the CD/PVA membrane. The addition of CD in the PVA
membrane determined the increasing of the swelling degree and preferential sorption of nPrOH and p-xylene, due to the fact that the affinity of CD for these isomers was stronger than
that for i-PrOH and o-xylene respectively [84].
The influence of the CD content in the membrane and the n-PrOH respectively p-xylene
content in the feed mixture on the separation factors and sorption and diffusion selectivities of
the CD/PVA membranes for the n-PrOH/I-PrOH and p-xylene and o-xylene mixtures by
evapomeation are presented in tables 12 and 13.
Table 12. Separation factors and sorption and diffusion selectivities of the CD/PVA and
PVA membrane for the n-PrOH/i-PrOH (50/50 w/w) mixture and p-xylene and o-xylene
(10/90 w/w) mixture by evapomeation versus the CD content [18, 83, 84]
CD content /
/ wt%
Separation of n-PrOH/i-PrOH
(50/50 w/w) mixture
αsorp.
αdiff.
αsep.
Separation of p-xylene and oxylene (10/90 w/w) mixture
αsep.
αsorp.
αdiff.
0
2.01
1.89
1.06
1.72
0.53
3.27
20
-
-
-
1.19
0.94
1.27
30
-
-
-
2.93
1.08
2.74
40
2.61
2.07
1.26
3.93
0.78
5.04
Table 13. Separation factors and sorption and diffusion selectivities of the CD/PVA (CD
content: 40 wt %) membrane for the n-PrOH/I-PrOH mixture and p-xylene and oxylene mixture by evapomeation versus the n-PrOH and respectively p-xylene,
concentration in the feed [83,84]
Content of feed /
/ wt%
n-PrOH
p-xylene
10
-
αsep.
αsorp.
αdiff.
15.2
3.68
4.14
50
-
10
30
2.61
3.93
3.26
2.07
0.78
1.86
1.26
5.04
1.75
-
50
70
90
1.86
1.99
0.63
1.06
1.48
1.03
1.75
1.34
0.61
It may be seen that a very high separation factor of organic liquid isomers through
polymer membranes has been obtained for PrOH isomers [84].
125
A similar situation is reported for the separation of xylene isomers [83].
These results show the CD/PVA membranes are good candidates for isomers separation
from organic liquid mixtures by evapomeation.
PVA/CD hydrogels swell in water. The swellability of PVA/CD hydrogels is marginally
higher than that of the PVA gel, indicating that the crosslink density is higher in the PVA/CD
system than in the PVA gel. The higher crosslink density may be an additional factor in
retarding the migration of the drug in the presence of CD.
2.3. Separation by Pertraction
Pertraction is a continuous membrane-based extraction process, which has been proposed
for, e.g., removing metal and organic pollutants from waste water treatment [86] and for
concentrating valuable components from complex broths in bioproduction [87] as a
consequence of solvent extraction. In this technology, the membrane contactor combines two
functions, i.e., separation and extraction. It generally consists of a hydrophobic liquid phase
so that the extraction and stripping of the solutes occurs in a three-phase system with two
liquid/liquid interfaces. To this purpose, different techniques, such as impregnation of a
microfiltration membrane by a circulating hydrophobic phase, supported liquid membrane
and hydrophobic membrane, have been applied [88].
A very effective way to improve the pertraction performances in permeability and
selectivity is to incorporate extractants into the hydrophobic phase, which react with a given
solute reversibly and selectively.
S. Touil et al. [88] have reported the efficiency of membranes of cyclodextrin (CD)containing PVA membranes (with CD covently grafted to the polymer chain) for the
geometrical xylene isomer discrimination using the pertraction (combination of separation
and extraction) technique. They found that in the presence of CD-containing membranes
permeability coefficients of xylene isomers are higher when compared to control PVA
membrane. It is also reported that α-CD is more effective to selectively extract the xylene
isomers than β-CD. Flux observed for pertraction of single isomers and of the o-/p- binary
mixtures was in the same order as the binding constants to α-CD i.e.p-xylene > m-xylene > oxylene. The fabricated membranes exhibit a p-xylene selectivity for low p-xylene feed mole
fraction (<70%) and a o-xylene selectivity for higher p-xylene feed mole fraction. The pxylene enrichment factor observed at 10% p-xylene in the feed equal to 6, is the higher value
ever reported for the separation of xylene isomers using CD containing membranes. The
effect of way how CD, in particular α-CD, is introduced in PVA membranes is analysed in
ref. 89. Physical trapping give rise to materials with an incorporation rate of 80 and 90% from
the starting CD, whereas covalent attachment was quantitative. In both cases, however, it is
found a high discrimination of p-and m-xylene over o-xylene.
126
2.4. Separation by Membrane Extraction
The development of membranes for, e.g., removing metal and organic pollutants from
wastewater treatment [86, 90] and for concentrating valuable components from complex
broths in bioproduction [87] is an attractive area.
Due to its structure and possibility to form complexes or inclusion compounds with
different organic or inorganic substances, PVA hydrogels could be used to retain Cu(II) ions
from waste waters (at pH values higher than 8). A green complex PVA-Cu (II) is obtained.
The following equation of reaction could describe the PVA-Cu (II) complex formation:
CH CH
2
OH
CH
2
CH2
CH
OH
2+
Cu
+
OH
CH CH
2
OH
H
H
CH O
O
CH
CH
2
2
CH
CH
2
Cu
2
CH
O
CH O
CH CH
2
CH
CH
H
H
2
This complex could be further used in S2- ions retaining from wastewaters. Sulphide ions
react with copper ions from the PVA matrix, leading to nanoparticles of CuS entrapped in the
hydrogel. PVA-Cu (II) green hydrogel becomes black as it can be seen in figure 6.
The repartition constant of Cu (II) ions between the PVA cryogel and water has been
determined as 13.45. The repartition constant of sulphide ions between the PVA-Cu(II)
complex and water is very close of the first value, due to the high affinity S2- to Cu2+ [92].
PVA hydrogel membranes obtained by freezing and thawing method could also retain
iodine, in the presence of iodide ions. Red or blue complexes are formed in function of iodine
concentration. A high repartition coefficient of iodine between cryogel and water has been
obtained. They are dependent on the iodine concentration, evidencing a high level of
interaction between PVA and iodine/iodide complex (K= 175 for 10-3 I2/I- aqueous solution
and K= 455 for 3. 10-3 I2/I- aqueous solution) [93].
Taking into account that the iodine extraction from an aqueous solution is generally done
by using very toxic and environmentaly dangerous organic solvents, such as CCl4, CHCl3,
extraction of iodine with PVA hydrogel, non-toxic and biodegradable, could be a good
candidate for “clean” technologies.
CH2
CH
CH
H
H
O
O
CH
CH
2
CH
CH
Cu
2
O
O
H
H
CH
2
CH 2
+
2
CH
CH
2
S
2-
CH
CH
2
OH
CH
OH
CuS
OH
OH
CH CH
2
CH
CH
2
127
a.
b.
Figure 6. Photographic aspect of PVA-Cu (II) complex (a) and PVA-Cu(II)-CuS composite [91].
Another important task in environmental protection is nowadays the effective
decontamination of medical wastewaters. The development of new medicines for the
treatment of oncologic and chronic diseases brings with it the need to efficiently
decontaminate media containing these medicines. The existing methods are intensely energy
consuming or environmentally non-friendly (e.g., the use of ion exchangers with amine
groups).
In the photodynamic therapy of cancer, for example, macrocyclic tetrapyrrholic
compounds named porphyrins are used. Porphyrin-containing wastewaters can negatively
affect the aquatic ecosystems (plants and fish population), even in very small concentrations.
Recent studies present a method adequate for the advanced purification of medical
wastewaters containing such porphyrins [94].
The method consists of the retention by sorption of the porphyrins on poly (vinyl alcohol)
(PVA) hydrogels. Poly (vinyl alcohol) (PVA) is selected as the polymer of choice for the
purification of industrial and medical wastewaters due to its capacity to form physically
crosslinked hydrogels with the advantages of non-toxic, non-carcinogenic and biodegradable
properties.
128
Some authors consider that poly(vinyl alcohol) hydrogels represent an efficient and
environmentally viable alternative advanced purification method for porphyrin-containing
medical wastewaters.
Many efforts to improve the efficiency and the selectivity of membrane processes are
based on molecular recognition properties.
The incorporation of cyclodextrins in polymeric membranes will improve affinity and
selectivity properties of those membranes due to the possible formation of host-guest
complexes by supramolecular interactions. Cyclodextrins (CD) are cyclic oligosacharides
having 6, 7, 8 or more glucose unities [95] called α-, β- and γ-CD, respectively. These
compounds show a large number of applications once they exhibit complex formation with
organic molecules, they are excellent models of enzymes which led to their use as catalysts,
both in enzymatic and nonenzymatic reactions, and they are natural products and readily
available. For these reasons, we can find applications of these compounds in analytical
chemistry [96], drug carrier systems [97], etc. Cyclodextrins are water soluble macrocycles
shaped like a rigid, truncated cone with a hydrophilic external surface and a relative non-polar
cavity [98]. In fact, the cavity is lined by hydrogen atoms and glycosidic oxygen bridges. The
non-bonding electron pairs of the glycosidic oxygen bridges are directed toward the inside of
the cavity, producing a high electron density and lending it some Lewis base character. As a
result of this special arrangement of the functional groups in the CD molecules, the cavity is
relatively hydrophobic compared to water while the external faces are hydrophilic. These
hydrophobic cavities provide an enormous host potential for molecular ability to form
inclusion complexes with a large variety of organic and inorganic compounds in different
solvents (including water) [99-101]. The selectivity originated from the different binding
constants to CD depends on the size and shape of guest molecules. This fitting effect has been
successfully exploited for separation of positional isomers and enantiomers in such
techniques as HPLC and capillary electrophoresis [102,103]. It appears from literature that
CD-containing membranes have been mainly based on the immobilization onto hydrophilic
polymers acting as a barrier for hydrophobic compounds and thereby limiting their non
selective diffusion [83,104,105].
Poly(vinyl alcohol) (PVA) seems to be one of the most efficient polymer matrix for CDcontaining membranes owing to its ability to form free-standing films and its hydrophilic
character due to the presence of hydroxyl groups. In these membrane materials CDs have
been either trapped in PVA [83,84] or covalently linked to the chain [106].
Retaining of different ions from solutions is a very important target for wastewaters
purification and for recovery of different ionic expensive species from solutions.
PVA is a non-ionic polymer, but it could be blended with ionic or ionizable polymers and
it could be copolymerized or grafted, giving materials that exhibit ion-exchange capacity.
So, the PVA/poly(sodium styrene sulphonate) [PSSNa] blend was obtained by casting
aqueous solution of polymers mixture (PVA with Mw= 124,000-186,000 and HD=99% and
PSSNa with Mw= 70,000). The resulted films were crosslinked with 1,2-dibromethane in
gaseous phase. A semi-interpenetrating network (SIPN) in which polyelectrolyte (PSSNa)
chains are trapped inside a based PVA network was obtained [44]. A totally miscible blend
with a very good film clarity and high mechanical resistance [44] resulted.
The membrane evidenced ion exchange capacity that depends on: crosslinking time (tc)
and the membrane composition. This capacity increases with the time of crosslinking from
0,8 to 2,0 meq/g after tc= 2 respectively 12 h. The best result for ion exchange capacity was
129
obtained for membranes with 45% PSSNa content. The membrane kept about 60% of the
initial exchange capacity after more than 2 years [44].
The blends swelling ratio in pure water is shown as a decreasing function of crosslinking
time [44].
The membrane, initial supple (tc<2 h) becomes stiff and brittle after a longer crosslinking
time (tc =8 h).
The PVA/PSSNa membranes evidence a high permselectivity, comparable with the one
of commercial ion exchange membrane as it can see in table 14, where were presented the
permeability coefficient (P) and the ratio P to D (diffusion coefficient) that express the effect
of porosity and of the electrolyte exclusion.
Table 14. Diffusion of sodium chloride at 25 ºC through a PVA/PSSNa
membrane* (Na+ form) [18, 44]
C / (mol L-1)
0.01
0.1
1
P / (cm2 s-1)
1.91×10-7
7.06×10-7
2.50×10-6
P/D
0.013
0.047
0.167
*Capacity: cp=0.98 meq/g. Swelling ratio:τg=0.47. Thickness of dry and swollen sample: 140 and
200μm.
Also, the PVA/Poly(1,1 Dimethylenepiperidinium chloride) (PDMeDMPCl) blend
membrane evidenced ion exchange capacity that increased with the time of crosslinking (tc)
from 0,92 to 1,2 meq/g after tc= 15min respectively 120 min and showed a maximum capacity
value, function of the weight fraction of PDMeDMPCl at 0.45 [44].
These membranes kept about 50% of the initial exchange capacity after more than 2
years.
The PVA/PDMeDMPCl blend membranes evidenced a lower permselectivity than
PVA/PSSNa membranes, probably because of a possible phases’ separation during the
solvent evaporation, as it can see from table 15 [44].
Table 15. Diffusion of sodium chloride at 25 ºC through
a PVA/PDMeDMPCl membrane* (Cl- form) [18,44]
*
C / (mol L-1)
0.01
0.1
1
P / (cm2 s-1)
2.38×10-6
6.31×10-6
7.17×10-6
P/D
0.16
0.42
0.48
Capacity: cp=0.83 meq/g. Swelling ratio:τg=0.67. Thicknesses of dry and swollen sample: 80 and
150μm.
130
The PVA/PAcr. Ac. blends may also act like an ion exchange membranes if they are
treated with 1,2-dibromoethane in gas phase. The average capacity of ion exchange is 6
mequivalent /g and depends on the weight fraction of the crosslinkable polymer [44].
Biosorption or bioaccumulation, the process of passive cations binding by dead or living
biomass, represents a potentially consecutive way of removing toxic metals from industrial
wastewaters. Biosorption could be employed most effectively in a concentration range below
100 mg L-1, where other techniques are inactive or too expensive.
Metal ion binding during biosorption processes has been found to involve a complex
mechanism, such as ion-exchange, complexation, electrostatic attraction or micro
precipitation.
There have been some indications that ion-exchange plays an important role in metal
sorption by algal biomass. Although numerous papers on the metal–microorganism
interactions are available in the literature, still large uncertainties exist. Biosorbents are
complex and variable materials. The composition of cell wall, to which metal ions are bound,
depends not only on biosorbent species, but also on environmental conditions of its growth.
Recent studies confirmed that Azolla Caroliniana Wild fern, which is known as an
effective bioacumulator in living state, is effective also in dry state (higher than 91% for Cr
(III) ions retention) [107].
The dried fern particles have been also treated with nitric acid aiming to eliminate of
cations initially present in the fern’s body and to enhance its bioaccumulation capacity, but no
important modification has been evidenced by this treatment [108].
The use of Azolla Caroliniana dry fern in water depollution avoids the problems of plant
acclimatization in different climate conditions or polluted water characteristics and the water
re-pollution by toxics delivery from died fern maintained in water.
The insertion of dried fern in a polymeric matrix avoids the fern particles mechanical
degrading and permits the bioaccumulating material regeneration and it is reworking,
determining the effectiveness of this advanced cleaning wastewater.
Taking into account the non-toxicity and biodegradability of PVA, this depollution
method is an ecological one.
2.5. Separation by Ultrafiltration
Ultrafiltration (UF) is a membrane separation technique used to separate extremely small
particles and dissolved molecules in fluids, using suction or pressure. In membrane separation
systems, liquid containing two or more components comes into contact with a membrane that
permits some components (for example, water in the fluid) to pass through the membrane (the
permeate), while other components cannot pass through it (the retentate). The physical and
chemical nature of the membrane (e.g., pore size and pore distribution) affect the separation
of the liquid and its components. The primary basis for separation is molecular size (normally
higher than 15-200 Å), although other factors such as molecule shape and charge can also
play a role. Molecules larger than the membrane pores (0.001 to 0.1 μm) will be retained at
the surface of the membrane (not in the polymer matrix as they are retained in microporous
membranes) and concentrated during the ultrafiltration process.
Compared to non-membrane processes (chromatography, dialysis, solvent extraction, or
centrifugation), ultrafiltration is far gentler to the molecules being processed, does not require
131
an organic extraction which may denature labile proteins, maintains the ionic and pH milieu,
is fast and relatively inexpensive, can be performed at low temperatures (for example, in the
cold room), and is very efficient and can simultaneously concentrate and purify molecules.
The retention properties of ultrafiltration membranes are expressed as Molecular Weight
Cutoff (MWCO). This value refers to the approximate molecular weight (MW) of a dilute
globular solute (i.e., a typical protein) which is 90% retained by the membrane. However, a
molecule’s shape can have a direct effect on its retention by a membrane. For example, linear
molecules like DNA may find their way through pores that will retain a globular species of
the same molecular weight.
There are three generic applications for ultrafiltration. a) Concentration: ultrafiltration is a
very convenient method for the concentration of dilute protein or DNA/RNA samples. It is
gentle (does not shear DNA as large as 100 Kb or cause loss of enzymatic activity in proteins)
and is very efficient (usually over 90% recovery). b) Desalting and Buffer Exchange
(Diafiltration): ultrafiltration provides a very convenient and efficient way to remove or
exchange salts, remove detergents, separate free from bound molecules, remove low
molecular weight materials, or rapidly change the ionic or pH environment. c) Fractionation:
ultrafiltration will not accomplish a sharp separation of two molecules with similar molecular
weights. The molecules to be separated should differ by at least one order of magnitude (10×)
in size for effective separation. Fractionation using ultrafiltration is effective in applications
such as the preparation of protein-free filtrates, separation of unbound or unincorporated label
from DNA and protein samples, and the purification of PCR products from synthesis
reactions.
Ultrafiltration (UF) is an important component in wastewater treatment and in food
industry [109,110]. With increasing concerns and regulations in environment as well as in
food safety, the process of ultrafiltration has become more critical, whereby new technology
development to provide faster and more efficient water treatment is not only necessary but
also urgent. Currently, conventional polymeric UF membranes are prepared mainly by the
phase immersion process, typically generating an asymmetric porous structure with two major
limitations: (1) relatively low porosity and (2) fairly broad pore-size distribution [111,112].
As a result, these membranes suffer two deficiencies: low flux rate due to the low
porosity (i.e., limited permeability) and high fouling rate due to the asymmetric pore-size
distribution having small pores on the surface [113].
In fact, the main problem with UF, however, is the flux decline caused by the irreversible
adsorption of foulants onto the surface or even inside the pores of the membrane.
Solute adsorption often involves hydrophobic interactions—hydrophobic membranes
have a high tendency to foul in water treatments. However, many hydrophobic membranes
remain the most useful media for ultrafiltration due to their superior performance in terms of
mechanical, chemical and thermal stability.
One approach to reduce fouling is using hydrophilic polymers, such as cellulose acetate
(CA). Although CA membranes have outstanding properties in reducing membrane fouling,
they lack long-term chemical, thermal and biological stability. Therefore, much research has
focused on the development of good hydrophilic UF membranes using a high hydrophilic
polymer.
To avoid, or diminish the fouling process, a blend of PVA with cellulose (CELL) has
been obtained by spin coated of the PVA (M=50 000; 99% hydrolysis degree) /
glutaraldehyde (GA) solution (corresponding to 0.005 or 0.01 moles of GA/ mole of PVA
132
repeat unit) mixture onto the regenerated cellulose membranes (M=10 000) [114]. A
composite structure has been obtained.
This hydrogel coating may penetrate the larger pores of the cellulose membrane and can
exclude protein from entering them (100% protein retention). So, the hydrogel coating
reduces the irreversible fouling of the cellulosic surface.
Relative water fluxes varied from 97.4 to 46.8 % as the thickness of the coating under
hydrostatic pressure varied from 0.8 to 5.2 μm.
This blend is recommended as thin-gel composite membranes for bovine serum albumin
ultra-filtration [114].
Polyvinyl alcohol (PVA) polymer is an attractive material to be developed as a new type
of UF membrane with good anti-fouling characteristics. PVA membranes have a high level of
mechanical strength, low fouling potential, longterm thermal resistance and pH stability. It
has also been shown that PVA has good resistantce to most solvents besides strong polar
solvents such as water, dimethyl acetamide, and N-methyl-2- pyrrolidone.
Many studies relative to PVA-based membrane materials focused on modifying
commercial membranes to improve their anti-fouling performance [115,116]. For example,
Na and Liu [117] reported that a PVA-based composite UF membrane could improve
membrane hydrophilicity and its anti-fouling performance. The anti-fouling PVA composite
membranes were dynamically prepared with an aqueous solution containing PVA, crosslinking agents and additives passed through porous substrate membranes such as
polyacrylonitrile, polyvinylidene fluoride and Nylon.
X. Wang et al. [118] reported a new type of ultrafiltration membrane based on a different
type of nanostructured porous support—electrospun nanofibrous scaffold in conjunction with
a very thin layer of hydrogel coating to minimize fouling. Both the nanofibrous mid-layer
support and the top coating layer were manufactured from crosslinked hydrophilic poly(vinyl
alcohol) (PVA), where the degree of hydrolysis and the molecular weight of PVA were
simultaneously adjusted to partially optimize the filtration performance and the mechanical
durability. In that study PVA is the base material for fabrication of both the porous
nanofibrous mid-layer support and the non-porous top coating layer. PVA is often used in
ultrafiltration because of its superb hydrophilicity, biocompatibility, chemical and thermal
stability. However, as PVA is water-soluble, it must be crosslinked to form water-resistant
articles. PVA can be crosslinked through the reaction with hydroxyl groups using a wide
range of chemicals [119,120]. X. Wang et al. synthesised a new high flux ultrafiltration
nanofibrous composite membrane containing a crosslinked PVA electrospun scaffold and a
PVA hydrogel coating.
The crosslinked electrospun scaffold using 96% hydrolyzed PVA with high molecular
weight (85 000–124 000 g/mol) exhibits the best overall mechanical performance with high
tensile, strength and elongation. The crosslinking reaction only resulted in a minor shrinkage
in volume (<5%) in the electrospun scaffold, whereby the resulting porosity was relatively
high (>80%). The PVA coating layer on the electrospun scaffold was crosslinked by using
GA at varying concentrations.
Although the PVA hydrogel coating layer is macroscopically non-porous, it acts
microscopically as a mesh of hydrophilic chains connected by crosslinking points. The mesh
size can be controlled by the degree of crosslinking in the hydrogel and the best permeation
rate and filtration efficiency is achieved by using the GA/PVA repeat unit ratio of 0.06 to
crosslink the top PVA layer. The ultrafiltration test indicates that the flux rate of PVA
133
nanofibrous composite membranes is at least several times better than those of existing thin
film composite membranes [121-123], where its performance can be further optimized by
reducing the top layer thickness or changing the layer composition.
Another way of using PVA for UF membranes is by modifying PVA by controlling
hydroxyl groups. In this way the pore structure can be easily adjusted by the method phase
inversion. Otherwise, once PVA is a water –soluble polymer it is difficult to form porous UF
membranes with an ideal morphological structure by the method of wet phase inversion
directly when water is used as a coagulation bath.
Acetalization of PVA is commercially used in the modification of PVA [124]. In general,
formaldehyde, acetaldehyde and butyraldehyde have been used in acetalization of PVA.
However, the hydrolyzing temperature of poly(vinyl formal) and poly(vinyl butyral) is higher
than their deformation temperature. The hydrolysis and crosslinking for both poly(vinyl
formal) and poly(vinyl butyral) membranes are difficult to perform directly below their
deformation temperature. The crosslinking of the acetalized PVA with glutaraldehyde is easy
to carry out without damaging the membrane shape and structure. In the Ref. 124 a number of
hydrophilic UF membranes using the acetalized PVA is presented. The UF permeation tests
were carried out using bovine serum albumin (BVA) solution as the feed instead of water.
The modified PVA membrane exhibits a high level of water permeation along with good
retention of BSA. It was found that the modified PVA UF membranes are hydrophilic and
showed a good tendency dramatically to relieve protein fouling, thereby providing a better
alternative to commercial UF membranes.
3. OTHER DOMAINS OF MEMBRANES APPLICATION
3.1. Fuel Cells
Ion conducting polymers containing strong acidic groups (e.g., sulfonic acid) are of
interest for a broad range of applications, such as biosensors, chemical sensors, catalysts,
actuators, ion-exchange membranes and polymer electrolyte membrane (PEM) fuel cells
[125-127]. PEM fuel cells, in particular, are being investigated as replacements to current
power sources used in transportation and portable electronics [128]. In this application, the
ion conducting polymer or PEM serves as both a cell separator, separating the anode from the
cathode, and an electrolyte, conducting protons from the anode to the cathode. Although there
are a number of advantages to PEM fuel cells (e.g., renewable fuels, environmentally benign,
high efficiencies), there are also a number of key shortcomings with current PEMs that hinder
fuel cell efficiency. These shortcomings include low proton conductivity at higher
temperatures, poor water management and high fuel crossover. Fuel crossover is a main
concern as it applies to the methanol fuel-based PEM fuel cell (also known as the direct
methanol fuel cell (DMFC)).
Direct-methanol fuel cells (DMFCs) have attracted considerable attention for certain
mobile and portable applications, because of their high specific energy density, low poison
emissions, easy fuel handling, and miniaturization [129,130]. However, the methanol
permeation through electrolyte membranes (usually called methanol cross-over) in DMFCs
still is one of the critical problems hindering the commercialization [131,132]. Nafion®, a
134
poly-(perfluorosulfonic acid) membrane, is the major membrane used in polymer electrolyte
membrane fuel cells (PEMFCs) presently. However, Nafion® membrane has a poor barrier
property to methanol crossover (high methanol permeability). The methanol crossover to
cathode not only reduces fuel efficiency, but also increases the overpotential of the cathode,
thus resulting in lower cell performance [133]. The reason is known to be originated from
protonic drag of methanol and diffusion through the hydrophilic channels within the
membrane. Therefore, the effective methods for reducing methanol cross-over are to decrease
the average diameter of ion-rich hydrophilic domains and increase the hydrophobicity of
membrane surface.
To date, much effort has been undertaken to develop new alternatives. For example,
sulfonated aromatic polymers, i.e., polymers with the sulfonic acid groups directly attached to
the main chain or carrying short pendant side chains with terminal sulfonic acid units, attract
increasing interest because of their chemical and thermal stability, and the ease of the
sulfonation procedure. Some of the proposed polymers are sulfonated polysulfone (SPSU)
[134] sulfonated poly(phenylene oxide) (SPPO) [135] sulfonated poly-(ether ether ketone)
(SPEEK) [136] poly(phenylquinoxaline) (PPQ) [137] and poly(benzeneimidazole) (PBI)
[138].
Poly(2-acrylamido-2-methyl-1-propanesulfonic acid)(PAMPS) was found to show higher
proton conductivity than partially hydrated Nafion due to the sulfonic acid groups in its
chemical structure [139]; consequently it can be chosen as a component for a new protonconducting electrolyte membrane [140]. However, PAMPS, shows also some limitations as,
for example, is highly water-soluble. Another key factor for the development of protonconducting polymer electrolyte membranes is the water swelling. Extreme swelling causes a
loss of the dimensional stability, while low swelling reduces proton conductivity because of
low water absorption of the membranes. Cross-linking is an efficient means to limit the
swelling, also yielding the dimensional and thermal stability of the membranes. [141-143].
Another consideration is alcohol cross-leaking, which is a key issue in the practical use of
DMFC, but it can be controlled effectively by adjusting the cross-linking density of the
prepared membranes. [144]. J. Qiao et al. [144] have synthesised a family of conducting
polymer membranes of chemically modified poly(vinyl alcohol) - poly(2-acrylamido-2methyl-1-propanesulfonic acid) (PVAPAMPS) prepared on the basis of a new concept of
binary chemical cross-linking. It has been demonstrated that the excessive swelling of pristine
PVA-PAMPS can be well controlled by chemical cross-linking using nbutylaldehyde/terephthalaldehyde,
n-hexylaldehyde/terephthalaldehyde,
and
noctylaldehyde/terephthalaldehyde as binary cross-linking agents. By changing the spacer
length of the auxiliary crosslinkers, PVA-PAMPS membranes produce promising swelling
characteristics and very good mechanical properties and flexibilities. The type and the amount
of water absorbed by the chemically cross-linked PVA-PAMPS polymer blends are
dependent not only on the sulfonic acid amount, but also on the spacer length of the CH2
chain in the auxiliary crosslinkers and the cross-linker composition. The membranes show a
larger sorption of nonfreezing water relative to freezing water. For a PVA-PAMPS of 1:1.5 in
mass, with O5T5 as a binary cross-linking agent, a proton conductivity of 0.12 S cm- 1 at 25
°C and of 0.098 S cm-1 at 5 °C is reported. The same authors [145] have mofidied PVAPAMPS polymer blends by introducing a further polymer, the poly(vinylpyrrolidone) (PVP).
The proton conductive polymer membranes PVA–PAMPS–PVP has the best proton
conductivity of 0.088 S cm-1, at 25 ºC, for a polymer composition PVA:PAMPS:PVP of
135
1:1:0.5 in mass, which is comparable to commercially available Nafion117, and a methanol
permeability of 6.1×10-7 cm2 s-1, one third of Nafion 117 methanol permeability (1.7×10-6
cm2 s-1 [146]), at room temperature.
The use of a modified PVA membrane as a proton-exchange membrane is reported in the
Ref. 147. The chemical structure of poly(vinyl alcohol) membranes is modified via
sulfonation, using sulfophthalic acid (sPTA) as a sulfonating agent. The ion-exchange
capacity (IEC), water uptake, methanol permeability and proton conductivity properties are
evaluated for a set of sulfonated PVA membranes, with a variety of degrees of substitutions.
The permeability of methanol and proton conductivity of these polymers are compared with
those of Nafion115. The values of methanol permeability and proton conductivity obtained
are 18.0 × 10-7 cm2 s-1 and 0.112 S cm-1 respectively. Methanol permeability values of the
membranes treated with 10% sPTA, at different cross-linking times, are around 5 × 10-7 cm2
s-1, and proton conductivity values of the sulfonated PVA membranes ranged between 0.024
and 0.035 S cm-1.
The effect of annealing temperatures (65 – 250 ºC) and blend composition of Nafion®
117, solution-cast Nafion®, poly(vinyl alcohol) (PVA) and Nafion®/PVAblend membranes
for application to the direct methanol fuel cell is reported in [148]. These authors have found
that a Nafion®/PVAblend membrane at 5 wt% PVA (annealed at 230 ºC) show a similar
proton conductivity of that found to Nafion® 117, but with a three times lower methanol
permeability compared to Nafion® 117. They also found that for Nafion®/PVA (50 wt%
PVA) blend membranes, the methanol permeability decreases by approximately one order of
magnitude, whilst the proton conductivity remained relatively constant, with increasing
annealing temperature. The Nafion®/PVA blend membrane at 5 wt% PVA and 230 ◦C
annealing temperature had a similar proton conductivity, but three times lower methanol
permeability compared to unannealed Nafion® 117 (benchmark in PEM fuel cells).
3.2. Sensors
The sensitivity of hydrogels to a large number of physical factors like temperature [149],
electrical voltage [150], pH [151-153], concentration of organic compounds in water [154],
and salt concentration [155] make them promising materials for a broad range of applications
as microsensors [156] and microactuators [154] in MEMS devices.
The following principles for the pH value detection are used in sensors based on the
swelling behavior of hydrogels: changes of the holographic diffraction wavelength in optical
Bragg grating sensors [157], shifts of the resonance frequency of a quartz crystal
microbalance in microgravimetric sensors [158], a bending of micromechanical bilayer
cantilevers [153], as well as a deflection of silicon membranes in piezoresistive pressure
sensors [159].
The swelling ability of pH-sensitive hydrogels depends on the functional acidic or basic
groups at the polymer backbone. Due to the dissociation of these groups and the influx of
counterions, the concentration of ions in the hydrogel is higher than in the surrounding
solution. This causes a difference in osmotic pressure and results in a solution flux into the
hydrogel and, consequently, a swelling. The interaction and repulsion of charges along the
polymer chain also lead to an increased swelling. Equilibrium of ionic gels occurs when the
elastic restoring force of the polymer network balances the osmotic forces. During the
136
swelling process hydroxide ions are transported into the neutral gel, while during the
shrinkage protons diffuse into the gel and neutralize the negative charged acidic carboxylate
groups. This ion diffusional flux induces an electrical potential difference that drives the
electromigration of the ions in the direction opposite to that of the diffusion.
In so called “Donnan equilibrium” the diffusional flux of the ions in one direction is
equal to the electromigrational flux in the opposite direction, resulting in a net zero mass
transport and a net zero charge transport. The change of the electrical potential at the gel–
solution interface is a function of the pH value of the surrounding solution. A Nernst–Planck
equation coupled with the Poisson and the mechanical equilibrium equations can be used to
describe the gel swelling/deswelling process [160]. Because the gel response is typically
diffusion driven, the time response of the volume change approximately follows the square of
the sample dimension. Scaling to micro-dimensions enhances the time response.
Consequently, a reduction of the sample size improves the sensor performance. G. Gerlach et
al. discuss the influence of the preparation conditions of hydrogel (poly(vinyl
alcohol)/poly(acrylic acid) blend films on the sensitivity and response time of the chemical
and pH sensors [161]. These authors have used swelling degree hydrogel properties as
chemo-mechanical transducers for pH value variation. The hydrogel swelling leads to a
bending of a thin silicon membrane and, by this, to an electrical output voltage of the sensor
chip. The influence of the gel swelling/deswelling kinetics on the response time and longterm signal stability of proposed pH sensors leads to a signal drift. Such drift depends on the
pH value of the ambient solution and is caused by the slow continuous change of the
electrical potential at the gel–solution interface. The influence of previous gel swelling states
can be minimized by a prolonged rinsing in de-ionized water after every measurement at high
pH values. It is described that measurements in solutions with pH < 3 and large pH changes
should be avoided in order to maintain sufficient sensor sensitivity for a long time. In order to
achieve high signal reproducibility of pH sensors, a compensation of previous output signal
values should be used.
Due to the chemical interactions between PVA and boric acid that lead to directly
proportionally of the swollen hydrogel shrinking and the boric acid concentration, a sensor for
this acid, difficult to determine by classical titration because of its weakness, has been
proposed [162].
The development and applications of optical chemical sensors have grown rapidly.
Among all sensors, optical pH sensors have received the most attention because of the
importance of pH measurement in various scientific research and practical applications [163].
Optical pH sensors are based on pH-dependent changes of the absorbance or luminescence of
certain indicator molecules immobilized on/in certain solid substrates. The immobilization of
pH indicators to solid substrates is a key step in the development of optical pH sensors. Till
now, there are three widely used methods for immobilization of pH indicators namely,
adsorption or impregnation; covalent binding and entrapment. The adsorption and entrapment
methods are relatively easy, but the leaking out of the indicators is a serious problem. The
covalent binding method is relatively complicated and time-consuming, but very reliable
since the indicators is not likely to leak out [164].
There have been many reports in which the immobilization method was covalent binding.
In fact, many pH indicators used in above reports own at least one active amino or carboxyl
group so that they can be covalently bound relatively easily to a solid substrate [165,166].
Kostov et al. had discussed the immobilizing process of Congo red, neutral red and phenol
137
red to an activated diacetylcellulose membrane, and found that the indicator of phenol red
was difficult to be immobilized via their method because of no active amino [167]. On the
other hand, three factors that impact on the longterm stability should be considered, namely,
the pH indicators themselves, the substrates and the linking bonds between the indicators and
substrates. The commonly used ester linkage and acid-amide linkage are not very stable in
acidic or alkaline aqueous conditions.
Polymeric pH indicators, phenolphthalein-formaldehyde (PPF) and o-cresolphthaleinformaldehyde (CPF) were synthesized with phenolphthalein and o-cresolphthalein reacted by
formaldehyde under alkaline conditions, respectively. They can be immobilized in hydrolyzed
cellulose diacetate membranes (HCDA) mainly due to macromolecular entrapment, and can
be covalently bound to poly(vinyl alcohol) (PVA) via the considerable newly produced
hydroxylmethyl groups [168,169]. Phenol red (phenolsulfonphthalein) and its derivatives are
commonly used for pH determination.
Phenol red immobilized PVA membrane for an optical pH sensor is developed based on
the same approach, since the molecular structure of phenol red is similar to that of
phenolphthalein. Phenol red was first reacted with the formaldehyde to produce
hydroxymethyl groups, and then it was attached to PVA membrane via the hydroxymethyl
groups. The changes of spectra characteristics after immobilization, the ionic strength effects,
response time, reproducibility and long-term stability of the sensor membrane are discussed
by Z. Liu et al. [170].
Sol–gel-based biosensors have attracted an enormous scientific attention is the last
decades [171-179]. Despite the volume of the published work, inherent drawbacks associated
with the nature and the synthetic routes followed for the preparation of such gels still exist.
These include cracking of the films, high concentration of methanol/ ethanol in the resulted
sol, and the most important point regarding the development of amperometric-based
biosensors, the lack of conductivity.
Constantinos G. Tsiafoulis et al. report the electrochemical behaviour of a composite film
based on ferrocene intercalated V2O5.nH2O xerogel (FeCp2–VXG) with photocrosslinkable
polyvinyl alcohol with styrylpyridinium residues (PVA–SbQ), in order to be used as an
electrocatalyst and host protein platform to develop an amperometric biosensor.
PVA–SbQ has been extensively used as a matrix for the immobilization of proteins [180183]. The hydrophilicity of the polymer matrix, the mild conditions that are used during the
immobilization and photopolymerization procedure make PVA–SbQ an effective support
material for the immobilization of proteins.
Using glucose oxidase as a model enzyme, prospects of GOx–PVA–SbQ/FeCp2–VXG
modified electrodes for further biosensor work in terms of working stability and storage
stability, dynamic range, compatibility to proteins, applicability to near neutral pH,
permeability and electrocatalytic activity are evaluated. Comparing with other xerogel based
architectures, vanadium pentoxide xerogel shows to be superior in terms of conductivity and
compatibility to enzymes. The proposed electrocatalyst provides about 20% increase of the
sensitivity compared with the pure mediator, is compatible with biomolecules and its
applicability over the useful pH range for most of the (bio)sensors applications indicates
promise for further use.
Low-cost, disposable, SiO2/Si3N4 chemical field effect transistor (ChemFET)
microsensors have been fabricated for pH measurements and adapted to biochemical
applications by using polyvinyl alcohol (PVA) enzymatic layers deposited and patterned
138
either by dip-coating, or spin-coating and photolithographic techniques. Both processes have
been compared for the development and optimization of a creatinine-sensitive enzymatic field
effect transistor (Creatinine-EnFET). The Creatinine-EnFET has been characterized by linear
detection properties (sensitivity around 30 mV/pCreatinine) on the [10–1 000 μmol L−1]
concentration range.(Creatinine-EnFET) [184]. Chronic end-stage kidney failure affects many
patients in the world. Since its development in the 1960s, kidney dialysis has allowed a great
number of patients to survive. So far, these techniques, and haemodialysis in particular, have
been under constant development so that the quality of health care and the patients’ life
expectancy can be improved. To go further, dialysis efficiency must be known precisely,
requiring a continuous monitoring of different chemical species concentrations into the blood:
urea, creatinine as well as the H+, K+ and Na+ ions. Creatinine is the end product of creatine
metabolism in mammalian cells. Therefore, it is an important diagnostic substance in
biological fluids. Creatinine can be used for the diagnosis of renal, thyroid and muscle
function. It plays a major role in treatment with external dialysis. Normal range for plasma
creatinine is 35–140 μmol L−1. However it can reach concentrations higher than 1000 μmol
L−1 in the case of kidney dysfunction. Thus, creatinine detection has to be developed in the
[10 – 1000 μmol L−1] concentration range for haemodialysis applications.
A highly sensitive amperometric biosensor for glutamate has been fabricated by
immobilizing enzyme in a photo-crosslinkable polymer, polyvinyl alcohol bearing a
styrylpyridinium (PVA-SbQ), membrane on a palladium deposited screen-printed carbon
electrode is reported in Ref. 181. The polymer was previously reported to be suitable for
fabrication of a thin enzyme membrane (about 1 mm thick) [185]. Enzyme can be
immobilized in the PVA-SbQ matrix with high surface density and retain their functional
characteristics to a large extent for several months upon repetition of wetting and drying
[186]. Moreover, enzymes can be immobilized in this polymer using photolithography
techniques [187], which can be adapted to mass production using ordinary screen printing or
semiconductor-fabrication processes on a planar electrode [188].
Strong electrochemical interference from oxidizable species, such as ascorbic acid and
uric acid, in the biological samples exposes a serious problem for the practical operation of
amperometric biosensors with a working potential of 0.4 V or higher [189]. For example,
electrochemical oxidation of ascorbic acid (AA) generates the dehydroascorbic acid (DAA),
with the loss of two electrons and the consequent loss of hydrogen ions. One way to solve this
problem is to modify the electrode surface with a permselective membrane. A variety of
polymer membranes have been reported to be useful for eliminating interferents [190-192].
These polymers show permselective properties based on size exclusion (e.g. poly-l-lysine and
poly (4-stryenesulfonate) membrane) and/or charge interaction between solutes and the
membrane (e.g., Nafion).
Biosensors fabricated on the Nafion and polyion-modified palladium strips are reported
by C.-J. Yuan [193]. They found that Nafion membrane is capable of eliminating the
electrochemical interferences of oxidative species (ascorbic acid and uric acid) on the enzyme
electrode. Furthermore, it can restricting the oxidized anionic interferent to adhere on its
surface, thereby the fouling of the electrode was avoided. Notably, the stability of the
proposed PVA-SbQ/GOD planar electrode is superior to the most commercially available
membrane-covered electrodes which have a use life of about ten days only. Compared to the
conventional three-dimensional electrodes the proposed planar electrode exhibits a similar
139
long-term stability, but is smaller, more responsive and more versatile. The manufacturing
processes used in the semiconductor industry can be adapted to produce these electrodes at a
unit cost that is low enough to ensure cost-effectiveness.
The blend of PVA with PEG- modified glucose oxidase could be used as glucose sensor
characterized by the linearity of calibration curve in the range of concentration by 5 × 10-5 - 5
× 10-3 mol glucose L-1 [194].
3.3. Biochemical/Medical Applications
In the recent years, the scientists’ position concerning the diseases treatments was
completely changed. No longer is the treatment of specific diseases, such as diabetes, asthma,
cardiac problems, osteoporosis, cancer etc. based only on conventional pharmaceutical
formulation. Biology and medicine are being to reduce the problems of disease to problems of
molecular science, and are creating new opportunities for treating and curing disease. Such
advances are closely related with advances in biomaterials and are leading to a variety of
approaches for relieving suffering and prolonging life [195].
An exponential increase of the biomaterials application could be noted in the last years.
R. Langer and N.A. Peppas reported the main domains of biomaterials application that
could be schematically represented in figure 7.
Figure 7. Repartition of the main domains of biomaterials applications.
The suitable materials for the above mentioned domains are polymers, metals and
ceramics. Among these, polymers play an important role. Even the polymers have a lot of
remarkable properties that could be used in biomaterials design, the interaction between these
artificial materials and tissues and blood could create serious medical problems such as clot
formation, activating of platelets, and occlusion of tubes for dialysis or vascular grafts. In the
last few years, novel techniques of synthesis have been used to correlate desirable chemical,
physical and biological properties of biomaterials.
One of the widely used categories of polymers for biomaterials design is that of homo-or
copolymers, which could generate hydrogels. Hydrogels are three-dimensional polymer
networks that could swell in water without dissolution and that, due to their high water
content and rubbery nature, are very similar to natural tissues and could be considered
140
biocompatible. Also, hydrogels may provide desirable protection for drugs, peptides and
proteins from the potentially harsh environment in vicinity of the release site. Hydrogels
could be also excellent candidates as biorecognizable biomaterials that could be used as
bioadhesive systems, as targetable carriers of bioactive agents or as conjugates with desirable
biological properties.
PVA is a well known polymer with large possibilities to be used as biomaterial, due to its
non-toxicity, biocompatibility, non-carcinogenity, capability to react with other compounds
and to be blend with a lot of polymers, changing its initial neutral network with positively or
negatively charged one. Also, by modifying their initial structural characteristics such as
molecular weight, hydrolysis degree, OH groups tacticity, some of PVA properties could be
modified, such as mechanical and thermal resistance, water solubility, and chemical stability.
Also their capability to be crosslinked by chemical or physical routs, to be blended with
different polymers or copolymers, to be graft or copolymerize with different chemical
partners lead to obtaining of intelligent hydrogels those stimuli-responsive properties could be
relatively easy to tailor.
Also, PVA hydrogels evidenced a very good behaviour in contact with skin and other
tissues, mucosa, or blood. PVA exhibits a bioadhesive nature, shape-memory properties,
avoid the protein adsorption onto the gel surface and is biocompatible.
Recent reports [1,196] showed that PVA hydrogels are used as blood-compatible
material, as contact lenses, as membranes for plasmapheresis, as artificial skin, as vocal cord
reconstruction, as articular cartilage, in controlled drug delivery as neutral non-biodegradable
matrix (in human body conditions), but more recent studies evidenced that by blending, by
grafting or by copolymerization, by crosslinking by different methods, PVA-based hydrogels
could be use also as temperature, pH, electrolyte-sensitive biomaterials.
Polyvinyl alcohol (PVA), which is a water soluble polyhidroxy polymer, is one of the
widely used synthetic polymers for a variety of medical applications [197] because of easy
preparation, excellent chemical resistance, and physical properties. [198] But it has poor
stability in water because of its highly hydrophilic character. Therefore, to overcome this
problem PVA should be insolubilized by copolymerization [43], grafting [199], crosslinking
[200], and blending [201]. These processes may lead a decrease in the hydrophilic character
of PVA. Because of this reason these processes should be carried out in the presence of
hydrophilic polymers. Poly(vinyl pyrrolidone), PVP, is one of the hydrophilic, biocompatible
polymer and it is used in many biomedical applications [202] and separation processes to
increase the hydrophilic character of the blended polymeric materials [203,204]. An
important factor in the development of new materials based on polymeric blends is the
miscibility between the polymers in the mixture, because the degree of miscibility is directly
related to the final properties of polymeric blends [205].
A very complete study, effect of pH, concentration of SA, PVA/PVP ratio and the
temperature on the SA release, concerning the controlled delivery of SA from PVA/PVP
membranes is given in the Ref. 206. Four main conclusion arise from this study: a) the
presence of PVP increased the released amount of SA; suitable PVA/PVP ratio was found to
be as 60/40 (v/v) for PVA/PVP membranes; b) the release percentage of SA through
PVA/PVP membranes and swelling degrees of the PVP-40 membranes increase with an
increase in the pH of donor solution; the pH of the acceptor solution do not affect much the
transfer of SA through PVP-40 membranes; c) grafting of PVA with VP is more effective
than blending with PVP for the release of SA; and d) the increase in the temperature increase
141
the transfer of SA; the release percentage for SA is found being 57.5 % and 66.6 % at 32 ºC
and 37 ºC, respectively.
Delivery of hydrophilic molecules such as proteins and DNA for therapeutic application
is generally considered a great challenge [207,208], because these molecules are rapidly
degraded by enzymes found under in vivo conditions both intracellularly at the site of
application as well as in the general circulation, causing low bioavailabilities and requiring
frequent injections [209]. Nanoscale carriers such as nanoparticles and nanocomplexes have
reached increasing attention, since they can be administered by various routes, including the
intravenous and intranasal routes [210,211]. Controlled and sustained release of these drug
candidates can be accomplished using microspheres and implants from biodegradable
polymers [207,212]. The classic copolyesters of lactic and glycolic acid (PLGA) are not ideal
for protein and DNA delivery since inactivation and uncontrolled release is a consequence of
poor compatibility between lipophilic polymers and hydrophilic drug candidates [213,214].
This is especially the case for DNA, where the complexation capabilities and protecting
abilities of the carrier substance are very important. M. Wittmar et al. [215] selected PVA,
once it is biocompatible and can be eliminated from the body by renal excretion [216,217].
To this polymer backbone, amine groups were covalently coupled in a polymer-analogous
reaction using carbonyl diimidazole (CDI) to introduce cationic charges under physiological
conditions [218,219]. This modification affects the colloidal stability of carrier systems by
imparting positive surface charges on one hand [220] and increasing the protein or DNA
loading by electrostatic interactions on the other hand [221,222]. As the secondary and
tertiary amino-groups functions possess lower cytotoxicity, diamines, and PVA were coupled
via the hydrolytically stable urethane bond [223]. The resulting PVA can be used in different
ratios to complex DNA.
K.S. Oh et al. [224] have used PVA-containing matrices as temperature sensitive drug
delivery systems. Their approach is based on the fact that the constant release is not the only
way to accomplish the maximum drug effect and the minimum side effects and the
assumption used for constant release rate sometimes fails its validity for physiological
conditions. Such difficulty can be overcome by technology that senses environmental stimuli
and appropriately controls the drug-release rate. Stimuli-sensitive polymers undergo phase
transition in response to changes in, for example, pH, temperature, or the metabolites [225227]. Especially, polymer materials with temperature-induced swelling transitions resulting
from both polymer–water and polymer–polymer interactions have been reported [228]. K.S.
Oh et al. have prepared a novel polymer complex gel composed of F-68 (Pluronic,
poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer) and
poly vinyl alcohol (PVA). The polymer complex gel if formed by intra/intermolecular
interactions via hydrogen bonding in water. For the application as a temperature-sensitive
delivery system of acetoaminophen, F-68/PVA complex gel is prepared with a form of
polymeric bead encapsulated by poly(lactide-co-glycolide)(PLGA) membrane and pulsatile
release of acetoaminophne, used as model drug, pattern is observed in response to pulsatile
change of temperature between 35 ºC and 40 ºC.
A new material with good antithrombogenic properties, suitable as biomedical material
which assures the endothelialization of the inner surface of a polyurethane tube to imitate the
inner wall of a natural blood vessel has been synthesized by blending PVA with
poly(carbonate urethane)(PCU) [229].
142
This blend was obtained by polymers mixture extrusion and extraction with the
azeotropic mixture of hexane/ethanol, and modifying the obtained polymer surface by
coupling of 4-isocyanato butanoic acid methyl ester (as a spacer molecule) to PVA blend,
saponification of methyl ester groups and coupling of 4-amino-TEMPO (2,2,6,6tetramethylpiperidine-1-oxyl) [229].
Generally is difficult to delimitate the medical or pharmaceutical application of PVA
hydrogels as gel matrix, micro spheres, aerosols or membranes.
Taking into account the consensual accept of the membrane concept, we could consider
as application in membrane form transerdmal patches, wound dressing, materials for tissue
engineering, thin coatings with imprintig gels for molecular recognition, biomembranes in
artificial organs, haemodialysis.
3.3.1. Transdermal Patches
The most common form of drug delivery is via the oral route. Although this has the
notable advantage of easy administration, it also has significant drawbacks namely poor
bioavailability due to hepatic metabolism and the tendency to produce rapid blood level
spikes (both high and low), leading to a need for high or frequent dosing, which can be both
cost prohibitive and inconvenient. Another method utilized in drug delivery is the systems
that deliver the drugs through the skin into the bloodstream, making them easy to administer.
In transdermal drug delivery, improved bioavailability, more uniform plasma levels, longer
duration of action resulting in a reduction in dosing frequency, reduced side effects and
improved therapy due to maintenance of plasma levels up to the end of the dosing interval,
and patient compliance could be possible.
Transdermal patch technology represents an important area of biomaterials, due to its
non-invasive character, ease to use, and a relatively high bioavailability. Generally, these
patches could deliver drugs from one to seven days. Currently, 11 drugs, or drugs
combinations are delivery through body via this method [195].
Nowadays, scientists are exploring various physical forces to enhance the transport
through the skin to expend the number of drugs being delivery such as electricity,
(iontophoresis, electroporation) or ultrasounds.
Drug delivery to the skin has been traditionally designed for dermatological drugs to treat
skin diseases or for disinfection of the skin itself. In recent years, a transdermal route has been
considered as a possible site for the systemic delivery of drugs. The possible benefits of
transdermal drug delivery include that drugs can be delivered for a long duration at a constant
rate, that drug delivery can be easily interrupted on demand by simply removing the devices,
and that drugs can bypass hepatic first-pass metabolism. Furthermore, because of their high
water content, swollen hydrogels can provide a better filling for the skin in comparison to
conventional ointments and patches. Versatile hydrogels-based devices for transdermal
delivery have been proposed [230].
Recently, porphyrins have been applied to cancer photodynamic therapy (also known as
photochemotherapy), a method based on applying a porphyrinic compound onto the tumour
and then irradiating with a light source. The porphyrin acts as a photosensitiser, transferring
its energy to the oxygen found in tumoral tissue, generating singlet (radicalic) oxygen, which
has the ability to oxidize tumour cells and also induce cell death (apoptosis). To stabilize and
to assure a convenient delivery of porphyrins their entrapment in a hydrogel matrix has been
proposed. Different porphyrins (figure 8), water soluble (5,10,15,20-tetra-sulphonato-phenyl
143
porphyrin, TSPP) and water insoluble (5,10,15,20-tetra-pyridil porphyrin, TPyP, and
5,10,15,20-tetra-phenyl porphyrin, TPP)) have been immobilized in PVA cryogel matrix.
TPyP: R=-C5NH4 ; TPP: R=-C6H5 ;TSPP: R= -C6H4-SO3-Na+
Figure 8. Structure of the porphyrins TPyP, TPP and TSPP.
The porphyrins structure and the PVA molecular weight determine differences in the
porphyrins sorption onto the PVA hydrogels, as it can be seen in figure 9 [231].
Figure 9. Comparison between the sorption degree of porphyrins on the PVA hydrogel, as function of PVA
molecular weight and porphyrin type.
One can conclude that PVA hydrogels represent an efficient encapsulation vehicle for the
studied porphyrins, both water soluble and non-water soluble. Their biocompatible,
biodegradable, non-toxic, and non-carcinogenic nature makes them especially effective for
pharmaceutical applications, but also for environmental uses, such as advanced wastewater
144
decontamination. Hydrogels prepared from high molecular mass PVA have a better sorption
profile for porphyrins, and are better suited for the preparation of controlled-release vehicles.
Also, PVA has a number of desirable characteristics that make it a good bioadhesive
polymer. It has mechanical strenght, high elasticity, and swells upon immersion in
water.Crosslinked PVA has been proposed as drug delivery carriers. In these gels the drug is
able to be released fast or slowly due to the gel’s high or low swelling ratio upon immersion
in water. Previous studies by Morimoto et al. [232] have shown that several drugs such as
indomethacin, glucose, insulin, heparin, and albumin can be released from crosslinked PVA
gels. PVA properties depend upon the degrees of polymerization and hydrolysis. The
solubility of PVA in water increases greatly as its degree of hydrolysis increases. Properties
such as water solubility, high tensile strength and tack make PVA useful as an adhesive with
fully hydrolyzed grades of PVA being water-resistant adhesives. PVA cryogel maximum
adhesion has been achieved after two freezing/thawing cycles, saples prepared by three and
four cycles still exhibit adhesive characteristics. The mucoadhesive and drugs release (i.e.,
theophyline and oxprenolol hydrochloride) behavior could be adjusted by degree of
crystalinity which depend on the number of freezing/thawing cycles.
3.3.2. PVA Based Materials as Wound Dressing
The current generation of medical dressing differs from their predecessors primarily
because they are based on non traditional polymers in this area. In creating new wound
coverings, instead of cellulose stock, other natural and synthetic polymers are being
increasingly used. One of them is PVA, because of its exceptional properties. Also, an
important change in dressing form should be noted: in many cases, preference is given to
granulated sorbents, hydrogels, films and sponges [233].
Applied to wounds, burns or surgical incisions, hydrogel materials cover the injured parts
of skin (wounds) and promote healing and skin growth.
There are two ways of wound treatment: under dry or wet conditions. In the former gauze
is applied to the skin, the latter calls for the use of hydrogels.
Since many agree that wounds heal faster in a wet environment, hydrocolloid type
materials mixed with gelatin, hydrophobic polymers and water have been developed and
already see practical use. However, these materials are mechanically weak and require
periodic change, and the residue must be removed by washing with physiological salt
solution. This process determines exfoliation of the new skin and delays healing. Also the
removing of the dressing induces pain.
To avoid all these drawbacks new wound dressing materials have been tested. So,
PEO/PVA hydrogel, crosslinked by electron beams, has been synthesized and tested as
dressing on animals wounds. Wounds dressed with a hydrogel healed almost completely
within 14 days, while those using gauze were only half-healed within that time. Clinical tests
confirmed the safety and effects of this product [234].
The main features for a hydrogel dressing are the following: to protect injured skin and
keep it appropriately moist to accelerate the healing process; to absorb liquids exuded by the
body; to prevent infection from external bacilli; to be non-toxic, non-irritant and noncarcinogenic; to be soft and high adhering to the skin; to have mechanical resitance; to have
high permeability; to resist to sterilizing process; to remove without pain; to be transparent to
allow observation of the healing process.
(a)
145
(b)
Figure 10. Hydrogel membrane (a) and their application as wound dressing (b).
New generation of therapeutic coverings have to be characterized also by the ability to
exercise a biologically active effect on wound. Incorporation of one or more drugs in the
polymeric matrix that acts as a vehicle with controlled delivery capacity makes the new
dressings able to exert anesthetizing, antimicrobial or combined effect. Also, the
immobilization of proteolytic enzymes and an antimicrobial on a polymer substrate helps by
decreasing the cleansing and healing time, especially in the purulent wounds treatment [235].
Table 16. Some exemples of systems used as new wound dressings
Polymer system/ drug
PVA/ proteolytic enzyme protease C/
polyhexamethyleneguanidine salt (PHMG)
(antimicrobial factor (AM))
a/-PHMG (C)= PHMG hydrochloride;
b/-PHMG (P)=PHMG phosphate
Properties
-PHMG influences the viscosity of the initial PVA
solution (a higher decrease has been observed in case
(a) then in case (b))
-(a) and (b) determines the decreasing of the activation
energy of viscous flow
-additive adding (sodium tetraborat as crosslinking
agent) determines the increasing of the spinning PVA
solution
-the porous structure of the film and the repartition of
the complex is influenced by the type of AM
Ref.
233
PVA film/ Sodium tetraborate/ Proteolytic
enzyme Protease C (Pr)+
polyhexamethyleneguanidine hydrochloride
[PHMG], as antimicrobial (AM)
-biological active material
-increases the AM desorption rateby 1.5-4.5 times
For PHMG with M, 10000, total desorption of AM
from the film could be obtained
236
PVA film/ Sodium alginate/ Proteolytic
enzyme Protease C (Pr)+
polyhexamethyleneguanidine hydrochloride
[PHMG], as antimicrobial (AM)
-biological active material
-decreases the rate of inactivation of Pr by 2 times
-decrease the amount of desorbed AM by 10 times,
giving the film self-disinfecting properties.
236
146
Polymer system/ drug
PVA film/ Sodium alginate (Alg)/ Proteolytic
enzyme Protease C (Pr)+, a cationic
polymeric antimicrobial (AM=Metacid)
PVA film/ Tetraborate (TB)/ Proteolytic
polymeric antimicrobial (AM=Metacid)
PVA film/ Sodium alginate/ Proteolytic
polymeric antimicrobial (AM=Fogucid)
PVA film/ Tetraborate (TB)/ Proteolytic
polymeric antimicrobial (AM=Fogucid)
PVA/β-CD/salicylic acid
PEO/PVA
PVA hydrogel UV crosslinked/ nitric oxide
acrylamide-functionalized nondegradable
poly(vinyl alcohol) (PVA), UV- photocrosslinked
Properties
-AM-s are derivatives of PMGH obtained by
neutralization with HCl (Metacid) and H3PO4
(Fogucid)
-The interactions between AM-s and PVA determine
the modifying of the composite film morphology and
as consequence the modifying of the water and water
vapors sorption (Metacid increases the films water
sorption and Fogucid decreases it).
-The films swelling capacity influence the AM-s
delivery: Fogucid is desorbed more rapidly than
Metacid.
-Incorporation of additives also influence the AM-s
desorption from the composite films: In both cases,
the AM-s desorption is more difficult, due to the
diffusion hindrances caused by the increasing of the
diffusing particles as a result of formation of a
complex, in the case of Alg., and caused by the
intermolecular crosslinks, in case of TB.
-The vapors water sorption rate gradually increases in
time for pure PVA films and decreases as absolute
values by comparing to PVA pure films when Alg or
TB are added; a more important decrease could be
obtained when AM with higher molecular weight is
added.
-β-CD forms inclusion complexes with different
water soluble substances i.e. salicylic acid
- The drug release from the PVA/β-CD gel is nearly
proportional to time
-wound dressing
NO release from NO-modified hydrogel occur over a
time period up to 48 h., and there were no associated
decrease in fibroblasts growth or viability in vitro
associated with NO hydrogels. Exogeneous NO
released from hydrogels wound dressing has potential
to modulate healing.
-As the PVA content increased from 10% to 20%,
protein flux decreased, with no trypsin inhibitor (TI)
permeating through 20% PVA hydrogels;
-Further increase in model drug release was achieved
by incorporating hydrophilic PVA fillers into the
hydrogel. As filler molecular weight increased, TI
flux increased.
- Release studies conducted using growth factor in
vehicles with hydrophilic filler showed sustained
release of platelet-derived growth factor (PDGF-β,β)
for up to 3 days compared with less than 24 hours in
the controls. In vitro bioactivity was demonstrated by
doubling of normal human dermal fibroblast numbers
when exposed to growth factor–loaded vehicle
compared to control.
Ref.
235
235
235
235
235
234
237
238
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3.3. Materials for Tissue Engineering
There are three ways in which materials have been shown to be useful in tissue
engineering:
•
•
•
the materials able to induce cellular migration or tissue recognition;
the materials are used to encapsulate cells and act as an immunoisolation barrier;
the materials are used as matrix to support cell growth and cell organization.
Some reports showed that PVA-base hydrogels could be used in all the above mentioned
ways.
So, poly(vinyl alcohol) (PVA), physically crosslinked by repeated freeze-thawing cycles
of polymer aqueous solutions, is widely employed to make hydrogels for biomedical
applications. To increase the similarity between hydrogels and natural tissues and to obtain
“polymeric hybrid tissues”, 3T3 cells have been incorporated, from a mouse fibroblast cell
line, into PVA hydrogels obtained by one freeze-thawing cycle using as a solvent complete
culture medium [239]. Hydrogels were also made using eight freeze-thawing cycles from
PVA solutions prepared using as a solvent either complete culture medium or water. Cell
adhesion experiments were performed by seeding 3T3 and human umbilical vein endothelial
cells (HUVEC) on to the hydrogel surface. The obtained results show that PVA is not
cytotoxic. Although PVA hydrogel surface characteristics do not seem to favor the adhesion
of substrate-dependent cells, encouraging results were obtained with the 3T3 cells
incorporation. DMA analysis indicates that the networks prepared by eight freeze-thawing
cycles possess a mechanical consistency comparable, even slightly better, than the ones
prepared by only one freeze-thawing cycle and used for the cell incorporation studies.
Esmaiel Jabbari and Saeed Karbasi [240] noted that fibroblast cells seeded on N-vinyl
pyrrolidone (NVP)-grafted PVA hydrogel, by using γ-radiation, had an extended oval
morphology while those seeded on Acr.Ac.-grafted PVA had a rounded spherical
morphology. These results support the use of NVP for grafting PVA to increase swelling and
improve cell viability [240].
In order to achieve the firm fixation of the artificial cornea to host tissues, composites of
collagen-immobilized poly(vinyl alcohol) hydrogel with hydroxyapatite were synthesized by
a hydroxyapatite particles kneading method. The preparation method, characterization, and
the results of corneal cell adhesion and proliferation on the composite material were studied.
PVA-COL-HAp composites were successfully synthesized. A micro-porous structure of the
PVA-COL-HAp could be introduced by hydrochloric acid treatment and the porosity could be
controlled by the pH of the hydrochloric acid solution, the treatment time, and the
crystallinity of the HAp particles. Chick embryonic keratocyto-like cells were well attached
and proliferated on the PVA-COL-HAp composites. This material showed potential for
keratoprosthesis application. Further study such as a long-term animal study is now required
[241].
PVA/collagen substrate has been succesfull used also for osteoblasts grow [1].
Prosthesis, made by a composite body comprising polyvinyl alcohol hydrogel and
ceramic or metallic porous body, has been proposed for a damaged bone, an artificial articular
cartilage or an artificial intervertebral disc repairing. With this prosthesis, PVA hydrogel
enhances lubrication and shock absorbing functions, and the porous body allows the ingrowth
148
and ossification of the bone tissue of a living body therein to affinitively connect said
hydrogel to the bones of the living body [242].
Nowadays the importance of knee meniscal function is recognized. The treatment for
meniscus injury has been changing from resection to repair. However, depending on the type
of injury, meniscectomy cannot be avoided. In consideration of the prognosis in such patients,
artificial meniscus using polyvinyl alcohol-hydrogel (PVA-H) with high water content has
been developed and performed an animal experiment as preliminary study. In the experiment
using rabbits, the lateral meniscus was replaced with an artificial meniscus in one knee side
and lateral meniscectomy was performed in another knee side of each rabbit. In the knees
treated by artificial meniscus replacement, regressive changes were initially observed but did
not progress after a certain period, and the articular cartilage state was good even after 1 year.
In addition, neither wear nor breakage of PVA-H was observed. These results suggest that
artificial meniscus using PVA-H with high water content compensates for meniscus function
and is clinically applicable. However, for clinical application some problems such as fixation
method, tolerance of PVA-H, remain to be solved [243,244].
To assess further the use of polyvinyl alcohol-hydrogel (PVA-H) artificial meniscus,
some mechanical tests about PVA-H and animal experiment have been performed. In
mechanical tests, it was found that a high water content PVA-H showed viscoelastic behavior
similar to that of human meniscus. Moreover, the frictional coefficient of PVA-H against
natural articular cartilage was also effective. In the animal experiment using rabbits, the
lateral meniscus was replaced with an artificial meniscus in one knee side and lateral
meniscectomy was performed in another knee side of each rabbit. In the results, the articular
cartilage state of knee joint implanted PVA-H meniscus was good even after 2 years, while
osteoarthrosis (OA) change progressed in meniscectomy knee joint. In addition, neither wear
nor breakage of PVA-H was observed. These results proved that an artificial meniscus using a
high water content PVA-H can compensate for meniscal function and might be clinically
applicable [245,246].
The main disadvantage of hydrogels is their poor mechanical properties after swelling. In
order to eliminate the disadvantage, hydrogels can be modified by physical blending
[247,248] or/and chemical modification by grafting [249-251], crosslinking method [252254] and semi-interpenetrating or interpenetrating polymer networks [255,256]. In order to
overcome this difficulties, blends of PVA and chitosan have good mechanical properties and
the applications of these blends have been reported [257,258] Chitosan (poly-β(1,4)-dglucosamine), a cationic polysaccharide, is obtained by alkaline deacetylation of chitin, the
principal exoskeletal component in crustaceans. As the combination of properties of chitosan
such as water binding capacity, fat binding capacity, bioactivity, biodegradability,
nontoxicity, biocompatibility, and antifungal activity, chitosan and its modified analogs have
shown many applications in medicine, cosmetics, agriculture, biochemical separation
systems, tissue engineering, biomaterials and drug controlled release systems [259-263].
Yang et al. [264] reported the preparation of PVA/chitosan blended membranes in various
ratios and treated with formaldehyde. They were interested in studying the effect of chitosan
content on the transport and equilibrium properties of membranes with of creatinine, uric acid
and vitamin B12.
5-Fluorouracil (5-FU) is an antineoplastic agent that usually arrests tumor cells at the G1S phase of the cell cycle and the choice in the treatment of carcinoma of colon or rectum; it is
also used in the treatment of precancerous dermatoses, especially actinic keratosis for which
149
is the treatment of choice if the lesions are multiple [265]. The cytotoxic anticancer drug often
causes severe side effects because it does not act selectively on the target. In order to control
the release rate of 5-FU, chitosan/ PVA blended hydrogel membranes can be used as the
protective drug coatings. It was found that the water content and water vapour transmission
rates on the blended hydrogel membrane increased with increasing chitosan content. In
antibacterial assessment, the antibacterial activity of all chitosan/PVA blended hydrogel
membranes is similar. The viable cell number of aurococcus on the various chitosan/PVA
blended hydrogel membranes is about (2.5 ±0.5)×107 cells/mL. The authors show that
permeability of solutes such as creatinine, 5-FU and vitamin B12 through chitosan/PVA
blended hydrogel membranes increase linearly with chitosan content in the blended hydrogel
membranes, whereas there is a sharp change of permeability of uric acid through the chitosan/
PVA blended hydrogel membrane when the chitosan content is changed from 60 to 80% in
the blended hydrogel membrane.
3.3.4. Biomembranes in Artificial Organs
Hydrogel hybrid-type organs designed for implantation consists of living cells
surrounded by suitable membranes. The living cells such as Langerhans islets, hepatoma (Hep
G2), hepatocytes, etc, secreste specific compounds in response to the changes in body fluids.
These systems work as a self-controlling bioreactor. The main point in design of an artificial
organ is the choice of the suitable material and the preparation technique for membrane
obtaining.
The main requirements for the membrane are:
•
•
•
•
•
permeabilty against water, oxygen and nutrients;
permeability for specific secretations of living cells;
impermeability to components of the immune system;
resistance to the biodegradability in the body conditions;
non-adhesive for proteins (avoiding their deposition)
Artificial organs could be obtained by two main techniques:
1. microencapsulation of a small amount of living cells in microcapsules that will be
injected into the organism;
2. design of a masive container with semipermeable membrane walls that contain a high
number of living cells and that could be implanted in the peritoneal cavity acting as a
substitute of the damaged organ [266].
The principle of a bioartificial pancreas design is presented in figure 11.
150
Figure 11. Scheme of a bioartificial pancreas surrounded by a hydrogel membrane [266].
Some methods used for artificial organs design are presented in table 17.
Table 17. Design of some artificial organs
Matrix
Crosslinker
poly(allyl
amine) and PVA
as extracellular
matrices
-
crosslinked
alginate covered
by a PVA
membrane
-alginate is
crosslinked by
Ca2+ions and PVA
is crosslinked by
GA
Entrapped
cells
hepatocytes
encapsulated
in Ba-alginate
capsules
Langerhans
islets
alginate matrix
covered with
PMMA
membrane
Langerhans
islets
semipermeable
membrane
pancreatic islet
tissue
Applications
Ref.
-bio-artificial liver (BAL)
that exhibit good
metabolic functions such
as albumin synthesis and
ammonia removal
-bio-artificial pancreas
-this procedure caused
denaturation of cellular
proteins
267
-The shell has been
deposit by interfacial
precipitation
-The cells are not
damaged by this
procedure and have a long
term of survival
- The development of the
bioartificial pancreas for
treatment of human
diabetes
266
266
268,269
As it could be seen from the table 17, some methods of membranes obtaining could
damage the living cells. The problems under study, related with artificial organs design are
not only the obtaining of the suitable membrane, but also the possibilities of providing the
suitable living conditions for the cells, avoiding their damage caused by the products of their
methabolism.
151
A lot of reports dials with biomembranes application in artificial kidney and pancrease
achieving and with haemodialysis problems [270-272] because hydrogels have the ability to
swell in water and retain a significant fraction of water within its structure without dissolving
and they have physical properties similar to those of human tissues and possesses excellent
tissue compatibility. Poly(vinyl alcohol) membranes satisfy the basic requirements for a
bioartificial pancreas: good permeability for glucose, insulin and albumin but the passage of
immunoglobulin G was completely prevented [273]. Furthermore, islets cultured in the PVA
tubular membranes can perform their function of secreting insulin after 30 days in the static
incubation study and rapidly releasing insulin through the membranes in response to changes
in concentrations of glucose in the dynamic perifusion experiment [274]. Experimental data
shown in Ref. 275 obtained from in vivo transplantation studies confirm that islets entrapped
by the PVA tubular membrane chamber could change the glucose level in diabetic rats. When
the m-2 [385] type of PVA chamber was implanted into streptozotocin induced diabetic rats,
nonfasting blood glucose levels dropped from 500 ± 35 mg dL-1 to the lowest value (210 ± 22
mg dL-1). Furthermore, the performance of the bioartificial pancreas can be enhanced by the
increased numbers of implanted chambers. If three m-2 chambers were implanted, nonfasting
blood glucose levels in the diabetic rats decreased to 130–160 mg dL-1 and such a low blood
glucose value was maintained for 1 month. This indicates that implanting three m-2 chambers
in the diabetic rats could provide improved permeability of insulin to normalize blood glucose
levels and improved survival of islets from the immune system of the recipient. Therefore,
this membrane provides adequate performance for secretory products in an application as a
synthetic extracellular matrix for a bioartificial pancreas.
3.4. Catalysis
Membrane reactors have found utility in a broad range of applications including
biochemical, chemical, environmental, and petrochemical systems. The variety of membrane
separation processes, the novel characteristics of membrane structures, and the geometrical
advantages offered by the membrane modules have been employed to enhance and assist
reaction schemes to attain higher performance levels compared to conventional approaches.
In these, membranes in a reactor existing as membrane laminates or physically separated
membranes with a fluid phase between them, can provide particular combinations for
functions, such as separation of products from the reaction mixture, separation of a reactant
from a mixed stream for introduction into the reactor, controlled addition of one reactant or
two reactants, segregation of a catalyst (and cofactor) in a reactor, immobilization of a
catalyst in (or on) a membrane. Membranes can act as both catalyst and reactor; membranes
perform a wide variety of functions, often more than one function in a given context.
Membranes in a reactor can be employed to introduce/separate/purify reactants and products,
to provide the surface for reactions, to provide a structure for the reaction medium, or to
retain specific catalysts [276].
Membranes can be used as a matrix for immobilization of a catalyst. Four basic types of
catalysts are relevant: (a) enzymes and (b) whole cells for biocatalysis; (c) oxides and (d)
metals for nonbiological synthesis. Biocatalysts will be considered first since their
immobilization in (or on) the membrane was explored much earlier. Five techniques have
been studied in varying degrees. They are (1) enzyme contained in the spongy fiber matrix;
152
(2) enzyme immobilized on the membrane surface by gel polarization; (3) enzyme adsorbed
on the membrane surface; (4) enzyme immobilized in the membrane pores by covalent
bonding; (5) enzyme immobilized in the membrane during membrane formation by the phase
inversion process of membrane making.
Membranes can also be used as a reactor where catalysts are used frequently. The
membrane may physically segregate the catalyst in the reactor, or have the catalyst
immobilized in the porous/microporous structure or on the membrane surface. The membrane
having the catalyst immobilized in/on it acts almost in the same way as a catalyst particle in a
reactor does, except that separation of the product(s) takes place, in addition, through the
membrane to the permeate side. All such configurations involve the bulk flow of the reaction
mixture along the reactor length while diffusion of the reactants/products takes place
generally in a perpendicular direction to/from the porous/microporous catalyst.
PVA/chitosan blend membranes can be applied for the synthesis of monoglyceride, when
used as a membrane enzyme reactor [277].
Lipases can catalyze hydrolysis of esters, synthesis of esters, trans-esterification, and
synthesis of some polymers. They have been applied in many fields including the food
industry, fine chemistry, and the pharmaceutical industry. The low stability of native lipases
makes them unsuitable for industrial applications. In order to use them more economically
and efficiently, their operational stability can be improved by immobilization. Numerous
efforts have been focused on the preparation of lipases in immobilized forms involving a
variety of both support materials and immobilization methods [278].
It was reported that PEGylated lipase entrapped in PVA cryogel could be conveniently
used in organic solvent biocatalysis [279]. This method for enzyme immobilization is more
convenient in comparison to other types of immobilization that take advantage of enzyme
covalent linkage to insoluble matrix, since the chemical step which is time consuming and
harmful to enzyme activity is avoided. The application of this catalytic system to the
hydrolysis of acetoxycoumarins demonstrated the feasibility of proposed method in the
hydrolysis products of pharmaceutical interest and to obtain regioselective enrichment of one
of the two monodeacetylated derivatives.
Monoglyceride (MG) is one of the most important emulsifiers in food and pharmaceutical
industries [280]. MG is industrially produced by trans-esterification of fats and oils at high
temperature with alkaline catalyst. The synthesis of MG by hydrolysis or glycerolysis of
triglyceride (TG) with immobilized lipase attracted attention recently, because it has mild
reaction conditions and avoids formation of side products. Silica and celite are often used as
immobilization carriers [281]. But the immobilized lipase particles are difficult to reuse due
to adsorption of glycerol on this carriers [282]. PVA/chitosan composite membrane reactor
can be used for enzymatic processing of fats and oils. The immobilized activity of lipase was
2.64 IU/cm2 with a recovery of 24%. The membrane reactor was used in a two-phase system
reaction to synthesize monoglyceride (MG) by hydrolysis of palm oil, which was reused for
at least nine batches with yield of 32–50%.
J. Xu et al. [283] have shown that immobilization of enzymes can be done using a
specially designed composite membrane with a porous hydrophobic layer and a hydrophilic
ultrafiltration layer. A polytetrafluoroethylene (PTFE) membrane with micrometer pores as
an excellent hydrophobic support for immobilization was employed for the porous
hydrophobic layer, and a biocompatible material of polyvinyl alcohol (PVA) which provided
a favourable environment to retain the lipase activity was used to prepare the hydrophilic
153
ultrafiltration layer. Enzyme molecules are adsorbed in pores of the hydrophobic layer and
deposited on the interface between the hydrophilic layer and the hydrophobic layer by
filtration. The PTFE layer supplied a large hydrophobic interface area to immobilize lipases
which is beneficial for lipase activation [284]. The ultrafiltration PVA layer played a key role
in controlling the enzyme loading and preventing enzymes from being dissolved into the
aqueous phase. Furthermore, the mass-transfer resistance of water and water-solubility
products through the hydrophilic membrane is lower than that through the hydrophobic dense
cortical layer of an asymmetric membrane, which could reduce the negative effect of
diffusion and product inhibition. A composite membrane with a porous PTFE layer and an
ultrafiltration PVA layer demonstrated high efficiency in immobilizing Candida rugosa
lipase. The immobilized enzyme membranes were used in a biphasic membrane reactor
(BMR) for the hydrolysis of olive oil. The optimum enzyme loading per unit membrane area
is 0.042 mg-protein cm-2. In the BMR, lipases on the surface of the membrane were removed
by the flow of organic phase, but the flow of the organic phase does not decrease the activity
of biocatalytic membranes. The lipase immobilized at the interface of the PTFE membrane
and PVA layer are stable. The maximum reaction rate per unit of membrane area (9.25 μmol
h-1 cm-2) is be higher than the value reported in the literature [285] (2.18 μmol h-1 cm-2) and
[286] (1.77 μmol h-1 cm-2). The immobilized lipase membrane in the BMR shows high
activity for more than 30 h of reaction, with little change in the activity.
One of the extensively used synthetic polymers used as a support for immobilization of
biocatalysts is polyacrylamide (PAAm) [287,288]. The major advantage is that it can be
polymerized either chemically or by using radiation. Advantages of γ-ray polymerization
against chemical polymerization is that the polymerization can be carried out even under
frozen conditions thus allowing the matrix to be molded to any form such as beads or
membranes [289-291]. However one of the major drawbacks of this polymer especially in a
membranous form is its brittleness.
PVA has also been extensively used for immobilization of biocatalysts in a membranous
form. As compared to PAAm, PVA is more hydrophilic and having adhesive property with
better tensile strength in dry conditions. But it has high swelling index and dissolves readily
in water when not cross-linked. PVA can be cross-linked using a variety of reagents including
γ-rays.
PVA/acrylamide blend membranes prepared on cheese cloth support by γ-irradiation
induced free radical polymerization can be used for urease entrapment. The enzyme urease is
entrapped in the membrane during polymerization process and using glutaraldehyde as crosslinking agent. The main advantage of this blend to this process is that it can be reused a
number of times without significant loss of urease activity [292].
But, glutaraldehyde (GA) is a well-known toxic reagent and its presence in the PVA
matrix as residuals unremoved by washing procedures could damage the organism tissues.
P.A. Ramires and E. Milella [293] proposed a technique of PVA/hyaluronic acid and PVAgellan membranes crosslinking, by using GA in vapors state. They evaluated the harmful
effects of GA residuals released from the membranes by the cytotoxicity and
cytocompatibility in vitro tests, based on the cell culture method. The results showed that
these materials have no toxic effects: they do not affect viability and proliferation nor exert
damages on mithocondrial and lysosomal functions. The use of GA in vapor phase as
154
crosslinking agent of natural and artificial polymer blends is demonstrated to be an effective
way to avoid the presence of toxic residuals into materials [293].
3.5. PVA and PVA Derivatives-Based Membranes
as Vapors and Gas Barrier
PVA films have high water-vapor permeability (water-vapor-transmission coefficient
PH2O is 270 g 0.1 mm/10 h m2 cm-Hg) [294] that increases rapidly with relative humidity and
with decrease in the hydrolysis degree.
PVA films have also a low gas permeability coefficient:
PH2 = 6.6 × 10-13 mL cm/(cm2 s cm-Hg); PO2= 6.24 × 10-17 mL cm/(cm2 s cm-Hg); PF2 <
-13
10 mL cm/(cm2 s cm-Hg); PN2 = 10-11 mL cm/(cm2 s cm-Hg); PCO2 = 10-13 mL cm/(cm2 s
cm-Hg) [294].
The gas permeability increases with increase the relative humidity, with decrease
hydrolysis degree of PVA, with increase temperature, and tends to decrease sharply as the
degree of crystallinity increases. The decrease in crystallinity and the decrease in Tg would be
expected to increase the gas permeability.
Because of its low gas permeability, PVA has excellent flavour-retaining properties [18].
Physical crosslinked PVA cryogel is considered to have a good permeability for oxygen
that is a desirable property for biomaterials [1].
Sometimes, in different systems, the oxygen presence is undesirable because of its
reactivity and tendency to oxidize the contact materials that leads to corrosion of metallic
materials or depreciation of food quality. Also oxygen could inhibit different chemical
reactions or could interfere in different analysis (RES, polaroghaphy, etc.).
Due to these practical aims, membranes with low oxygen permeability have been
developed. Some of them are PVA, PVA blends or their derivative membranes, due to the
PVA excellent oxygen barrier properties [18].
One of the PVA derivatives extensively used in this field is ethylene-vinyl alcohol
copolymer (EVOH). Their blends with different polyolefins are also effective as oxigen
barrier materials.
Blend film oxygen permeability is influenced by the film composition and morphology.
Generally, a heterogeneous structure, containing orientated fibrils and lamellae of EVOH
evidences lower oxygen permeability than that emphasized by a more homogeneous
morphology with finer dispersed particles (table 13 [295]).
The O2 permeability of the blends obtained in the batch mixer decreases (from 59.1 to
47.7 mm cm3/m2 day-1 atm-1 for EVOH / PPlv and from 53.6 to 43.3 mm cm3/m2 day-1 atm-1
for EVOH/ PPhv) with the increasing of EVOH content from 12.5 to 25 vol%.
The permeability for the extruded films was lower that those of the pressed films (22.1
mm-1 cm3/m2 day-1 atm-1 for 10 vol. % EVOH).
Dry EVOH/PP-g-maleic mldehyde (MAH) blend, obtained by moulded injection also
evidenced good barrier properties for toluene. This property is improved by increasing EVOH
concentration which determines both size and deformation of the minor phase increase,
indicating that the laminar structure becomes more pronounced [296]. But even the laminar
structure is maximized a moulded injection sample is not likely to reach a permeability as low
as expected for a multilayered system [296].
155
Oxygen and toluene permeability of the blend film decreases as a nonlinear function with
increasing the EVOH content, as it may be seen in table 19.
PPLv / (%)
PPhv / (%)
PP-g-MAH (%)
Remarks
HDPE / (%)
P O2 /
/ cm3 mm/
(m2 day-1 atm-1)
EVOH / (%)
Fibrils and lamellae
Fine dispersed
particles
Morphology
Table 18. Influence of the films “composition and of the blend
morphology on the films” permeability to O2 [295]
1225
1225
>25
-
X
-
-
58-80
Permeability independent of EVOH conc.
-
-
X
-
65-230
Permeability independent of EVOH conc.
-
-
X
-
>65
<12
<12
10
10
10
20
20
20
X
10
90
80
80
60
X
80
-
10
-
<65
<70
22-25
22.1
23.1-25.5
12.4
51.6
20
-
60
-
20
9.5
-interface between large particles of EVOH and
PP can run from one side to the other of the
film, created voids increasing the permeability.
-smaller EVOH particles .
-lover level of voids
-draw ratio=3.4
-draw ratio=2.8
-draw ratio=2.8-8.7
-draw ratio=3.4
-draw ratio=3.4
-poor adhesion between PP and HDPE
interfaces.
-draw ratio=3.2
-lamellae coexists with fibrils
HDPE= high density polyethylene; PPLv= polypropylene with low viscosity; PPhv= polypropylene
with high viscosity; PP-g-MAH= polypropylene graft maleic aldehyde.
Table 19. Oxigen and toluene permeability of melt-blended
EVOH-Nylon 6(L), measured at 30 ºC [297]
EVOH/Nylon 6(L)
100/0
75/25
50/50
25/75
0/100
P(oxygen)×1013
cm3 cm s-1 cm-2 cm-Hg-1
0.31
0.57
1.63
4.87
13.79
P (toluene)
g mm m-2 24h-1
0.08
0.10
0.14
0.23
0.29
The EVOH-COOH compatibilizer use determines the increasing of the blend film oxygen
permeability that becomes two orders of magnitude higher than that of a coextruded film with
the same percentage of EVOH [298]. That means that EVOH-COOH acts that an interfacial
agent.
Excessive emission of CO2 has caused the most dramatic increase in global atmospheric
temperature. So many countries’ governments and researchers pay much attention to how to
predict, control and reduce the amount of CO2, emission. Compared to the absorption and
156
adsorption techniques, membrane processes can be operated continuously and require less
energy for the separation or purification. However, commercial polymer membranes cannot
achieve both enough high selectivity and permeability to meet these needs. L. Xu et al. [299]
have shown that polyvinylidene fluoride (PVDF)-PVA hydrogel membranes contained
sodium carbonate solution and immobilized carbonic anhydrase can be used for removing
CO2 in air.
Hydrogel membranes are particularly attractive because of high permeability and
separation factor [300], and good stability for CO2/N2 separation [299]. PVDF hollow fiber
membrane modified by alkali was coated by PVA hydrogel on its surface and PVDF-PVA
hydrogel membranes show better hydrophilic performance. For carbonate hydrogel (sodium
carbonate concentration of 3.7 %) membrane, CO2, concentration from 1.3 % to 0.6 % in feed
gas could be decreased to 0.9-0.4 % at the outlet at 25 °C.
PVA/CELL blend could be also used to obtain the membranes with a low permeability
for CO2 [301].
In the last years, the replacement of gasoline with other new fuels became a priority
because of unavoidable depletion of natural petroleum sources.
The methanol/gasoline fuel has been proved to be one of the best replacements for
gasoline because of its low cost, high efficiency and low air pollution. Because of the
corrosive character of methanol, the metal vials for storing fuels have to be changed.
Polyolefins such as high density polyethylene (HDPE) have been considered as a potential
material for methanol/gasoline fuel storrage because of their low cost, lightweight, easy
design and processing, recyclability, safety, high chemical resistance to corrosion, and
flexibility. An important draw back of the HDPE use for this purpose is its poor permeation
resistance to hydrocarbon solvents, such as gasoline. Escaping of the gasoline vapor into the
atmosphere could determine serious environmental pollution.
Many efforts have been directed to finding methods that could reduce the HDPE
permeability. One of them is HDPE blending with polymers such as polyamide (PA) or PVA
with low permeability for hydrocarbons. To overcome the incompatibility between the nonpolar and polar polymers, a compatibilizer has to be present in these blends.
The high permeation resistance of the polymeric blend against the hydrocarbons depends
on the blend composition but also on the obtaining technique. So, multi-layer co-extrusion of
PE, compatibilizer precursor (CP) and PA, laminar blend blow molding of PE, CP and PA
blends, laminar blend blow molding of PE and modified PA (MPA) have been applied for
low permeation materials obtaining. Because PA and CP did not sufficiently increase the
HDPE permeation resistance, PVA has been introduced in the blend because of its recognized
high barrier qualities.
Good methanol/gasoline fuel permeation resistance together with clearly defined
MPAPVA and MPA laminar structures were found in containers blow-molded from
PE/PMPAPVA and PE/MPA blends, respectively, with an optimum CP of about 20 wt%
[302].
157
4. CONCLUSION
In the recent years, many researchers have devoted attention to the development of
membrane science and technology. Different important types of membranes, such as these
for: nanofiltration, ultrafiltration, microfiltration, separation of gases and inorganic
membranes, facilitated or liquid membranes, catalytic and conducting membranes, and their
applications and processes, such as wastewater purification and bio-processing have been
developed [303]. In fact, almost 40 % of the sales from membrane production market are for
purifying wastewaters.
Poly(vinyl alcohol) (PVA) has been characterized on many levels and examined for
numerous applications. It is a polymer of great interest because of its relatively simple
structure, easy processing, and potential use in biomedical and pharmaceutical fields. The
possibilities to control the PVA’s biodegradability make from PVA a friendly polymer. Also
the large possibilities to modify and control the PVA properties starting from synthesis
process (such as molar mass, hydrolysis degree, OH groups repartition on the polymeric
chain, tacticity) and also from its capability to react with a lot of reagents leading to polymer
analogous compounds or to be cross-linked by chemical or physical ways make from PVA a
versatile product. Also its capacity to be blend with other polymers or to be copolymerized
with different co-monomers or to be doped with organic or inorganic compounds or to
encapsulate drugs or enzymes enlarges the possibilities of PVA-based materials use. PVA
capability of film formation, its mechanical resistance, high optical properties and the
capacity of its hydrogels to swell in water and the hydrogels high sensitivity to the
environmental alterations could characterize PVA as an intelligent material with special
properties that could be tailored in function of the use interest.
Hydrogel membranes fulfill many of the important conditions for most of abovementioned application fields. Therefore, we have focused our paper on the applications of
PVA-based membranes in areas such as for separation membranar processes, fuel cells,
sensors, biochemical/medical applications, catalyst or PVA derivatives membranes as gas and
vapor barriers.
However, PVA is also extensively used in other different forms, such as gel matrices,
micro and nano spheres, aerosols, aqueous solution, films, powder etc. Although some of the
different types of PVA gels have been referred in chapter 3.3, it still remains much more to
say. This clearly proves that PVA is an old, yet new polymer or, in other words, an old
polymer with a promising future, due to its capacity to respond to all the actual society
priorities: clean technologies, non-toxicity, biocompatibility, biodegradability, intelligent
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Chapter 10
THE RESEARCH ON THE PROCESS OF THERMOMECHANICAL DESTRUCTION
IN POLYPROPYLENE
G. M. Danilova-Volkovskaya1 and E. A. Amineva2
1
Rostov-on-Don Agricultural Machinery State Academy
344023, Strana Sovetov Street, 1, Rostov-on-Don.
e-mail: [email protected]
2
Ushakov Naval State Academy
353900, Lenin Avenue, 93, Novorossiysk
ABSTRACT
There has been investigated the effect of thermo-mechanical impact conditions on
destruction kinetics in polypropylene melts. The conditions served as a basis for
obtaining quantitative dependencies and mathematical expressions aimed at describing
destruction processes.
Keywords: polypropylene, mechanical destruction, oxidation rate, hydroperoxides.
The research on the processes of mechanical destruction in deformed polypropylene (PP)
melts was conducted with the aid of stable radical (tripentachlorphenylmethyl) consumption.
There was defined the dependence of radical generation rate on shear rate. At low values γ it
is approximate to linear.
The rate of thermal priming of radicals at 220 °С equals Vi = 2.10 -7 mole/kg.sec.
The contribution of mechanical priming to the dependence of radical generation rate
becomes predominant as early as at γ =0,01 sec -1.
The temperature dependence of radical generation rate in the Arrhenius coordinates at
&
γ& =0,76 sec -1 has an extreme character (figure 1), passing the minimum at 200°С. The low
temperature part of the curve corresponds to negative activation energy which manifests the
predominance of mechanical priming process in this region. In the high-temperature region
168
G. M. Danilova-Volkovskaya and E. A. Amineva
thermal priming is substantially observed, activation energy in this part of the curve is
positive. Obviously, the area of minimal priming rates is optimal for processing since here
mechanical priming is not prominent any more, while thermal priming has not reached great
values yet. Under real processing conditions the position of the minimum at the temperature
dependence of priming rate can change due to the presence of oxygen. However, the
temperature defined in the current paper can be regarded as a starting point for searching
optimal temperature conditions.
At the initial period of mechanical destruction in a polypropylene melt in inert
atmosphere the concentration of macromolecules increases (figure 2). The dependence of
destruction rate (Vi ) on temperature is linear in the Arrhenius coordinates. After a certain
Figure 1. The temperature dependence of radical generation rate at γ& =0,76 sec -1.
Figure 2. The kinetics of changes in the concentration of PP macromolecules at thermo-mechanical impact:11800C, 2-2000C, 3-2300C.
The Research on the Process of Thermo-Mechanical Destruction in Polypropylene 169
period of thermo-mechanical impact (about 10 minutes) the concentration of macromolecules
−4
falls to a certain value (23.10 mole/kg), it doesn’t change further.
Oxidation decomposition of deformed isotactic PP manifests a number of noticeable
properties:
With the growth of deformation degree λ in polymer samples, the periods of oxidation
induction τ dramatically increase, τ is exponentially dependent on λ:
τ = τ 0 exp(aλ ) ,
(1)
where τ0 and a depend on oxygen pressure.
Oxygen uptake is described by a kinetic law:
[O2 ] = Ф2 (t −τ )2 ,
(2)
i.e. after induction period τ oxidation of an oriented polymer remains a chain degeneratebranch process with quadratic breakdown of kinetic chains. The law holds true only after
oxygen uptake equaling 2 . 10-2 mole/kg.
Orientation also influences initial oxidation rates, i.e. parameter Ф depends on λ but it
does not affect further stages, maximum oxidation rates don’t depend on λ at all. Upon
annealing the difference in the values of τ disappears.
The behaviour of chain-length distribution is non-characteristic: during thermal-oxidative
degradation of isotropic PP films the degradation shifts towards decrease in molecular mass,
while during oxidation in deformed films it shifts towards increase in molecular mass. It
means that with oxidation in isotropic samples in the induction period the destruction of
molecules prevails. On the other hand, with oxidation in deformed samples attachement and
cross-linking dominate.
A third peculiarity of oxidation in deformed PP is a dramatic decrease in the escape of
hydroperoxide, the main branching component. Hydroperoxide escape а sharply drops with
the growth of λ (figure 3), in accordance with equation
a = a 0 exp (− b λ ) ,
(3)
It implies that in deformed PP — unlike with oxidation of most isotropic non-deformed
polymers — oxygen changes into products other than peroxides (alcohols, ethers, ketones,
etc.).
This effect is not due to deformation impact on hydroperoxide stability: rate constants of
thermal decomposition of hydroperoxide in PP are the same for both isotropic and deformed
samples. Moreover, even at 20°С, when hydroperoxide is stable, its escape during radiationinduced oxidation sharply drops with the growth of λ.
At deformation there is no more than a slight change in degree of PP crystallization, at
annealing there is even an increase. Because oxidation is localized in the amorphous phase, it
was logical to expect that at annealing the induction period should grow and oxidation rate
170
G. M. Danilova-Volkovskaya and E. A. Amineva
should drop proportionally to degree of crystallization. Both of these suggestions fail;
therefore, the increase in thermo-oxidation stability in deformed PP is not connected with
changes in degree of crystallization.
Figure 3.The kinetics of oxygen uptake by deformed PP samples at deformation degree: λ:
= 0 (1), λ =
4,5 (2); λ = 7 (3); λ = 9 (4).
Neither is it connected with oxygen solubility and diffusion, since oxygen solubility in
deformed polymers decreases by 5-10 times, and diffusion coefficient lessens significantly.
Oxidation kinetics of oriented PP was measured under conditions of external priming.
The parameter specifying the oxidability of a polymer is slightly dependent on deformation.
For instance, at 200°С it only decreases by 1.5 times with λ changing from 0 to 10. This
unambiguously clarifies that the main reason for increase in thermal-oxidative stability of
deformed PP is a sharp drop in the escape of a branching agent (hydroperoxide), i.e. a
decrease in hydroperoxide escape.
This conclusion is consistent with experimental observations: in the induction period
chains are not initiated; after the induction period oxygen uptake occurs, but hydroperoxide
does not form, i.e. kinetic chains are missing. Oxygen is consumed only in priming events,
but the escape of radicals is insignificant and oxygen uptake in a chain reaction is negligibly
small. In priming events internal interaction of radicals prevails, which provides for
recombination, cross-linking and shift of chain-length distribution towards greater masses.
The nature of these interactions has not been explicitly defined, it could be explained by
disproportionation [1].
This accounts for low values of hydroperoxide escape, formation of cross-links and
alcohol groups during initial periods of deformed PP oxidation.
Chain decomposition of hydroperoxide, formed by means of valence transfer along the
molecule, is considered to be another reason for decrease in hydroperoxide escape.
Thus, slowdown in valence transfer rate and a dramatic decrease in the escape of radicals
during priming lead to depression of the oxidation process and to the lessening of branching
agent escape. Oriented deformation behaves like substances decomposing hydroperoxide
without formation of radicals, i.e. it is a means of “stabilisation in absence of a stabilser”.
The conducted investigations and the obtained quantitative dependencies and expressions
were used for developing a method of criterial assessment of the degree of thermo-
The Research on the Process of Thermo-Mechanical Destruction in Polypropylene 171
mechanical destruction in PP melts during processing under the conditions of intensive shear
deformations[2]
Figure 4.The kinetics of hydroperoxide formation in PP samples at deformation degree: λ = 0 (1), λ = 4,5 (2);
λ = 7 (3); λ = 9 (4).
CONCLUSIONS
There has been investigated the effect of thermo-mechanical impact conditions on
destruction kinetics in polypropylene melts. The conditions served as a basis for obtaining
quantitative dependencies and mathematical expressions aimed at describing destruction
processes.
REFERENCES
[1]
[2]
Baramboymb I.K. Mechanochemistry of high-molecular substances. – 3rd edition.
Moscow. The Chemistry publishing house, 1978, p. 34.
Danilova-Volkovskaya G.M. The effect of processing parameters and modifiers on the
properties of polypropylene and PP-based composite materials. — Doctoral Thesis
(technical sciences). 2005, p. 273.
Chapter 11
ZINCCONTAINING POLYMER - INORGANIC
COMPOSITE AS VULCANIZATION ACTIVE
COMPONENT FOR RUBBERS OF GENERAL AND
SPECIAL ASSIGNMENT
V. I. Ovcharov, I. A. Kachkurkina, O. V. Okhtina
and B. I. Melnikov
Ukrainian State Chemical-Technological University,
Dnepropetrovsk, Ukraine; [email protected]
ABSTRACT
In work the synthesis technology of zinccontaining polymer - inorganic composite
on the basis of products of secondary raw material processing at joint precipitating with
carbamide and formaldehyde (ZnCFO) is described.
The structure and properties of ZnCFO are investigated by the differencial-thermal
analysis, electronic microscopy and IR-spectroscopy.
The ZnCFO action as vulcanization active component of elastomeric compositions
on the basis of rubbers of general and special assignment with various vulcanization
systems is investigated.
The comparative estimation of ZnCFO efficiency depending on type of vulcanization
system is given.
The ZnCFO influence on character of formed morphological structure of rubbers is
determined by the method of percalation analysis.
Key words: Polymer-inorganic composite; Vulcanization active component; Elastomeric
composition; Vulcanization; Morphological structure; Physical-mechanical properties.
174
V. I. Ovcharov, I. A. Kachkurkina, O. V. Okhtina et al.
INTRODUCTION
Despite of 150-year's history of vulcanization process, it is impossible to consider that
fundamental and applied researches in direction of vulcanization systems perfection are
completed. For today one of the ways of rubbers properties improvement is the synthesis and
application of the new chemicals-additives, including, vulcanization active, that is connected,
first of all, with reduction of global stocks of zinc ores as basic raw material for reception of
traditional activator - zinc oxide. Besides, modern increase of industrial potential and the
accumulation of big quantity wastes derivate the problems of ecological character, which
require the emergency decision. Therefore creation of resourcesaving technologies of the new
compounds reception from products of secondary raw material processing has paramount
importance.
EXPERIMENTAL
Taking into account above told, in the work the efficiency of zinccontaining carbamideformaldehyde composite (ZnCFО) as vulcanization active component of various
vulcanization systems for rubbers of general and special assignment is investigated for the
first time.
The technological circuit of ZnCFО synthesis is developed in the Ukrainian State
Chemical-Technological University. ZnCFО is the product of reaction of carbamide and
formaldehyde polycondensation in zinc salts solution at recycling of metalcontaining wastes
of chemical manufactures. The material base of ZnCFО manufacture are fulfilled catalysts,
solutions from zincing and others zinccontaining wastes of various origin.
The maximal degree of zinc extraction (φ Zn2+) = 95-98 % and mass ratio of zinc
hydroxide to carbamide-formaldehyde component in composite (mZn(OH)2 : mCFО) = 1:0,7-1 is
achieved at the observance of the following technological parameters: temperature (Т) = 2535 0С; concentration of zinc salts in solution (с Zn2+) = 150-170 g/l; pH of zinc salts solution =
2; pH of the reactionary mix at complete precipitating Zn2+ = 7-8; pH of the reactionary mix
at polycondensation = 3-5; mole ratio of carbamide to formaldehyde (nC : nF) = 1:1 [1,2].
Figure 1. EM micrographs of the ZnO (a) and ZnCFO (b) particles (increase in 10000 times)
Zinccontaining Polymer - Inorganic Composite as Vulcanization…
175
The electronic microscopy method on the EM-125 (fig. 1) for definition of ZnCFО
particles size and characteristic of its surface was applied. Known zinc oxide was chosen as
the object of comparison. The electronic photos of powders testify, that new composite and
zinc oxide have external similarity under the form of particles, wide range on dispersiveness
(0,4-6,0 microns for zinc oxide, fig. 1a; 0,3-6,0 microns for ZnCFО, fig. 1b) also contain as
crystal as amorphous phases in their structure.
0
0
810 C
a)
0
450 C-460 C
exo
20
0
endo
40
Zn(OH)2
CF
ZnCF
0
0
200
b)
180 C
100
170 C -
0
0
80
90 C-100 C
60
400
600
800
0
t, C
1000
m, %
0
Zn(OH)2
CF
ZnCF
10
20
30
40
50
200
400
600
800
0
t, C
1000
Figure 2. Results of derivatographic researches of Zn(OH)2, CFO and ZnCFO: a – DTA curves, b – TG
curves
The definition of thermal stability of inorganic zinccontaining (Zn(OH)2), organic
carbamide-formaldehyde (CFO) components and ZnCFО composite was carried out by the
method of differencial-thermal analysis on the derivatograph "Q-1500 D" of F. Paulik, J.
176
Paulik, L. Erdey system in the temperature range 20-1000 0C at heating rate 10 0C/min and
mass of samples 200 mg. DTA and TG curves of researched products are given on fig. 2.
How it is shown, endothermic peak on DTA curve of Zn(OH)2 and greatest loss of weight at t
≈ 150 – 160 0C are caused by transition of hydroxide in oxide. DTA curves of CFO and
ZnCFО have external similarity on character of the thermal effects, however, for ZnCFО the
shift of maximum in range of lower temperatures is observed. So, peaks at t ≈ 90 – 100 0C are
caused by loss of atmospheric moisture containing in samples. Endothermic maximum and
greatest loss of weight (≈ 35 %) in temperature range 260 – 270 0C characterize the beginning
of CFO thermodestruction, and secondary exothermic peak at t ≈ 560 0C is caused by the
subsequent decomposition of sample. Unlike CFO on DTA curve of ZnCFО the first
endothermic maximum is observed at t ≈ 170 – 180 0C, and secondary exothermic - at t ≈
450 – 460 0C, describing decomposition of organic component. The occurrence of new
endothermic peak in range t ≈ 810 0C testifies about expansion of temperature range of
ZnCFО destruction process in comparison with CFO, because the temperature interval of
weight loss for CFO is 260 – 560 0C, and for ZnCFО - 170 – 810 0C, and ZnCFО has
extremely greater rest of weight. It is necessary to note, that ZnCFО at thermal action is
decomposed not achieving a melting point, that was confirmed by the method of definition of
melting temperature in capillary [3,4]. During experiment the intensive escape of gas and
change of sample colour from white to grey at temperatures 170 0C and 220 0C, appropriating
to first endothermic peak on DTA curve, were visually observed.
110
T, %
Zn(OH) 2
CFO
ZnCFO
2360
100
1384
90
80
70
1640
1550
60
50
1120
40
3350
30
20
10
400
800
1200
1600
2000
2400
2800
3200
3600
v, cm
4000
-1
Figure 3. IR-spectrums of absorption of ZnCFO and its inorganic (Zn(OH)2) and organic (CFO) parts
The study of ZnCFО also was carried out by the method of IR-spectroscopy on
spectrometer UR-20. For detection of possible chemical bonds between inorganic and organic
components in ZnCFО the spectras of Zn(OH)2, CFО and ZnCFО were studied (fig. 3) . As it
is shown, IR-spectrum of ZnCFО repeats the characteristic absorption bands of CFО at 3350,
1640 and 1550 cm-1, caused by presence of secondary amide group [5], at the same time the
177
H
R2C
N
group, is
intensity of absorption band in range 2340-2360 cm-1, identifying
considerably decreased [6]. In comparison with IR-spectrum of Zn(OH)2 on ZnCFО spectrum
the intensity of characteristic absorption band at 1384 cm-1 is decreased. The distinctive
feature of ZnCFО spectrum is the presence of absorption band at 1120 cm-1, which probably
corresponds to bonds (for example, coordination) between inorganic and organic components
of the composite. It is possible to assume, that the coordination bonds in the composite arise
H
R2C
N
group and zinc in Zn(OH)2.
between nitrogen atom of
The researches of ZnCFО compatibility with the matrix of isoprene rubber in plasticorder
"Brabender" PLE 6511 have shown, that the disperse process of composite is accompanied by
lower power consumption and its best compatibility in comparison with zinc oxide (fig. 4).
The absence of ZnCFО particles as extraneous impurities in rubber mix also was visually
observed, while the zinc oxide particles were well appreciable [7].
ZnCFO
ZnO
MV, N*m
70
65
60
55
50
45
0,0
2,5
5,0
7,5
activator, phr.
Figure 4. Rheological properties of the modeling unfilled rubber mixes on the basis of isoprene rubber with a
various type and contents of sulfur vulcanization activators
That is, the given results of experimental researches have confirmed composite,
chemically connected structure of ZnCFО with presence of functionally active groups, which
due to the organic-inorganic nature has certain relationship with a rubber matrix, is easy
dispersed and combined with its.
An estimation of ZnCFО efficiency as vulcanization active component was carried out in
modelling unfilled elastomeric compositions on the basis of isoprene, butadiene-nitrile,
chloroprene and butyl rubbers of sulphur, thiuram, peroxide, metaloxide and resin
vulcanization systems.
1 The researches were carried out by the professor E. Djagarova at University of Chemical Technology and Metallurgy (Sofia, Bulgaria)
178
The rubber compounds were mixed in a laboratory internal mixer, the tests of elastomeric
compositions were carried out according to working techniques and requirements of state
accepted standard [8,9].
The influence of ZnCFО concentration (3,0; 5,0; 7,0 phr) on formation of properties
complex of the unfilled rubber mixes and their vulcanizates on the basis of isoprene rubber of
the following recipe, phr: isoprene rubber - 100,0; sulfur - 1,0; di - (2-benzothiazolyl) disulfide - 0,6; N, N'-diphenylguanidine - 3,0; stearic acid - 1,0, was carried out in
comparison with the known activator - zinc oxide (5,0 phr). The analysis of Rheometer data
of sulfur vulcanization process of elastomeric compositions at 1550C (fig. 5) shows, that on
crosslink density and cure rate, about what the constants of speed in the main period (k2)
testify, they surpass the control composition with 5,0 phr of zinc oxide. Improvement of the
complex of elastic - strong parameters of rubbers with ZnCFО as at normal test conditions,
and after thermal air aging (tab. 1), probably, is caused by influence of the new activator on
vulcanization network character. So, the percent part of polysulfide bonds (C-Sx-C) and
amount of sulfur atoms appropriating to one crosslink (S atoms/crosslink) in vulcanizates
with ZnCFО are decreased, the percent part of disulfide bonds (C-S2-C) is increased (fig. 62).
M, dN*m
20
18
4
3
2
16
1
14
12
10
8
6
4
0
5
10
15
20
25
t,m in
30
Figur 5. Rheometer data of sulfur vulcanization process of modeling unfilled elastomeric compositions on the
basis of isoprene rubber at 1550C with ZnCFO as the activator:
1 – ZnO – 5,0 phr., k2 = 0,47 min-1;
2 - ZnCFO – 3,0 phr., k2 = 0,51 min-1;
3 - ZnO – 5,0 phr., k2 = 0,58 min-1;
4 - ZnO – 7,0 phr., k2 = 0,69 min-1
2 The researches were carried out by the professor W. M. Rzymski at Technical University (Lodz, Poland).
179
Table 1 Properties of the modeling unfilled vulcanizates on the basis of isoprene rubber,
containing various concentration of the ZnCFO activator
Parameter
ZnO
5,0 phr.
10,0/9,0*
27,0/20,5
890/735
39/28
38/35
62/60
300% Modulus, MPa
Tensile strength, MPa
Elongation at break, %
Tear strength, kN/m
Shore A hardness
Elasticity, %
Activator type
ZnCFO
3,0 phr.
5,0 phr.
10,0/9,0 11,0/10,0
26,0/22,4 28,5/22,8
830/750
835/750
41/38
43/39
40/36
42/38
66/64
69/65
7,0 phr.
10,0/9,0
20,6/19,4
835/730
40/32
42/38
68/64
The note: * - in the denominator the parameter value after thermal aging of the sample at 1000C×24 hrs
is given
ZnO as activator of sulfur
vulcanizat ion system
S
atoms
/ crosslink = 7,6
70%
26%
4%
ZnCFO as activator of sulfur
vulcanization system
S
atoms
/ crosslink = 7, 3
68%
28 %
4%
Figure 6. Influence of activator type on vulcanization network character of the elastomeric compositions:
- % part of C – Sx – C bonds;
- % part of C – S2 – C bonds;
- % part of C – S – C bonds.
180
That is, the analysis of the received results, has shown an opportunity of equal-mass
replacement of the traditional activator - zinc oxide on the new polymer - inorganic composite
(5,0 phr) at maintenance of a high activation level of sulfur vulcanization process of rubber
mixes on the basis of diene isoprene rubber and improvement of the physical-mechanical
properties complex of their vulcanizates.
sulfur vulcanization
system
ZnO 5,0 phr.;
M, dN*m
=0,29 min
-1
ZnO 3,0 phr.;
ZnCF
3,0 phr.;
2
=0,22 min
-1
ZnCF
5,0 phr.;
=0,25 min
2
-1
=0,29 min
-1
ZnCF
30
2
thiuram vulcanization
system
7,0 phr.;
2
M, dN*m
24
24
2
=0,33 min
-1
ZnCF
3,0 phr.;
=0,41 min
-1
2
Zn
5,0 phr.;
=0,56 min
2
-1
Zn
7,0 phr.;
=0,58 min
-1
2
18
18
12
12
6
6
0
5
10
15
20
25
0
30
5
10
15
20
25
30
t, min
t, min
peroxide vulcanization
system
ZnO 3,0 phr.;
M, dN*m
28
=0,11 min
-1
2
-1
ZnCF
3,0 phr.;
2
=0,08 min
ZnCF
5,0 phr.;
2
ZnCF
7,0 phr.;
2
-1
=0,12 min
-1
=0,13 min
24
20
16
12
8
4
0
5
10
15
20
25
30
t, min
Figure 7. Cure curves of vulcanization process of modeling unfilled elastomeric compositions on the basis of
nitrile-butadiene rubber at 1550C with various vulcanization systems.
181
It is known, that zinc oxide is not only activator of sulfur vulcanization of diene
rubbers, but also component of others vulcanization systems, therefore the further
research of the ZnCFО efficiency was carried out in elastomeric compositions on the basis of
polar butadiene nitrile rubber of general and special assignment of sulfur, thiuram and
peroxide vulcanization.
Influence of the ZnCFО contents (3,0; 5,0; 7,0 phr) on crosslink kinetics of the modelling
unfilled rubber mixes from NBR-26 of sulfur, thiuram and peroxide vulcanization of recipe,
phr: NBR-26 - 100,0; sulfur - 1,5; 2-mercaptobenzthiazole - 0,8; stearic acid – 1,5;
tetramethylthiuramdisulfide - 3,0; peroximon F-40 - 3,0, is possible to estimate on the data of
fig. 7. As it is shown, the increase of ZnCFО concentration results in increase of the
maximum torque and, accordingly, crosslink degree of elastomeric compositions, decrease of
optimum cure time, that, in turn, causes increase of cure rate, confirmed by counted constants
of speed in the main period (k2). The analysis of vulcanizates physical-mechanical properties
testifies, that with the increase of ZnCFО contents increase the tensile strength, hardness,
resilience; elongation at break and residual deformation at compression on 20 %. That is,
ZnCFО is effective component of given vulcanization systems, as at equal-mass replacement
of known zinc oxide (5,0 phr) the cure rate, the concentration of crosslink bonds are increased
and general properties complex of rubber mixes and their vulcanizates is improved.
M, dN*m
75
ZnCF
ZnCF
ZnCF
60
3,0 phr.;
5,0 phr.;
7,0 phr.
45
ZnO 3,0 phr.;
ZnO 5,0 phr.;
ZnO 7,0 phr.
30
15
0
5
10
15
t, min
Figure 8. Cure curves of metaloxide vulcanization process of modeling unfilled elastomeric compositions on
the basis of chloroprene rubber at 1550C with various type and contents of vulcanization agents
The comparative estimation of efficiency of zinc oxide and ZnCFО similar
concentrations (3,0; 5,0; 7,0 phr) as the agents of metaloxide vulcanization system was
carried out on example of modelling unfilled elastomeric compositions from chloroprene
rubber of recipe, phr: chloroprene rubber - 100,0; magnesium oxide - 7,0. Kinetic curves of
rubber mixes curing process at 1550C are shown on fig. 8. The analysis of the submitted data
testifies, that at increase of zinc oxide contents vulcanization kinetics is changed as follows:
the scorch time and optimum cure time are decreased, the cure rate is increase. Vulcanization
182
process of rubber mixes at ZnCFО presence proceeds similarly, however, they surpass on 1522 % compositions with zinc oxide on crosslink degree parameter. The estimation of elastic strong properties of rubbers in vulcanization optimum has shown, that ZnCFО provides them
higher parameters level and resistance to thermal air aging (tab. 2).
Table 2. Properties of modeling unfilled elastomeric compositions on the basis of
chloroprene rubber in vulcanization optimum
Parameter
Contents of ZnO, phr
Contents of ZnO, phr
3,0
5,0
7,0
3,0
5,0
7,0
Tensile strength, MPa,
unaged samples
22,2
25,5
28,3
24,1
26,3
28,9
0
17,8
20,4
22,6
19,5
21,3
23,4
0
16,2
18,6
20,7
17,6
19,5
21,3
120 С×12 hrs
120 С×24 hrs
Tear strength, kN/m
unaged samples
32
37
38
33
37
39
0
23
26
27
26
29
31
0
27
31
33
29
33
35
120 С×12 hrs
120 С×24 hrs
For continuation of research of ZnCFО efficiency in structure of various vulcanization
systems its was entered into the rubber mix on the basis of butyl rubber of resin vulcanization
of following recipe, phr: butyl rubber-1675 - 100,0; amberol ST-137 - 5,0; stearic acid - 3,0,
at equal-mass replacement of zinc oxide (3,0 phr). The influence of ZnCFО on kinetics of
resin vulcanization at 1600C is shown in a fig. 9, which analysis testifies, that in comparison
with control mix the researched composition is characterized by decrease of crosslink degree,
preservation of scorch time and reduction of optimum cure time, causing increase of cure rate.
I.e., at ZnCFО use as a component of resin vulcanization the acceleration of formation
process of crosslinking network with low density of crosslink bonds is observed which
explains the unsatisfactory level of physical-mechanical parameters of rubber. The ZnCFО
negative influence on properties of elastomeric compositions of resin vulcanization is caused
by interaction between the vulcanization agent (phenol-formaldehyde resin on the basis of poctylphenol – ST-137) and ZnCFО, that results in desactivation of resin as crosslinking agent
of resin vulcanization system.
183
M , dN*m
ZnO - 3,0 phr.
24
22
ZnCF
- 3,0 phr.
20
18
16
14
12
0
10
20
30
40
50
t, m in
60
Figure 9. Vulcanization kinetics of modeling unfilled elastomeric compositions on the basis of butyl rubber
of resin vulcanization at 1600C with ZnO or ZnCFO
Thus, from the analysis of results of experimental researches on estimation of ZnCFО
vulcanization activity in comparison with zinc oxide in structure of various vulcanization
systems (VS) follows, that its efficiency decreases in line (fig. 10):
sulfur VS > thiuram VS > metaloxide VS > peroxide VS > resin VS
%
40
35
30
25
20
15
10
5
0
sulfur VS
thiuram VS
metaloxide VS
peroxide VS
Figure 10. Change of elastomeric compositions properties (%) with various vulcanization systems at ZnCFO
presence (in comparison with ZnO):
- crosslink degree (∆М, dN·m);
- tear strength (В, кN/m).
184
Taking into account the ZnCFО positive influence on formation of the complex of the
physical-mechanical characteristics of vulcanizates on the basis of various rubbers and
theoretical preconditions about interrelation "recipe - structure - property", it was interested to
define the morphology features of elastomeric compositions. With this purpose the
percalation method of the analysis by the rheometer data of rubber mixes was used [10].
According to the theory of interrelation "recipe - structure - property" the maximum level
of the physical-mechanical characteristics of elastomeric compositions is realized at condition
of heterogeneous structure formation with the minimal particles size of heterophase (r - value,
opposite to tangent of the corner of kinetics curve inclination) and its optimum contents. The
analysis of data submitted on the fig. 11 shows, that replacement of zinc oxide on ZnCFО
composite in various vulcanization systems for rubbers of general and special assignment
influences on morphological structure of compositions, reducing the particles size of
heterophase and providing thus high complex of the elastic-strong properties of vulcanizates.
It is necessary to note, that at increase of the ZnCFО contents from 5,0 up to 7,0 phr
parameter r essentially does not change and keeps the minimal value. I.e., the best complex of
properties have the compositions with ZnCFО, in which the morphology with the minimal
particles size of heterophase is formed at its contents ≈5,0 phr. The given statement is
coordinated with the results of physical-mechanical tests of vulcanizates, received by
experimental method.
isoprene rubber of sulfur vulcanization
nitrile-butadiene rubber of sulfur vulcanization
nitrile-butadiene rubber of thiuram vulcanization
nitrile-butadiene rubber of peroxide vulcanization
chloroprene rubber of metaloxide vulcanization
r
isoprene rubber of sulfur vulcanization
nitrile-butadiene rubber of sulfur vulcanization
nitrile-butadiene rubber of thiuram vulcanization
nitrile-butadiene rubber of peroxide vulcanization
chloroprene rubber of metaloxide vulcanization
r
0,40
0,40
0,36
0,36
0,32
0,32
0,28
0,28
0,24
0,24
0,20
0,20
0,16
0,16
0,12
0,12
0,08
0,08
0,04
0,04
0,00
0,00
0
1
2
3
4
5
6
7
0
1
2
3
4
contents of ZnO, phr
a)
5
6
7
contents of ZnCFO, phr
b)
Figure 11. Dependence of particles size of heterophase of modeling unfilled compositions on the basis of
various rubbers with different vulcanization systems from the ZnO (a) or ZnCFO (b) contents
It is possible to explain the decrease of ZnCFО efficiency as component of various
vulcanization systems for rubbers of general and special assignment in the earlier submitted
line (fig. 10) also by character of formed morphology of compositions. So, at use of ZnCFО
as the activator of sulfur vulcanization the structure of rubbers with the minimal value of
parameter r is formed, and at transition from sulfur to peroxide vulcanization of elastomeric
compositions the particles size of heterophase is increased (fig. 11 b).
185
CONCLUSION
Generalizing results of researches of the ZnCFО efficiency as the component of various
vulcanization systems for rubbers of general and special assignment, it is possible to make the
following conclusions:
1. ZnCFО is the chemically connected composite with presence of functionally active
groups, which due to the organic-inorganic nature, is easy dispersed and combined
with rubber matrix;
2. ZnCFО is the effective vulcanization active component of the sulfur, thiuram,
peroxide and metaloxide vulcanization systems for isoprene, nitrile-butadiene and
chloroprene rubbers; at the same time it is not effective in resin vulcanization system
for butyl rubber. On a degree of positive influence on the properties of elastomeric
compositions vulcanization systems with ZnCFО are arranged in a line:
sulfur VS > thiuram VS > metaloxide VS > peroxide VS;
3. ZnCFО at the contents ≈5,0 phr promotes to formation of morphological structure of
compositions with the minimal particles size of heterophase, that is realized in the
improvement of physical-mechanical properties of rubbers.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
Melnikov B.I., Perekhrest O.A., Demidov D.V., Machula S.L. // Khimichna
Promislovist Ukraini. 2000. N 3. P. 32-35.
Kachkurkina I.A., Ovcharov V.I., Okhtina O.V. // Voprosi Khimii i Khim.
Tekhnologii. 2005. N 5. P. 134-139.
Uendland U. Termicheskie metodi analyza. Mir, Moskva, 1978. P. 526.
Ćwiczenia laboratoryjne z chemii I technologii polimerów / Pod red. Ireny
Słowikowskiej. Ofycyna Wydawnicza Politechniki Warszawskiej, Warszawa, 1997.
P. 244.
Kalinina L.S. Kachestvenniy analyz polimerov. Khimiya, Moskva, 1975. P. 248.
Gordon A., Ford R. Sputnik khimika. Mir, Moskva, 1976. P. 541.
E. Djagarova, D. Jeveleva, Z. Zdravkov. Une possibilité d’élargir l’information
obtenne par le plasticorder Brabender // J. of the Univ. of Chem. Technology and
Metallurgy. 2002. V. 37. N 3. P. 71-78.
Averko-Antonovich I.U., Bikmullin R.T. Metodi issledovaniya strukturi I svoystv
polimerov. Kazan. Gos. Tekh. Univ., Kazan, 2002. P. 604.
Laboratorniy praktikum po tekhnologii rezini. Osnovnie svoystva rezin i metodi ih
opredeleniya. Khimiya, Moskva, 1976. P. 240.
N.M. Gavriluk // Khimichna Promislovist Ukraini. 1996. N 4. P. 37-41.
Chapter 12
FORMATION OF CARBON NANOSTRUCTURES AND
SPATIAL-ENERGY STABILIZATION CRITERION
G. А. Korablev* and G. E. Zaikov*
Institute of biochemical physics after N.M. Emanuel,
119991, 4 Kosygina St., RAS, Russia, Moscow
ABSTRACT
Spatial-energy criterion of structure stabilization was obtained. The computation
results for a hundred binary systems correspond to the experimental data. The basic
regularity of organic cyclic compound formation is given and its application for carbon
nanostructures is shown.
Keywords: spatial-energy parameter, compound stabilization, carbon nanostructures.
INTRODUCTION
The problem of a priory assessment of stable structure formation is one of the main
problems of chemical physics and material science. Its solution, in turn, is directly linked with
the regularities of isomorphism, solubility and phase-formation in general. Surely, such
problems can be cardinally solved only based on fundamental principles defining the system
of physical and chemical criteria of a substance and quantum-mechanical concepts of physics
and chemistry of a solid suit it.
*
*
G.А. Korablev: E-mail: [email protected]
G.E. Zaikov: E-mail: [email protected]
G. А. Korablev and G. E. Zaikov
188
But many computations of phase-formation based on the application of pseudo-potential,
quantum-mechanical techniques, statistic-thermodynamic theories are carried out now only
for comparatively small number of systems, for instance [1-3]. A lot of papers dedicated to
the phenomenon of isomorphic replacement, arrangement of an adequate model of solids,
energy theories of solid solutions, for instance [4-7]. But for the majority of actual systems
many problems of theoretical and prognostic assessment of phase-formation, solubility and
stable phase formation are still unsolved.
This paper is developing the method where complex initial characteristics of an atom are
used as a criterion of structure stabilization.
SPATIAL-ENERGY PARAMETER (Р-PARAMETER)
The introduction of Р-parameter as a criterion of structural interactions is based on the
assumption that the resulting energy in the system: orbital-nucleus, immediately responsible
for inter-atomic interactions, can be calculated based on the principle of adding reverse values
of some primary atom characteristics in initial state [8]. In this model Р0-parameter is a
tabulated constant spatial-energy characteristics of each orbital of an atom.
The criterion
Р
E
=
Р
r
0
has a physical sense of some averaged energy of valence
i
electrons in the atom at a distance ri from the nucleus.
The reliability of initial equations and regulations was proved with numerous calculations
and comparisons. In particular, it was shown [8] that РE-parameter numerically equals the
energy of valence electrons in a statistical atom model and is a direct characteristic of electron
density in the atom at the given distance from the nucleus.
Spatial-energy principles of isomorphic replacement were found:
1. Complete (100%) isomorphic replacement at approximate equality of P-parameters
of valence orbitals of interchangeable atoms:
Р
'
E
≈ РE
"
2. Р-parameters of atom valence orbital with the least value determine the orbital that is
mainly responsible for isomorphism and structural interactions.
But isomorphism is a particular case of phase-formation. Therefore, when we take its
ratios as a basis and take coordination into account it can be assumed that the following
condition has to be performed for atoms of a stable homogeneous crystalline structure:
Р
К
'
or:
≈ Р
К
"
E
1
⎛ Р0 N
⎜⎜
⎝ Kr
E
(1)
2
⎞ ⎛ Р0 N
⎟⎟ ≈ ⎜⎜
⎠ ⎝ Kr
1
⎞
⎟⎟
⎠
2
;
Р1 ≈ Р 2
(2)
Formation of Carbon Nanostructures and Spatial-Energy Stabilization Criterion
where:
Р
E
=
РN
0
r
189
, К – coordination number of atoms, r – dimensional bond
characteristic of the given atom, N – number of homogeneous atoms in the compound
formula.
Based on the physical sense of РE-parameter the given condition (2) is the condition of
equality of effective values of structure atom orbitals (in the assumption of paired inter-atom
interaction). In a more complicated case when the central atom (A1) has heterogeneous
surroundings consisting of atoms (А2, В, С) at different inter-nuclear distances, the condition
of stable structure formation looks as follows:
''
'''
' N
P0 N
1
N
= P 0 + P 0 N 2 + P 0 3 + ...
Kr
К 1 r1 К 2 r 2 К 3 r 3
(3)
Here, the left-hand part of equation refers to the central atom, and the right-hand part of the
equation refers to the atoms surrounding it.
Let us apply the correlations (2, 3) to some types of crystalline structures using tabulated
values of Р0-parameters calculated and given in [8]. At the same time, for structures with
basic ionic and metallic bond the values of Р0-parameters calculated via the atom ionization
energy (Е) were used – table 1.
CRYSTALS WITH BASIC IONIC BOND
Equation (2) contains the value of actual dimensional bond characteristic of the given
atom in the structure. In crystals with basic ionic bond, the ion radius can be applied as such
dimensional bond characteristic (with a certain approximation), i.e. the stabilization condition
for such structures is as follows:
N 1 Р '0 N 2 Р "0 ⎛ Р E ⎞ ⎛ Р E ⎞
≈
;⎜
⎟ ≈ ⎜ ⎟ ; Р1 ≈ Р 2
К 1 r к К 2 r а ⎝ К ⎠1 ⎝ К ⎠2
(4)
where rk – cation radius, ra – anion radius.
Table 2 contains the results of some calculations following the equation (4) for several
structures, such as NaCl. In all calculations mainly the ion radii by Belov-Bokiy (first line)
and partly – Goldschmidt and Poling (second line) were used. Comparisons of such
calculative parameters (РE/К) of structure atoms (7th and 8th columns) prove the equality of
these values with the precision of up to 25%.
To determine the structure type from equation (4) it is necessary to calculate the ratio of
coordination number of cation and anion (K1/K2) and taking into consideration the ratio of
cation and anion radii values (in the model of rigid spheres), the structure itself can be
determined.
Table 1. Р–parameters of some atoms calculated via the ionization energy
Atom
Н
С
N
O
F
Cl
Br
I
Na
Al
Fe (II)
Fe (III)
Σ Р0
Рi =
ΣР 0
ri
(Å)
q2
(eVÅ)
Р0
(eVÅ)
13.595
11.260
24.383
47.860
0.5295
0.596
0.596
0.620
14.394
35.395
35.395
37.243
4.7985
5.641
10.302
16.515
4.7985
(eV)
9.0624
2s1
64.480
0.620
37.243
19.281
51.739
86.810
2p1
2p1
2p1
2s1
2s1
2p1
2p1
2p1
3p1
4p1
5p1
3s1
3p1
3s1
3s1
4s1
4s1
3d1
14.54
29.60
47.426
77.472
97.89
13.618
35.118
17.423
12.268
11.84
10.451
5.138
5.986
18.829
28.440
7.893
16.183
30.64
0.488
0.487
0.487
0.521
0.521
0.414
0.414
0.360
0.728
0.851
1.044
1.713
1.311
1.044
1.044
1.227
1.227
0.365
52.912
52.912
52.912
53.283
53.283
71.380
71.380
94.641
59.842
73.346
77.65
10.058
26.44
27.119
27.119
26.57
26.57
199.95
6.257
11.329
16.078
22.966
26.012
5.225
12.079
5.882
8.125
8.859
9.567
4.694
6.055
11.396
14.173
7.098
11.369
10.564
6.257
17.586
33.664
56.63
82.642
5.225
17.304
5.882
8.125
8.859
9.567
4.694
12.822
36.111
68.984
108.69
158.62
12.621
41.797
16.389
11.161
10.410
9.1638
2.7402
31.624
23.939
18.462
15.046
29.026
23.656
Valence
orbitals
Е (eV)
1s1
2p1
2p1
2s1
ri
(eVÅ)
ri (Å)
Рi =
ΣР0
ri
Note
1.36
(eV)
3.528
for Н-
2.60
0.20
19.900
258.7
for С4for С4+
1.48
22.746
for N3-
0.15
1.36
1.36
1.345
1.81
1.96
2.20
0.98
550.9
3.8419
12.724
4.3774
4.4890
4.5199
4.3486
4.7898
for N5+
for Ofor О2-
191
Table 2. Spatial-energy criterion of stable phase formation
in the structures of Na-Cl type
Atom
Structure
Orbital
Po
(eVÅ)
К
ri
(Å)
Р'e/к1
F
М'F
2р1
2s1
5.882
6.432
6
6
1.33
1.33
1.36
0.737
0.806
0.786
Cl
M'Cl
3р1
8.125
6
1.81
0.748
Br
М'Br
4р1
8.859
6
1.96
0.753
J
М'J
5р1
9.567
6
2.20
2.16
0.725
0.740
Li
LiГ
2s1
3.487
6
0.68
0.78
0.855
0.740
Nа
NaГ
3s1
4.694
6
0.98
0.798
К
КГ
4s1
5.06
6
1.65
0.634
Rb
RbГ
5s1
5.728
6
1.49
0.641
Сs
CsF
6s1
6.106
6
1.05
0.617
0.788
H
М'Н
1s1
4.794
6
1.36
0.588
0.798-0.617
Sr0,ВаО
2Р2
17.304
6
MgO,CaO
2р2+2р2
22.653
6
1.36
1.32
1.36
1.32
2.121
2.185
2.776
2.860
Bа
BаО,ВаS
6s2
16.172
6
1.38
2.190
2.195
2.412
2.533
3.298
2.120
1.894
Sr
SrO
5s2
17.367
6
1.20
2.412
2.185
4s2
15.803
6
1.04
2.0ЗЗ
2.776
1.06
2.485
2.664
3s2
15.436
6
0.74
3.477
2.860
0.78
3.298
2.78
1.82
1.894
2.195
1.74
1.981
2.195
1.82
2.664
3.298
O
Са
Mg
СаO
СаS
MgO
MgS
ВаS
3p2
20.682
6
МgS
S
CaS
3р2 +3р2
29.092
6
SrS
Eu
Ti
Р''e/к2
0.798-0.617
0.806-0.725
1.74
2.78
2.485
1.82
2.664
2.412
EuO
6s2
18.978
6
1.24
2.551
2.776
TiO
Зd
9.483
6
0.78
2.026
2.121
2
Nomenclature: М' – metal of 1st group (Li, Na, K, Rb, Сs);
Г – halogen; M'' – metal of 2nd group (Mg, Ca, Sr, Ba).
CRYSTALS WITH IONIC-COVALENT AND METALLIC BONDS.
INTERMETALLIDES
Numerous and various structures belong to these classes of compounds, moreover, a lot
of them are practicable.
Compounds of metals with each other belong to intermetallic compounds in the narrow
sense. However, the distinct border between them cannot be made as there is no such border
192
G.А. Korablev and G.E. Zaikov
between metals and non-metals, and their properties frequently change considerably
depending upon the composition and temperature. I.e. rational theory of phrase stability has to
be the same for different types of structures.
When we apply the initial model to double compounds with ionic-covalent and metallic
bonds, the calculations were made based on the equation (2) for 45 binary structures in the
assumption of paired inter-atomic interaction. The results of some of them are given in table
3.
Analogous calculations were made for dozens of crystalline structures of penetration –
metal carbides and hydrocarbides (only some of them are given in table 4). In all these cases
the relative difference of values of P-parameters of interacting systems can be considered the
stability criterion – (coefficient α) based on the following equation:
α
E
=
Р − Р ⋅ 100%
(Р 2+ Р1) 2
2
1
(5)
On the results of all these calculations it can be concluded: stable structures are formed if
αST<(25-30)%.
Formation of Carbon Nanostructures
After different allotropic modifications of carbon nanostructures (fullerenes, tubules)
have been discovered, a lot of papers dedicated to the investigations of such materials, for
instance [9-15] were published, determined by the perspectives of their vast application in
different fields of material science.
However, a strictly defined model of such system formation does not currently exist. To
further study the problem of nanostructure phase-formation the methodology of Р-parameter
is applied in this paper.
The main conditions of stability of these structures formulated based on modeling the
compositions of over thirty carbon clusters are given [9]:
1. Stable carbon clusters look like polyhedrons where each carbon atom is threecoordinated.
2. More stable carbopolyhedrons containing only 5- and 6-term cycles.
3. 5-term cycles in polyhedrons – isolated.
4. Carbopolyhedron shape is similar to spherical.
5. In polyhedrons – even number of apexes, 12 pentagons and any number of hexagons.
Let us show some possible explanations of such experimental data based on the
application of spatial-energy concepts. As before we will consider the approximate equality
of effective energies of interacting subsystems as the main condition for the formation of
stable structure based on the following equation:
⎛ Р0 ⎞ ⎛ Р0 ⎞
⎜
⎟ ≈⎜
⎟ ; Р1 ≈ Р 2
⎝ КR ⎠1 ⎝ КR ⎠ 2
193
(2а)
where К – coordination number, R – bond dimensional characteristic, N – number of
homogeneous atoms in the structure.
At the same time, the phase-formation stability criterion (coefficient α) is the relative
difference of parameters Р1 and Р2 that is calculated following the equation (5) and is
αST<(20-25)%.
During the interactions of similar orbitals of homogeneous atoms Р '0 = Р "0 . When
N1=N2 –
K 1 R1 ≈ K 2 R 2
(6)
Let us consider these initial notions as applicable to certain allotropic carbon
modifications using dimensional characteristics and values of Р-parameters that are given in
[8] and table 1.
1. Diamond. Modification of structure where К1=4, К2=4;
Р '0 = Р"0 ,
R1=R2, Р1=Р2
and α=0. This is absolute bond stability.
2. Non-diamond carbon modification for which
R
4+
2
Р '0 = Р"0 ,
К1=1; R1=0,77Å; К2=4;
= 0.2Å , α=3.82%. Absolute stability due to ionic-covalent bond.
3. Graphite.
Р '0 = Р"0 , К1=К2=3, R1=R2, α=0 – absolute bond stability.
4. Chains of hydrocarbon atoms consisting of the series of homogeneous fragments
with similar values of P-parameters.
5. Cyclic organic compounds as a basic variant of carbon nanostructures. Apparently,
not only inner-atom hybridization of valence orbitals of carbon atom takes place in
cyclic structures, but also total hybridization of all cycle atoms.
And not only the distance between the nearest similar atoms by bond length (d) is the
basic dimensional characteristic, but also the distance to geometric center of cycle interacting
atoms (Д) as the geometric center of total electron density of all hybridized cycle atoms.
Then the basic stabilization equation for each cycle atom will take into account the
average energy of hybridized cycle atoms:
Table 3. Spatial-energy criterion of stabilization of crystalline structures
Atom
Structures
1
As
Fe
2
As2Fe
As2Fe
AgSb
AgAs
AgCd
AgAs
Ag (I)
As (I)
Ag
Ag (I)
Pt (II)
Sb (I)
As (III)
Al (III)
Au (I)
Al (I)
Pt (II)
Al (III)
Se (II)
As (III)
Zn (III)
Au
Au
Structure
type
Orbitals
∑P
'
0
К
R
'
И
R'
P
'
( Å)
8
1.48
(eV)
9
3.698
3.846
0.529
12
1.44
1.48
0.411
0.462
7.108
2
1.44
4.936
5S1
6S2
7.108
24.043
12
12
1.38
1.572
1.452
ZnS
W
W
CaF2
CaF2
ZnS
ZnS
5P1
4P3
3S2+3P1
6S1
3P1
6S2
3S2+3P1
4P2
8.742
37.448
31.624
8.909
6.055
24.043
31.624
22.614
12
4
8
8
4
8
4
4
ZnS
4P3
39.448
AsSn
NaCl
4P3
AuCd
AuSb
Au2Pb
Mg
Cu
Mg
Ag2S
Ag2O
Ag3Pt
Ag3Pt
AuSb
AgSb
AlAs
AlAu4
AlAu4
Al2Pt
Al2Pt
Al2Se3
Al2Se3
AsJn
AsGa
(eVÅ)
5
8.210
18.462
6
3
6
5S1
7.108
12
Mg
4P1
8.210
Cu2O
5S1
Cu
Cu
Mg
3
FeS2
FeS2
4
Mg
4S2
( Å)
7
0.8
1.13
1.13
1.61
1.49
1.44
1.43
1.38
1.43
1.6
0.452
14.282
2.764
3.092
2.180
2.178
11.057
10.609
4
1.48
6.663
40.749
4
1.66
6.137
6S1
8.909
12
1.44
0.516
6S1
8.909
12
1.44
1.032
0.69
"
P
(eV)
10
3.846
3.698
0.452
0.462
0.446
0.524
0.411
3.996
4.164
1.452
1.572
0.516
0.411
13.87
3.092
2.764
2.178
2.180
10.608
11.057
6.137
6.776
6.617
6.663
0.446
0.452
1.045
Atom
Structures
1
K
Bi
2
Bi2K
Bi2K
CuCd3
AgCd3
AgZn3
NiMo
NiMo
LiAg
LiAg
CdSe
CdS
CdTe
PtGa2
SnNi3
SnNi3
TiCu3
TiCu3
PtMg7
PtMg7
Sb3Cu10
Sb3Cu10
Ga2S3
Ga2S3
GeS2
GeS2
Ni2Al3
Ni2Al3
Cu3Se2
Cu3Se2
Cd (I)
Ag (II)
Ni (II)
Mo (II)
Li
Ag (I)
Cd (II)
Pt (VI)
Ni (II)
Sn (IV)
Ti (IV)
Cu (I)
Pt (V)
Mg
Sb (III)
Cu (I)
Ga (III)
S (II)
Ge (IV)
S (II)
Ni (II)
Al
Se (II)
Cu (I)
Structure
type
3
Cu2Mg
Cu2Mg
Mg
Mg
Mg
Orbitals
∑P
4
4S1
6P1
(eVÅ)
5
5.060
12.971
6
12
12
8.349
1
5S
2
9
'
0
К
R
'
И
R'
P
'
1.28
(eV)
9
0.634
0.594
12
1.56
1.338
36.965
18.838
20.872
3.487
7.108
12
12
12
8
8
1.44
1.24
1.39
1.44
2.139
1.266
1.252
0.641
0.617
( Å)
7
1.33
( Å)
8
W
W
5S +4d
4S2
5S2
2S1
5S1
ZnS
5S1+4d1
16.671
4
1.56
2.672
CaF2
SnNi3
SnNi3
6S2+5d4
4S2
5P2+5S2
4S2+3d1
4S1
6S2+5d3
3S2
5P3
4S1
4S2+4P1
3P2
4P2+4S2
3P2
4S2+3d2
3S2+3P1
4P2
4S1
136.65
18.838
69.505
46.839
13.165
96.496
15.436
41.870
7.081
37.678
20.682
61.176
20.682
28.765
31.624
22.614
13.165
8
12
12
12
12
12
12
12
12
4
2.667
4
2
8
12
6
8
1.38
1.24
1.58
1.46
1.28
1.38
1.60
1.61
12.377
3.798
3.666
2.673
2.571
5.827
5.628
6.502
6.02
13.456
12.783
11.003
11.364
5.799
5.529
3.906
3.857
Mg
0.68
1.39
1.82
1.39
1.82
1.24
1.43
1.93
1.28
"
P
(eV)
10
0.594
0.634
1.221
1.266
2.302
1.252
1.266
0.617
0.641
2.929
2.840
2.915
13.554
3.666
3.798
2.571
2.673
5.628
5.827
6.02
6.502
12.783
13.456
11.364
11.003
5.529
5.799
3.857
3.906
Table 4. Spatial-energy criterion of carbide and hydride formation
Atom
Structure
Orbitals
Р0 (eVÅ)
К
Ri(Å)
[(N/P0)/(KRi)]1
C
carbides
2Р2 + 2P2
51.739
6
2.6
3.317
α-Fе
FеС cementite
4S2
18.462
6
0.6
3.846
3.317
α-Fe
FеС
4S2
18.462
6
0.6
2.885
3.317
Тi (II)
TiС
4S2
17.026
6
0.76
3.639
3.317
V(II)
VC
4S2
17.162
6
0.72
3.973
3.317
Cr(II)
CrC
4S2
18.869
6
0.83
3.769
3.317
Zr(II)
ZrC
5S2
18.547
6
0.925
3.342
3.317
Нf(II)
HfO
6S2
19.826
6
0.963
3.432
3.317
W(II)
WC
6S2
23.344
8
0.956
3.052
3.317
Ce(II)
CеC
6S2
23.4778
6
1.125
3.478
3.317
Nb(II)
NbC
5S1 + 4d1
16.669
6
0.62
3.429
3.317
SC(II)
ScC
4S2
16.599
6
0.912
3.033
3.317
Mn(II)
МnС
4S2
18.025
6
0.91
3.301
3.317
Ti(I)
TiH
4S1
6.795
14
0.841
0.578
0.588
Ti (II)
TiH2
4S2
17.026
12
0.76
1.819
1.613
H
TiH2
1S1
4.794
4
1.36
1.763
1.619
1
3.487
6
0.66
0.655
0.882
4.794
6
1.36
0.682
0.655
Li
LiH
2S
H
LiH
1S1
[(N/P0)/(KRi)]2
197
"
⎛ ∑ P0 ⎞ ≈ ⎛ ∑ P0 ⎞ ; ' ≈ "
⎟ P P
⎟ ⎜
⎜
Кd
КД
⎠ ⎝
⎝
⎠
'
i
(7)
i
where ΣР0=Р0N; N – number of homogeneous atoms, Р0 – parameter of one cycle atom, К –
coordination number relatively to geometric center of cycle atoms. Since in these cases К=N,
the following simple correlation appears:
P '0 ≈ P "0 ;
d
Д
Р
'
E
≈
Р
"
(8)
E
During the interactions of similar orbitals of homogeneous atoms
d≈Д
Р '0 ≈ Р"0 , then:
(8а)
Equation (8) reflects a simple regularity of stabilization of cyclic structures:
In cyclic structures the main condition of their stability is an approximate equality of
effective interaction energies of atoms along all bond directions.
The corresponding geometric comparison of cyclic structures consisting of 3, 4, 5 and 6
atoms results in the conclusion that only in 6-term cycle (hexagon) the bond length (d) equals
the length to geometric center of atoms (Д).
d=Д
Such calculation of α following the equation analogous to (5), gives for hexagon α=0 and
absolute bond stability. And for pentagon d≈1.17Д and the value of α=16%, i.e. this is the
relative stability of the structure being formed. For the other cases α>25% - structures are not
stable. Therefore hexagons play the main role in nanostructure formation and pentagons are
additional substructures, spatially limited with hexagons. Based on stabilization equation
hexagons can be arranged into symmetrically located conglomerates consisting only of 3 or 7
hexahedrons.
A conglomerate of three hexagons contains one central atom and 12 atoms around it. A
conglomerate of seven hexahedrons comprises 12 external and 12 internal (common) atoms.
In these two cases geometric centers of hybridized molecular orbitals of each hexahedron are
equidistant from such nearest centers of a conglomerate. This, apparently, explains the
experimental fact that polyhedrons of carbon clusters represent an icosahedron – 12-apex
crystalline structure each apex of which is connected with five other apexes.
Following such a model, for instance, clusterС60 can be formed of two structures 3
hexagons in each and two structures 7 hexagons in each (2х3+2х7=20) plus 12 pentagons
between them located separately and acting as a binding formation.
It is assumed [12] that defectless carbon nanotubes (NТ) are formed as a result of rolling
the bands of flat atomic graphite net. The graphite has a lamellar structure, each layer of
198
G.А. Korablev and G.E. Zaikov
which is composed of hexagonal cells. Under the center of hexagon of one layer there is an
apex of hexagon of next layer. Such a transition from graphite plane to nanotube should be
accompanied by the change of coordination numbers of carbon atoms. Coordination numbers
are 3 and 12 – for some atoms, and 3 and 2 – for other atoms. All this can be found in
accordance with the stabilization formula based on the given pattern.
Examples:
From equation (2а) we have:
К1 ≈ R2
К 2 R1
Then:
1. For graphite
2. For ionic-covalent bond
3. For ionic-ionic bond:
К
К
К
К
К
К
1
2
И
К
4+
И
4−
И
R ≈ 1.675Å ≈ 2 : 1
R 0.77Å
0.77 Å
= R =
≈ 4 :1
0
.
2
Å
R
2.60Å
≈R =
≈ 13 : 1
0
.
2
Å
R
=
2
1
К
И
4−
И
4+
И
These are 13 atoms of hexagons, the central atom of which has the coordination of 12
atoms. The process of rolling flat carbon systems into NT is, apparently, determined by
polarizing effects of cation-anion interactions resulting in statistic polarization of bonds in a
molecule and shifting of electron density of orbitals in the direction of more electronegative
atoms.
Thus, the spatial-energy notions given allow characterizing in general the directedness of
the process of carbon nanosystem formation.
GENERAL CONCLUSIONS
1. The introduction of spatial-energy criterion of structure stabilization is substantiated.
2. The application of this criterion to cyclic systems on the example of carbon
nanostructure formation is given.
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[3]
[4]
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nanocluster. // PТТ, 199 , v.41, №4, p. 740-743.
Yu.E. Lozovik, A.M. Popov. Formation and growth nanostructures – fullerenes,
nanoparticles, nanotubes. // Success in physical science, 1997, v.167, №7, p.751-774.
A.V. Eletsky. Carbon nanotubes. // Success in physical science, 1997, v.167, №9, p.
945-972.
A.L. Kolesnikov, A.E. Romanov. On discminary approach for describing fullerene
structure. // PТТ, 1998, v.40, №6, p. 1178-1180.
S.M. Dunaevsky, M.N. Rozova, N.A. Klenkova. Electron structure of graphite
nanotubes. // PТТ, 1997, v.39, №6, p. 1118-1121.
Chapter 13
THE STRUCTURAL TREATMENT OF
LIMITING CONVERSION DEGREE FOR
SOLID-STATE IMIDIZATION
L. Kh. Naphadzokova, G. V. Kozlov
and M. A. Tlenkopachev1
Kabardino-Balkarian State University,
Chernishevsky st. 173, Nalchik-360004, Russian Federation
1
National University of Mexico, Mexico
ABSTRACT
It was shown, that limiting conversion (in the given case - imidization) degree is
defined by purely structural parameter – macromolecular coil fraction, subjected
evolution (transformation) in chemical reaction course. This fraction can be correctly
estimated within the framework of fractal analysis. For this purpose were offered two
methods of macromolecular coil fractal dimension calculation, which gave coordinated
results.
Keywords: polyamides; solid-state; polymerization; nanocomposites; FTIR; catalysis.
INTRODUCTION
The authors [1] studied kinetics of poly (amic acid) (PAA) solid-state imidization both in
the presence of nanofiller (layered silicate Na+-montmorillonite) and without it. It was found,
that temperature imidization Ti raising in range 423-523 K and nanofiller contents Wc increase
in range 0-7 phr result to essential imidization kinetics changes expressed by two aspects: by
essential increase of reaction rate (reaction rate constant of first order k1 increases about on
two order) and by raising of conversion (imidization) limiting degree Qlim: from about 0,25
for imidization reaction without filler at Ti=423 K up to 1,0 at Na+-montmorillonite content 7
202
phr and Ti=523 K. Let’s mark too, that all kinetic curves conversion degree-reaction duration
Q(t) have typical shape of curves with autodeceleration characteristic for fractal reactions,
i.e., either fractal objects reactions, or reactions in fractal spaces [2]. Differently speaking,
indicated reaction aspects in sufficient degree have general character. If for the first effect (k1
increase) the authors [1] offered probable chemical treatment considering nanofiller as
catalyst, then the second effect (Qlim raising) did not obtain explanation, although its
theoretical and practical significance is obvious. Therefore the purpose of the present paper is
structural treatment of limiting conversion degree in solid-state imidization process based on
the general principles of fractal analysis.
EXPERIMENTAL
The kinetics of PAA, synthesized from 4,4/-oxydianiline and pyromellitic dianhydride,
solid-state imidization both in filler absence and with addition of 2 phr Na+-montmorillonite
was studied [1]. The nanofiller was treated by solution of P-phenylenediamine in HCl and
then washed by de-ionized water to ensure a complete removal of chloride ions. The
conversion (imidization) degree Q was determined as a function of reaction duration t with
the aid of Fourier transformation of IR-spectra bands 726 and 1014 cm-1. The samples for
FTIR study were obtained by spin-coating of PAA/Na+-montmorillonite mixture solution in
N,N-dimethylacetamide on KBr disks, which then were dried in vacuum for 48 h at 303 K. It
was shown, that the used in paper [1] method gives exfoliated nanocomposites. The other
details of nanocomposites polyimid/Na+-montmorillonite synthesis and study in paper [1]
were adduced. The solid-state imidization process was made at four temperatures Ti: 423,
473, 503 and 523 K.
It is known [3], that macromolecular coil in various polymer’s states (solution, melt, solid
phase) represents fractal object characterized by fractal (Hausdorff) dimension Df. Specific
feature of fractal objects is distribution of their mass in the space: the density ρ of such object
changes at its radius R variation as follows [4]:
⎛R⎞
ρ = ρ dens ⎜ ⎟
⎝a⎠
D f −d
,
(1)
where ρdens is density of material, which consists of fractal object in dense packing
assumption, a is lower linear scale of object fractal behavior, d is dimension of Euclidean
space, in which is fractal considered (it is obvious, that in our case d=3).
From the equation (1) ρ decrease at Df reduction follows, as always Df<d, that, naturally,
simplifies reagents access in macromolecular coil inner regions and results to the fuller
chemical transformations, i.e., to conversion degree Q increase. Besides, it is known [4], that
at macromolecular coil formation by irreversible aggregation mechanisms in its central part
The Structural Treatment of Limiting Conversion Degree…
203
densely-packed region is formed, where chemical reactions proceeding is impossible.
Proceeding from that, it is possible to confirm, that for a chemical reaction only the part of
macromolecular coil is accessible, which is the larger, the smaller its fractal dimension Df. In
the leaking coil case (Df≤1,5 [3]) both low- and high-molecular substances can pass freely
through it and this assumes, that in such case the value Q=1,0. At Df=2,5 chemical reaction
ceases and gelation process [5] begins. This means, that at reaching Df=2,5 Q=0. The
indicated estimations allow to write the fractional exponent ν for chemical reactions similarly
to the definition, accepted in paper [6]:
ν = D f − ( D f gel − 1) = D f − 1,5 ,
where
D f gel
(2)
is the value Df at gelation, equal to 2,5.
Let’s remind, that according [7] the value ν characterizes system states fraction, un
changing in its evolution process. In case of chemical reactions generally and imidization
process particularly this assumes, that the value ν characterizes macromolecular coil part
inaccessible for chemical transformations. Then the accessible for such transformations coil
part β is determined as follows [8]:
β = 1 − ν = 2,5 − D f
.
(3)
Proceeding from the said above, it’s possible to define the limiting conversion degree
Qlim by the following identity [8]:
Qlim = β .
(4)
Therefore, the estimation Qlim problem brings to the question of fractal dimension Df
determination. At present two methods of indicated dimension determination one exist. First
method consists of using of chemical reactions fractal kinetics general relationship [9]:
Q~t
( 3− D f ) / 2
,
(5)
where Q is conversion degree, t is reaction duration.
Plotting of the dependences Q(t) in log-log coordinates allows to determine the value Df
according to the slope of these dependences in their linearity case. In figure 1 the mentioned
dependences for process of PAA imidization without filler are shown. As can be seen, these
dependences are linear, that allows to make estimation Df by the indicated method.
204
Figure 1. The dependences of imidization degree Q on reaction duration t in log-log co-ordinates for PAA
imidization process at temperatures: 423 (1), 473 (2), 503 (3) and 523 K (4).
As it is shown in paper [1], imidization process corresponds to the first order reactions.
For such reaction it can be written [10]:
dQ
= k1 (1 − Q) ,
dt
(6)
where k1 is the first order reaction rate constant.
Differentiating the relationship (5) by t and equaling the derivatives dQ/dt in (5) and (6),
let’s obtain the equation, which can be considered as the second method [10] of the estimation
Df:
t
( D f −1) / 2
=
C
,
k1 (1 − Q)
(7)
where C is constant determined from boundary conditions and in the imidization process case
equal to 0,25 min-1 and the values k1 were adduced in paper [1].
In figure 2 the comparison of dimensions Df calculated by two methods ( D f and
1
D f2
respectively) is shown. As can be seen, both these methods given close values Df and
therefore further their average magnitude will be used, i.e., Df=( D f + D f )/2.
1
2
Further parameters β can be made estimated according to the equation (3) and compared
with the limited conversion degree Qlim, obtained experimentally [1]. Such comparison for
PAA imidization process without filler and in the presence of 2 phr Na+-montmorillonite at
The Structural Treatment of Limiting Conversion Degree…
205
four indicated above temperatures of imidization in figure 3 is shown. Good enough
correspondence of theory and experiment (their average discrepancy is equal to ~12%) was
obtained, that confirms the offered treatment correctness.
Figure 2. The comparison of macromolecular coil fractal
D f1
and
D f2
calculated according to the
relationships (5) and (7), respectively, for PAA imidization process without filler (1) and in the presence of 2
phr Na+-montmorillonite (2).
Figure 3. The dependence of limiting imidization degree Qlim on parameter β value for PAA imidization
process without filler (1) and in the presence of 2 phr Na+-montmorillonite (2).
206
CONCLUSIONS
Therefore, the results obtained in the present paper assume, that limiting conversion (in
given case-imidization) degree is defined by purely structural parameter – macromolecular
coil fraction, subjected to the evolution (transformation) in chemical reaction course. This
fraction can be correctly estimated within the framework of fractal analysis. For this purpose
two methods of macromolecular coil fractal dimension calculation have been offered, which
give co-ordinates results.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Tyan HL, Liu YC, Wei KH. Polymer. 1999; 40: 4877-4886.
Kozlov GV, Zaikov GE. J. Balkan Tribolog. Assoc. 2004; 10: 1-30.
Baranov VG, Frenkel SYa, Brestkin YuV. Doklady AN SSSR. 1986; 290: 369-372.
Brady RM, Ball RC. Nature. 1984; 309: 225-229.
Kozlov GV, Shustov GB, Zaikov GE. J. Balkan Tribolog. Assoc. 2003; 9: 467-514.
Kozlov GV, Batyrova HM, Zaikov GE. J. Appl. Polymer Sci. 2003; 89: 1764-1767.
Nigmatullin RR. Teoretich. I Matematich. Fizika. 1992; 90: 354-367.
Kozlov GV, Shustov GB. In book: Proceeding of International Seminar “Fractal and
Applied Synergetics. FIPS-01”. 2001. MSOU, Moscow, p. 155-157.
[9] Novikov VU, Kozlov GV. Uspekhi Khimii. 2000; 69: 378-399.
[10] Kozlov GV, Zaikov GE. Teoretich. Osnovy Khimichesk. Tekhnologii. 2003; 37: 555557.
Chapter 14
A SOLID-STATE IMIDIZATION AND
HETEROGENEITY OF REACTIVE MEDIUM
L. Kh. Naphadzokova1, G. V. Kozlov1 and G. E. Zaikov2
1
360004, Russia, Nalchik, Chernishevsky st., 173
2.
Institute of Biochemical Physics, Russian Academy of Sciences,
119991, Russia, Moscow, Kosygin st., 4
ABSTRACT
It was shown, that the conception of reactive medium heterogeneity is connected
with free volume representations, that it was to be expected for diffusion-controlled solid
phase reactions. If free volume microvoids were not connected with one another, then
medium is heterogeneous, and in case of formation of percolation network of such
microvoids – homogeneous. To obtain such definition is possible only within the
framework of the fractal free volume conception.
Keywords: Imidization, nanofiller, reactive medium, heterogeneity, fractal free volume.
INTRODUCTION
The authors [1] studied kinetics of poly (amic acid) (PAA) solid phase imidization in the
presence of nanofiller (Na+-montmorillonite) and in its absence. It was found out, that the
kinetic curves conversion (imidization) degree Q versus reaction duration t were have typical
for polymerization reactions shape with autodeceleration showing imidization rate reduction
as time is passing. As it is known [2], such curves Q(t) are specific for reaction passing in
heterogeneous medium and are described by the simple relationship:
k ~ t −h ,
(1)
208
were k is the reaction rate, h is the heterogeneity exponent (0<h<1) turning into zero only for
homogeneous samples; then behaviour becomes classical: k=const.
The mentioned shape of imidization kinetic curves assumes its passing in heterogeneous
medium and the relationship (1) supposes the strong effect of this heterogeneity degree
characterized by exponent h on reaction rate. Therefore the present paper purpose is
clarification of reactive medium heterogeneity physical significance in case of PAA solid
phase imidization and factors defining the value of medium heterogeneity exponent.
EXPERIMENTAL
The kinetics of solid state imidization of PAA, synthesized from 4,4/-oxydianiline and
pylomellitic dianhydride, both without filler and with addition of 2 and 5 weight % Na+montmorillonite [1]. The nanofiller is processed by solution of P-phenylenediamine in HCl
and then washed with de-ionized water to ensure a complete removal of chloride ions. The
conversion (imidization) degree Q was determined as a function of reaction duration t with
the aim of Fourier transformation of IR-spectra bands 726 and 1014 cm-1. The samples for IR
studies were prepared by spin-coating of mixture PAA/Na+-montmorillonite solution in N,Ndimethylacetamide on KBr disks. Then the KBr disks were dried in vacuum at 303 K for 48
h. It was shown, that the used in paper [1] method gives exfoliated nanocomposites. The other
details of polyimide/Na+-montmorillonite nanocomposites synthesis and studies in paper [1]
were cited. The solid state imidization process was made at four temperatures Ti: 423, 473,
503 and 523 K.
The solid phase imidization process in the most simple and general form can be
represented as follows [3]:
A+A → inert product,
(1)
where A is reagent, which in considered case is PAA.
The type (1) reaction can be described by the following scaling relationship for diffusioncontrolled reactions [3]:
ρ A ~ t − ds / 2 ,
(2)
where ρA is concentration of nonreacted reagent A, which further was accepted equal to (1Q), ds is spectral dimension of reactive medium.
In figure 1 the dependence ρA(t) in double logarithmic coordinates, corresponding to the
relationship (2), for solid state imidization reaction without filler at the four mentioned above
imidization temperatures Ti are shown. As can be seen, the received dependences are linear
and according to their slope the value ds can be obtained. The Ti increase in the range 423-523
A Solid-State Imidization and Heterogeneity of Reactive Medium
209
K results to substantial growth of reactive medium connectivity degree characterized by
dimension ds: from 0,42 up to 1,68. Let’s mention, that such ds increase occurs without
reactive mixture composition change. This means, that the energetic restrictions result to the
appearance of fractal space, in which instead of value ds effective spectral dimension
d s′
must be use, reflecting the existence of the mentioned above restrictions and connected with
ds by the equation [2]:
d s′ = β d s ,
(3)
where β is parameter, characterizing a distribution of reagent “jumps” (motion) times.
Figure 1. The dependences ρA=(1-Q) on t in log-log coordinates, corresponding to the relationship (2), for
PAA solid state imidization without filler at temperatures: 423 (1), 473 (2), 503 (3) and 523 K (4).
In its turn, the values
d s′ = 2(1 − h) .
d s′
and h are connected with one another by the equation [2]:
(4)
In figure 2 the dependence h(Ti) is shown, from which follows rapid decrease h or
increase of homogeneity of reactive medium at Ti raising. At Ti≈540 K exponent h=0, i.e.,
reactive medium becomes homogeneous. The authors [1] have show that the melting
temperature Tm for studied polyimides is about equal to 800 K. On the basis of the known law
of two-thirds
210
Tg
Tm
=
2
,
3
(5)
the polyimide glass transition temperature Tg can be estimated as equal to ~533 K.
Differently speaking, as it was expected [4], reactive medium in case of solid state
imidization becomes homogeneous (Euclidean) at glass transition. The shape of the curve
h(Ti), adduced in figure 2, i.e., h goes to zero at temperature raising, assumes, that the fractallike effects, namely,
d s′
variation, are connected with energetic disorder [2]. In such case the
energetic state of polymer structure can be characterized by excess energy localization
regions dimension Df [5]. The value Df can be estimated according to the following equation
[6]:
Df =
4πTi
ln(1 / f g )Tg
,
(6)
where fg is relative fluctuational free volume, for determination of which the following
method is used. Firstly the relative fraction of local order region (clusters) ϕcl was estimated
according to the percolation equation [4]:
ϕ cl = 0,03(1 − k )(Tg − Ti ) 0,55 ,
(7)
where k is crystallinity degree, which is equal to ~0,2 [1].
Further fraction of loosely-packed matrix of polymer structure ϕl.m. [4] was estimated:
ϕ l .m. = 1 − ϕ cl − k ,
(8)
and then the value fg was determined as follows [7]:
f g = 0,113ϕ l .m. .
(9)
211
Figure 2. The dependence of heterogeneity exponent h of reactive medium on imidization temperature Ti for
PAA solid state imidization at Na+-montmorillonite contents Wc: 0 (1), 2 (2) and 5 (3) weight %.
In figure 3 the dependence h(Df) is adduced, from which follows the expected result: a
polymer structure energetic excitation degree raising, due to thermal energy “pumping” at Ti
increase, results to h reduction. At Df≈6,3 the reactive medium becomes homogeneous (h=0).
Therefore, the data of figures 2 and 3 give the answer to the question, at what conditions
h=0, i.e., when the reactive medium becomes homogeneous. Nevertheless, the physics of this
process remains vague. The glass transition gives singularities neither in fg behaviour, nor in
Df behaviour. Therefore for explanation of heterogeneous↔homogeneous medium transition
let’s use representations of the conception of fractal (local) free volume
f gfr
[6]. According
to this conception free volume microvoid is necessary to simulate not by three-dimensional
sphere, as it was accepted in classical polymer physics [8], but by Df-dimensional sphere. In
this case between fg and
fg
where
fr
⎛ Vh fr
= f g ⎜⎜
⎝ Vh
Vh fr
f gfr
the following relationship [6] was obtained:
⎞
⎟⎟ ,
⎠
(10)
and Vh are volumes of free volume microvoid in case of its simulation by Df- and
three-dimensional sphere, respectively.
The value Vh can be estimated as follows [6]:
212
V
1/ 3
h
⎛ T − Ti
= ⎜⎜ m
⎝ Tm
⎞
⎟⎟
⎠
−ν
,
(11)
where percolation index ν was accepted equal to 0,85 [6].
Figure 3. The dependence of heterogeneity exponent h of reactive medium on excess energy localization
regions dimension Df for PAA solid state imidization. The notation is the same, that in figure 2.
Further from geometrical considerations in assumption of three-dimensional microvoid of
free volume its radius rh can be estimated and then
Vh fr can be calculated according to the
equation [6]:
π f rh f
=
.
( D f / 2)!
D /2
Vh
fr
D
In figure 4 dependence h(
(12)
f gfr )is
adduced where the value
f gfr
was calculated
according to the equations (10)-(12). As follows from the data of this figure, the value h=0 or
reactive medium homogeneity at
value
f gfr
speaking, at
f gfr =0,34 is achieved. Let’s recollect, that the mentioned
corresponds to percolation threshold for overlapping spheres [6]. Differently
f gfr =0,34 fluctuational free volume microvoids, simulated by Df-dimensional
sphere, form continuous percolation network or continuous diffusion channels. Therefore,
213
between heterogeneous and homogeneous reactive medium, at any rate, in case of solid state
imidization, quantitative difference exists. For heterogeneous reactive medium dehydration
product (water molecule), which is in free volume microvoid, forces to expect the opening of
overlapping it neighboring microvoid, after that it makes “jump” from the first to the second
and further the process repeates. For homogeneous reactive medium such process of
“expectation” is not required by virtue of the existence of through percolation channels of free
volume. Let’s mark, that the mentioned processes of “jumps” are realized on local level.
Figure 4. The dependence of heterogeneity exponent h of reactive medium on relative fractal volume
f gfr
for PAA solid state imidization. The notation is the same, that in figure 2.
And lastly, in figure 5 the dependence of coefficient β in the equation (3) on
adduced. Again the value β reaches it limiting magnitude β=1 (i.e.,
The relationship between β and
β = 2,94 f gfr .
f gfr
f gfr
is
d s′ = d s ) at f gfr =0,34.
is given by the simple empirical equation:
(13)
The plot of figure 5 demonstrates, that the energetic restriction, defining transition from
ds to
d s′ , is the necessity of “jumps” of reaction products or reagents between free volume
microvoids. It is clear, that the Ti raising decrease “jump” expectation time and the formation
of through percolation channels of free volume microvoids cancels these restrictions.
214
Figure 5. The dependence of the coefficient β in the equation (3) on relative fractal free volume
f gfr
for
PAA solid state imidization. The notation is the same, that in figure 2.
CONCLUSIONS
Therefore, the results of the present paper showed, that the notion of reactive medium
heterogeneity connected with free volume representations, that was expected for diffusioncontrolled solid phase reactions. If free volume microvoids were not connected with one
another, then medium is heterogeneous, and in case of formation of overlapping percolation
network of such microvoids – homogeneous. To obtain such definition is possible only within
the framework of the fractal free volume conception.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
Tyan H.-L., Liu Y.-C., Wei K.-H. Polymer, 1999, v. 40, №11, p. 4877-4886.
Kopelman R. In book: Fractals in Physics. Eds. Pietronero L., Tosatti E. Moscow, Mir,
1988, p. 524-527.
Meakin P., Stanley H.E. J. Phys. A, 1984, v. 17, №1, p. L173-L177.
Kozlov G.V., Novikov V.U. Uspekhi Fizichesk. Nauk, 2001, v. 171, №7, p. 717-764.
Balankin A.S. Synergetics of Deformable Body. Moscow, Ministry Defence SSSR
Publ., 1991, 404 p.
Kozlov G.V., Sanditov D.S., Lipatiov Yu.S. In book: Achievements in Polymer Physics
and Chemistry Field. Ed. Zaikov G.E. a.a. Moscow, Khimiya, 2004, p. 412-474.
[7]
[8]
215
Belousov V.N., Beloshenko V.A., Kozlov G.V., Lipatiov Yu.S. Ukrainskii Khimich.
Zhurnal, 1996, v. 62, №1, p. 62-65.
Sanditov D.S., Bartenv G.M. Physical Properties of Disordered Structures. Novosibirsk,
Nauka, 1982, 256 p.
Chapter 15
FRACTAL-LIKE KINETICS OF REESTERIFICATION
REACTION IN CATALYST PRESENCE
1
2
Institute of Biochemical Physics, RAS,
ABSTRACT
It was shown, that the reesterification reaction without catalyst can be described by
mean-field approximation, whereas introduction of catalyst (tetrabutoxytitanium) is
defined by the appearance of its local fluctuations. This effect results to fractal-like
kinetics of reesterification reaction. In this case reesterification reaction is considered as
recombination reaction and treated within the framework of scaling approaches. Practical
aspect of this study is obvious-homogeneous distribution of catalyst in reactive medium
or its biased diffusion allows to decrease reaction duration approximately twofold.
Keywords: reesterification, kinetics, catalyst, diffusion, scaling, mean-field approximation.
INTRODUCTION
Saturated complex polyesters, particularly, poly (butylene terephthalate) (PBT) are used
as engineering thermoplastics possesing good thermo – and wearstability, excellent moulding.
These properties also allow to use them as matrix material for polymer composites [1]. One of
the perspective ways of search of effective catalysts for such systems is kinetic study of the
reesterification model reaction, performed in the presence of various catalysts and comparison
it with the results of the similar reaction without catalyst. Clarification on the example of
model system of the most effective catalysts list allows to use them for obtaining both filled
and nonfilled PBT and compare catalytic activity of various catalysts. The purpose of the
218
present paper is the comparative analysis of reesterification reactions without and in the
presence of tetrabutoxytitanium (TBT) within the framework of modern physical concepts [24].
EXPERIMENTAL
The reesterification model reaction kinetics of methylbenzoate by heptanole-1 in catalyst
(TBT) presence and without it was studied at 443 K on the gas chromatograph «Biokhrom»
using diphenyloxide according to the earlier described method [5] as an internal standard. The
rate constant k1 was calculated according to the equation of irreversible reaction of the first
order.
TBT of mark «tch», is used which was distiled in vacuum, three times selecting fraction
with boiling temperature Tb=430-432 K at pressure 1,33 Gpa [6]. Obtaited by such method
fraction was preserved under molecular sieve 4 A.
For kinetic studies four-neck retort was scavenged by argon and poured methylbenzoate
and heptanole-1 into it. After immersion of the retort into preliminary heated up to 443 K
silicone oil, TBT was introduced. Catalyst concentration made into reactionary mixture 0,10
mol.% in calculation on reagent, taken in deficiency. Every definite time intervals probes
were taken by a calibrated syringe through self-covered membrane. The taken reactive
mixture was cooled by injecting in preliminary weighted amount of standard solution. The
taken probes were analyzed on gas chromatograph as described above with using helium as
gas-carrier [5].
In figure 1 the kinetic curves of reesterification reactions without catalyst and in the
presence of TBT are shown. The attention is draw by itself both quantitative and qualitative
differences of these Q(t) curves. The quantitative difference is expressed by much faster
growth Q at t increase due to catalyst presence that was expected. The qualitative change is
reflected in the Q(t) curve form change. If in the absence of TBT linear dependence was
obtained, which indicates on the reaction proceeding in Euclidean (homogeneous) space [7],
then in TBT presence a typical curvilinear Q(t) dependence was obtained with reaction rate
dQ / dt decrease with t increase. Such reactions are typical for heterogeneous (fractal)
mediums [8] owing to which they are called fractal-like. The dependence
dQ / dt
this case is described by the relationship [8]:
dQ −h
~t ,
dt
(1)
on t in
Fractal-Like Kinetics of Reesterification Reaction in Catalyst Presence
219
where h is the heterogeneity medium exponent, which varies within the limits 0<h≤1 for
fractal mediums and equal to zero for homogeneous medium. In the last case dQ / dt =const
and dependence Q(t) is linear that can be observed for reesterification reaction without
catalyst (figure 1).
Figure 1. The kinetic curves conversion degree time (Q-t) for reesterification reaction without catalyst (1) and
in TBT presence (2).
Let’s consider the reasons of reesterification reaction fractal-like kinetics in TBT
presence. This reaction can be described in general form as recombination reaction of
reagents A and B [4]:
A+B → inert product.
(2)
Within the framework of the mean-field theory the reagent A concentration decay ρA=ρB is
given by the equation [4]:
ρA ~
1
,
k1t
(3)
where k1 is reaction rate constant.
In figure 2 the comparison of calculated according to the relationship (3) and determined
experimentally functions ρA(t) is adduced, where ρA is determined as (1-Q). As can be seen,
for the reesterification reaction without catalyst ρA decay as t increase is excellently described
within the framework of the mean-field theory, whereas in TBT presence ρA decay is much
slower, than it was predicted by the relationship (3). As it was known [4], the last effect is due
220
to local fluctuations of reagents distributions and in this case the function ρA(t) is given as
follows:
ρ A (t ) ~ t − α
(4)
ρ A (t ) ~ exp(− At α )
(5)
and
for short and long reaction times, respectively. In the relationships (4) and (5) the exponent α
is defined by space dimension d, in which a reaction proceeds, A is constant.
Figure 2. The dependences of reagent A concentration decay ρA on reaction duration t for reesterification
reaction without catalyst (1, 3) and in TBT presence (2, 4).
For recombination reaction described by the equation (2), can be written [4]:
α=
d
.
4
(6)
Let’s note three important aspects followed from the model [4] application for description
of reesterification reaction. At first as reesterification reactions with TBT and in it absence
proceed in identical conditions, then from the comparison of figure 1 kinetic curves follows,
that the reaction fractal-like behaviour in TBT presence is due to local fluctuations of catalyst
distribution in reactive medium. Secondly the division of reaction duration into short and long
221
times is connected with reagents and catalyst diffusion. At local fluctuations presence small
enough regions by size ξ exist, where positive or negative TBT fluctuations are large enough.
If we obtain characteristic scale of time tξ, which is required for passing of diffusible particle
the distance ξ, then the condition t<tξ gives short times and t>tξ – long times. And, thirdly, the
equation (6) gives the value of exponent α for free diffusion of reagents. In case of biased
(with preferential orientation) diffusion the value α is determined as follows [4]:
α=
d +1
,
4
(7)
i.e., for three-dimensional space in case of biased diffusion α=1. In this case the scaling
approach [4] gives the relationship (4), analogous to the equation (3). This correspondence is
confirmed by the figure data. Therefore, the present result allows to make a conclusion, that
the intensive stirring of reactive medium results to reagents biased diffusion (namely,
methylbenzoate and heptanole-1), but TBT diffusion remains unbiased.
Figure 3. The dependences of reagent A concentration decay ρA on reaction duration t in log-log coordinates
for reesterification reaction in TBT presence.
In figure 3 the dependence ρA(t) in log-log coordinates, corresponding to the relationship
(4), for the reesterification reaction in TBT presence is adduced. As can be seen, this
dependence breaks down into two linear parts with different slopes. For the first part (t<90
min.) the slope is equal to ~0,75, i.e., corresponded to the equation (6) for reaction proceeding
in three-dimensional Euclidean space (d=3). For the second part (t>90 min.) the slope is equal
to ~3, i.e., not corresponded to possible value of this exponent for recombination reaction or
other analogous reactions, for which the value α is limited from above by the value 1,5 [2-4,
9]. This means, that for the considered reesterification reaction times smaller of 90 min. it’s
necessary to identify as short times, i.e., on this temporal interval reactive particles
concentration decay controls by local fluctuations of TBT distribution, and times equal or
222
larger that 90 min. – to long times, where TBT is homogeneously distributed. This means,
that in the last case the function ρA(t) should be described by the relationship (5). Actually,
adduced in figure 4 the dependence ρA on td/4 in log coordinates is linear, that confirms the
assumption made above.
Figure 4. The dependences of reagent A concentration decay ρA on parameter td/4 (d=3) in log coordinates in
the case of long times for reesterification reaction in TBT presence.
CONCLUSIONS
Therefore, the reesterification reaction without catalyst can be described by mean-field
approximation, whereas introduction of catalyst (TBT) is defined by the appearance of its
local fluctuations. This effect results to fractal-like kinetics of reesterification reaction. In this
case reesterification reaction is considered as recombination reaction and treated within the
framework of scaling approaches. Practical aspect of this study is obvious-homogeneous
distribution of catalyst in reactive medium or its biased diffusion allows to decrease reaction
duration approximately twofold.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
Chen J.-H., An Y.U., Kim S. J., Im S. Polymer, 2003, v. 44, №23, p. 5655-5661.
Grassberger P., Procaccia I. J. Chem. Phys., 1982, v. 77, №12, p. 6281-6284.
Kang K., Redner S. Phys. Rev. Lett., 1984, v. 52, №12, p. 955-958.
Naphadzokova L.Kh., Vasnev V.A., Tarasov A.I. Plast. Massy, 2001, №3, p. 39-41.
Cullinane N.M., Chard S.J., Price G.F., Millward B.B., Langlois G. J. Appl. Chem.,
1951, v. 1, №3, p. 400-406.
[7]
[8]
[9]
223
Kozlov G.V., Zaikov G.E. Teoretich. Osnovy Khimich. Tekhnologii, 2003 v. 37, №5,
p. 555-557.
Anacker L.W., Kopelmam R. J. Chem. Phys., 1984, v. 81, №12, p. 6402-6403.
Redner S., Kang K. J. Phys. A, 1984, v. 17, №2, p. L451-L455.
Chapter 16
DESCRIPTION OF THE MODEL REESTERIFICATION
REACTION WITHIN THE FRAMEWORK OF
A STRANGE DIFFUSION CONCEPT
1
2
Institute of Biochemical Physics, RAS,
ABSTRACT
It is shown, that there is principal difference between the description of generally
reagents diffusion and the diffusion defining chemical reaction course. The last process is
described within the framework of strange (anomalous) diffusion concept and is
controled by active (fractal) reaction duration. The exponent α, defining the value of
active duration in comparison with real time, is dependent on reagents structure.
Keywords: esterification, kinetics, catalysis, diffusion, microstructure.
INTRODUCTION
One of the perspective ways of search of effective inorganic filler-catalysists for complex
polyesters is kinetic study of the reesterification model reaction, performed in the presence of
various inorganic compounds [1]. Such method allows to use the obtained results in the
synthesis process of the filled complex polyesters [2].
Synthesis processes in common case can be considered as a complex system of selforganization, developing during time, that results to formation of time-dependent fractal
structures [3]. In such reactions the important role is played by diffusive processes, which in
the considered case have very specific nature. This specificity is due to the fact, that in
chemical reactions not all reagents contacts occur with proper for reaction’s product
226
formation orientation of reacting molecules. This aspect of reaction is accounted for by steric
factor p (p≤1) [4]. Variation p can result to the change of a diffusion type, reaction’s product
structure and, as consequence, to the rate of chemical reaction change. This question can be
explained by a simple example. As it is known [5], characteristic size r(t) of a region, which
can be visited by the reagent molecule during time t, is equal to:
r (t ) ~ t 1 /( 2 + θ ) ,
(1)
where θ is connectivity index of reactive medium.
For the case of classical Gaussian diffusion θ=0 and, believing r(t)=2 and t=4 relative
units, the equality within the framework of the relationship (1) will be obtained. Such equality
assumes p=1, i.e., each contact of reagents molecules results to reaction product formation.
Let’s assume, that the value p decreases up to 0,05, i.e., only one from 20 contacts of reagents
molecules forms a new chemical species. This means the increase t in 20 times and then at
r(t)=2 and t=80 relative units from the relationship (1) will be obtained θ=4,33. Since θ is
connected with dimension of walk trajectory of reagents molecules dw by the simple equation
[5]:
dw = 2 + θ ,
(2)
then θ increase results to dw raising, i.e., slows down the chemical interaction process.
In its turn, the value dw is connected with Hurst exponent H by the equation [5]:
dw =
1
H
.
(3)
The change θ from 0 up to 4,33 results to raising dw from 2 (Brownian motion) up to
dw=6,33 according to the equation (2) and to H reduction from 0,5 up to 0,158 according to
the equation (3). As it is known [5], subdiffusive (slow) transport processes correspond to the
value 0≤H≤0,5 and classical Gaussian diffusion – H=0,5. Therefore, the decrease p from 1,0
up to 0,05 results to the qualitative change of diffusion type too: it changes from Gaussian
classical to anomalous (strange). Let’s note, that the mentioned transition can occur without
changing of general diffusive processes in reactive medium too, since it is due to «rejection»
of all diffusive phenomena, not resulting to the chemical reaction, i.e., to formation of new
chemical substance. Proceeding from the said above, the purpose of the present paper is to
study diffusive processes influence within the framework of the offered treatment on main
characteristics of reesterification model reaction.
Description of the Model Reesterification Reaction…
227
EXPERIMENTAL
The kinetics of reesterification model reaction of methylbenzoate by heptanole-1 in mica
presence was studied at 443 K. Mica catalytic activity was determined on the observed rate
constant of the first order k1 at the twentieth multiple of heptanole-1 excess and mica contents
30 mass.% in calculation on the methylbenzoate [2].
The reesterification kinetics was studied on the gas chromatograph «Biokhrom» with
using as the internal standard diphenyloxide according to the earlier described method [1].
The rate constant k1 was calculated according to the equation of irreversible reaction of the
first order.
The mica «Flagopit» with polydispersity 0,749 and average probable particles size
0,23×10-6 m is used. The initial mica (conditional designation NMM) and also mica
chemically modified by sodium hydroxide (SMM) and sulphur acid (AMM) were applied.
Earlier it was shown [6], that for reaction of type
A+B → inert products
(4)
the scaling relationship is true:
ρA ~ t D/4 ,
(5)
where ρA is concentration of «surviving» in the reaction process particles, t is reaction
duration, D is dimension controlling the reaction course.
In case of reaction course in the Euclidean spaces the value D is equal to the dimension
of this space d and for fractal spaces D is accepted equal to spectral dimension ds [6]. By
plotting ρA=(1-Q) (where Q is conversion degree) as a function of t in log-log coordinates the
value D from the slope of these plots can be determined. It was found, that the mentioned
plots fall apart on two linear parts: at t<100 min with small slope and at t>100 min the slope
essentially increases. In this case the value ds varies within the limits 0,069-3,06. Since the
considered reactions are proceed in Euclidean space, that is pointed by a linearity of kinetic
curves Q-t, this means, that the reesterefication reaction proceeds in specific medium with
Euclidean dimension d, but with connectivity degree, characterized by spectral dimension ds,
typical for fractal spaces [5].
The authors [5] have formulated fractional equation of transport processes, having the
following form:
∂ α ψ ∂ 2β
=
( Bψ ) ,
∂t α ∂r 2β
(6)
228
where ψ=ψ(t,r) is distribution function of particles,
∂ 2β ∂r 2β
is Laplacian operator in d-
dimensional Euclidean space and B is relation of transport generalized coefficient and d. The
introduction of fractional derivatives
∂ α ∂t α
allows to account for the effects of memory
(α) and nonlocality (β) in context of common mathematical formalism [5]. The introduction
of fractional derivative
∂ α ∂t α
in the kinetic equation (6) allows to account for random
walks in fractal time (RWFT) – «temporal component» of strange dynamical processes in
turbulent mediums [5]. The absence of any noticeable jumps in particles behavior serves as
the distinctive feature of RWFT; in this case root-mean-square displacement 〈r2(t)〉 increases
with t as tα. The parameter α has sense of fractal dimension of «active» time, in which real
walks of particles look as random process; interval of active time is proportional to tα [5].
In its turn, the exponent 2β in the equation (6) accounts for instantaneous jumps of
particles (Levy «flights») from the one region of turbulence in to another. The existence of
turbulence zones in reesterification reaction follows with the necessity from intensive stirring
of reactive medium as by virtue of inert gas passing, as owing to mechanical stirring.
Therefore, exponents relation α/β gives relation of RWFT contact frequencies and Levy
«flights». The value β in the first approximation can be adopted as constant and then relation
α/β will be inversed proportional to waiting time of chemical reaction realization.
Depending on concrete value α persistent (superdiffusive, 1<α≤2) and antipersistent
(subdiffusive, 0≤α<1) processes are distinguished. In case of antipersistent processes active
time represents itself Cantor’s set (0≤α<1), consisting breakings in any point of t ray.
Breakings corresponded to those time moments, in which particle at a regular time «sticks» in
turbulent field. On the contrary, persistent processes assume a faster course (1<α≤2) of active
time in comparison with real time t [5]. The value α/β can be determined according to the
relationship [5]:
α ds
=
β d
.
(7)
We assume that the dependence of Q on active time tα should be linear and namely
according to these considerations choose the value β=0,25. Constructed by the indicated
method the dependence at t=60 and 300 min in figure 1 is adduced. As can be seen, it is
approximately linear and passed through coordinates origin. Attention is attracted by the fact,
that active time tα is much smaller (in 50-150 times) than real time t. Although this difference
is due to the above made value β choice and, consequently, α, it imagines close to reality. So,
for reesterification in the presence of NMM and SMM the value Q≈0,20 is achieved during
300 min, whereas in other polycondensation reactions at analogous conditions synthesis is
practically completed during 20 min [7], i.e., it proceeds approximately in 60 times faster.
Analytically the relationship Q(tα) for reesterification reaction can be expressed as follows:
Q=0,108tα.
(8)
229
Further let’s consider the question, which parameters define the value α and, hence, the
active time value tα. As it is known [5], the relation α/β is connected with exponent μ at t in
the generalized transport equation as follows:
α
= μ.
β
(9)
Figure 1. The dependence of conversion degree Q at t=60 and 300 min on active time tα for reesterification
reaction without mica (1) and in presence NMM (2), SMM (3), AMM (4).
In its turn, μ and Hurst exponent H are connected between themselves like this [5]:
μ=2H.
(10)
At definite conditions the value H is defined by dimension Df (Euclidean or fractal) of
reaction product (heptylbenzoate molecule) only [8]:
H = 2 − Df
.
(11)
The combination of the equations (9)-(11) allows to obtain the simple theoretical
relationship between α and Df (at condition β=0,25):
α = 0,5(2 − D f ) .
(12)
The value of dimension Df can be determined with the aid of the following equation [9]:
230
t
( D f −1) / 2
=
c1
,
k1 (1 − Q)
(13)
where c1 is constant estimated from boundary conditions and accepted in the present paper
equal to 8×10-4 c-1.
The value Df characterizes reagents (methylbenzoata and heptanole-1) and the final
product of reesterification reaction (heptylbenzoate) structure. It is found, that Df variation
makes 1,48-1,96. In figure 2 the comparison of value α, calculated according to the equations
(9) and (12), as the function of Df is adduced. As it is expected, α increase at Df reduction is
observed and also a good correspondence of calculation according to the two mentioned
equations. This means, that the value α and, hence, reaction active time tα, is defined by
reagents structure in the reesterification reaction process.
The data of figure 2 demonstrate, that at the present choice β=0,25 in reesterification
reaction course only antipersistent (subdiffusive) transport processes are possible (α=1 is
achieved for low-molecular substances with Df=0 only), i.e., active time is always smaller
than real time. This indicates on the important role of Levy «flights» in strange diffusion type
definition.
Figure 2. The dependence of exponent α, calculated according to the equations (9) (points) and (12) (solid
line), on reagents molecules dimension Df for reesterification reaction. The legend is the same, as in figure 1.
CONCLUSIONS
Therefore, the results of the present paper have shown, that there is the principal
difference between the description of generally reagents diffusion and the diffusion defining
chemical reaction course. The last process is described within the framework of strange
231
(anomalous) diffusion concept and is controlled by active (fractal) reaction duration. The
exponent α, defining the value of active duration in comparison with real time, is dependent
on reagents structure.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
Naphadzokova L.Kh., Vasnev V.A., Tarasov A.I. Plast. Massy, 2001, №3, p. 39-41.
Vasnev V.A., Naphadzokova L.Kh., Tarasov A.I., Vinogradova S.V., Lependina O.L.
Soed. A, 2000, v. 42, №12, p. 2065-2071.
Karmanov A.P., Matveev D.V., Monakov Yu.B. Doklady RAN, 2001, v. 380, №5,
p. 635-638.
Barns F.S. Biofizika, 1996, v. 41, №4, p. 790-802.
Zelenyi L.M., Milovanov A.V. Uspekhi Fizichesk. Nauk, 2004, v. 174, №8, p. 809-852.
Korshak V.V., Vinogradova S.V. Nonequilibrium Polycondensation. (Rus.), Moscow,
Nauka, 1972, 695 p.
Feder E. Fractals, New York, Plenum Press, 1989, 242 p.
Kozlov G.V., Bejev A.A., Lipatov Yu.S. J. Appl. Polymer Sci., 2004, v. 92, №4,
p. 2558-2568.
Chapter 17
ESTIMATION OF VAPOR LIQUID EQUILIBRIUM OF
BINARY SYSTEMS TERT-BUTANOL+2-ETHYL-1HEXANOL AND N-BUTANOL+2-ETHYL-1-HEXANOL
USING ARTIFICIAL NEURAL NETWORK
H. Ghanadzadeh and A. K. Haghi*
The University of Guilan, P. O. Box 3756, Rasht, Iran
ABSTRACT
Vapor-liquid equilibrium (VLE) data are important for designing and modeling of
process equipments. Since it is not always possible to carry out experiments at all
possible temperatures and pressures, generally thermodynamic models based on
equations on state are used for estimation of VLE. In this paper, an alternate tool, i.e. the
artificial neural network technique has been applied for estimation of VLE for the binary
systems viz. tert-butanol+2-ethyl-1-hexanol and n-butanol+2-ethyl-1-hexanol. The
temperature range in which these models are valid is 353.2-458.2K at atmospheric
pressure. The average absolute deviation for the temperature output was in range 2-3.3%
and for the activity coefficient was less than 0.009%. The results were then compared
with experimental data.
Keywords: VLE data; Binary system; artificial neural network.
1. INTRODUCTION
The precise vapor-liquid equilibrium (VLE) data of binary mixtures like alcohol-alcohol
are important to design many chemical processes and separation operations. The VLE
investigations of binary systems have been the subject of much interest in recent years[1-9].
*
A.K. Haghi: Corresponding author e-mail: [email protected]
234
Conventional method of estimating the VLE is based on equations of state (EOS). These
EOS although derived from strong theoretical principles and involve a number of adjustable
parameters in terms of binary interaction parameters, as well as parameters in mixing rule
equations. Furthermore, the binary interaction parameters that are functions of both
temperature and composition need to be calculated at every temperature at which the VLE is
required. The iterative method of estimation of VLE using EOS makes it unsuitable for real
time control. The development of numerical tools, such as neural networks, has paved the
way for alternative methods to estimate the VLE [10–14]. It has attracted considerable
interest because of its ability to capture with relative ease the non-linear relationship between
the independent and dependent variables. Several authors have reported application of ANN
for estimation of thermodynamic properties such as estimation of viscosity, density, vapor
pressure, compressibility factor and VLE. A ANN model for estimation of vapor pressure
from aerosol composition, relative humidity and temperature has been reported by Potuchuti
and Wexler [15]. Chouai et al. [16] have used a ANN model for estimating the
compressibility factor for the liquid and vapor phase as a function of temperature and pressure
for several refrigerants. ANN has also been used for estimating the shape factors as a function
of temperature and density for a number of refrigerants that can be used in the extended
corresponding state model [17,18]. Lagier and Richon [19] have used ANN model for
estimation of compressibility factor and density as a function of pressure and temperature for
some refrigerants. Although a number of papers have been published with experimental data
for vapor liquid equilibrium for various systems and estimation of VLE using conventional
thermodynamic models, not many have used this technique for estimating the VLE. A ANN
based group contribution method for estimation of liquid phase activity coefficient have been
suggested by Petersen et al. [10] that can be used for estimation of VLE. A multilayer
perceptron with a single hidden layer has been used by Guimaraes and McGreavy [11] for
estimating the VLE of benzene–hexane system. Sharma et al. [12] have used the multi-layer
perceptron model to estimate the VLE for the methane–ethane and ammonia–water systems.
They have also highlighted the advantage of ANN over conventional EOS for estimating the
VLE systems containing polar compounds. Ganguly [13] on the other hand, has used the
radial basis function to estimate the VLE for several binary and ternary systems. Urata et al.
[14] have estimated the VLE using two multi-layer perceptrons. The input parameters for the
first ANN are normal boiling point divided by molecular weight, density and dipole moment
for both the components and the output is a negative or positive sign. The second ANN has an
extra input of mole fraction of one of the components in the liquid phase in addition to the
inputs of the first ANN. The output from the second ANN is logarithm of the activity
coefficient for that component. Using the logarithmic activity coefficients, vapor liquid
composition and equilibrium temperature were estimated. Mohanty [15] has used a single
multilayer perceptron for estimating the VLE of carbon dioxide–difluoromethane system.
In this paper, attempt has been made to use ANN for estimating the VLE for the systems
tert-butanol+2-ethyl-1-hexanol and n-butanol+2-ethyl-1-hexanol.In the next section, the
theory of ANN has been explained and the type of ANN which is used for estimating the
VLE has been defined. In section 3, the data inputs to the network has been shown at
atmospheric pressure and in temperature range of 353.2-458.2 K within the results and in
section 4, the outputs of ANN has been compared with experimental results.
Estimation of Vapor Liquid Equilibrium of Binary Systems…
235
2. ARTIFICIAL NEURAL NETWORK THEORY
The driving force behind the development of the ANN models is the biological neural
network, a complex structure, which is the information processing system for a living being.
Thus ANN mimics a human brain for solving complex problems, which may be otherwise
difficult to solve using available mathematical techniques. The advantage of using a ANN
model is that it does not require any other data except the input and output data. Once the
model has been adequately trained, the input data is sufficient to estimate the output. The
other advantage is a single model can be used to get multiple outputs. From its initiation in
the early forties till today there are hundreds of ANN architecture developed, however, there
are a few such as multi-layer perceptron and radial basis function that are more popular and
find wide applications. Details have been dealt with elsewhere [21,22], therefore only a brief
description of multilayer perceptron neural network that belongs to the feed forward neural
network architecture in general has been described.
2.1. The Multi-Layer Perceptron (MLP) Network
This type of network is composed of an input layer, an output layer and one or more
hidden layers (figure 1). Bias term in each layer is analogous to the constant term of any
polynomial. The number of neurons in the input and the output layer depends on the
respective number of input and output parameters taken into consideration. However, the
hidden layer may contain zero or more neurons. All the layers are interconnected as shown in
the figure and the strength of these interconnections is determined by the weights associated
with them. The output from a neuron in the hidden layer is the transformation of the weighted
sum of output from the input layers and is given as (1)
(1)
The output from the neuron in the output layer is the transformation of the weighted sum
of output from the hidden layer and is given as (2)
(2)
where pi is the ith output from the input layer, zj is the jth output from the hidden layer wij is
the weight in the first layer connecting neuron i in the input layer to neuron j in the hidden
layer, w˜ kj is the weight in the second layer connecting neuron j in the hidden layer to the
neuron k in the output layer and g and ˜g are the transformation functions. The transformation
function is usually a sigmoid function with the most common being (3) ,
(3)
236
The other commonly used function is (4),
(4)
One of the reasons for using these transformation functions is the ease of evaluating the
derivatives that is required for minimization of the error function.
q1
z0
qr
1
r
1
2
Output layer
z1
Hidden layer
Bias=1
Bias=1
p0
z0
n
1
Input layer
d
p1
pd
Figure 1. Multilayer perception with one hidden layer.
3. NEURAL NETWORK MODEL
The neural network model for the two binary systems viz. tert-butanol+2-ethyl-1-hexanol
and n-butanol+2-ethyl-1-hexanol is based on the experimental data reported by Ghanadzadeh
et al. [23]. The summary of the data is shown in tables 1 and 2. All neural networks take
numeric input and produce numeric output. The transformation function of a neuron is
typically chosen so that it can accept input in any range, and produce output in a strictly
limited range. Although the input can be in any range, there is a saturation effect so that the
unit is only sensitive to inputs within a fairly limited range. Numeric values have to be scaled
into a range that is appropriate for the network.
The three input parameters to the multi-layer perceptron are the atmospheric pressure and
the mole fraction of liquid(X1) and vapor (Y1) phases. The output parameter is the boiling
temperature.
237
Table 1. The experimental data of VLE for 2-ethyl hexanol+TBA [23]
T (K)
459.7900
445.5325
436.1964
428.8066
422.7940
388.2300
380.5000
372.1293
X1
0.0000
0.0050
0.0100
0.0150
0.0199
0.0899
0.1599
0.2299
Y1
0.0008
0.2984
0.4755
0.5892
0.6667
0.9200
0.9542
0.9666
T (K)
368.9010
366.7212
363.8160
361.6598
360.6300
359.5657
357.0900
355.5700
X1
0.3000
0.4399
0.5100
0.6499
0.7200
0.7899
0.8599
0.9300
Y1
0.9730
0.9797
0.9819
0.9858
0.9877
0.9899
0.9925
0.9957
Table 2. The experimental data of VLE for 2-ethyl hexanol+NBA [23]
T (K)
458.15
452.6213
444.5697
441.3355
418.6233
409.6233
405.6594
X1
0.0000
0.0049
0.0112
0.0200
0.0900
0.1685
0.2300
Y1
0.0008
0.2994
0.3245
0.398
0.7289
0.8125
0.8480
T (K)
402.8900
400.9500
399.5000
398.2821
396.1976
393.3350
392.0000
X1
0.3000
0.3400
0.4400
0.5100
0.6500
0.8600
0.9270
Y1
0.8703
0.8845
0.9110
0.9234
0.9235
0.9576
0.9768
At first, this network has been learned by the experimental inputs and output. During the
training period, optimizing the weights minimizes the error between the experimental and
estimated boiling temperature. The derivatives of the error function with respect to the
weights are estimated using the error back propagation technique, in which the error in the
output layer is propagated backwards to estimate the derivatives in the lower layer [21]. The
minimization of the error function is then carried out using the gradient descent method in
which the weights are moved in the direction of negative gradient. Varying the number of
neurons in the hidden layer carries out training. The model with the minimum number of
neurons in the hidden layer that gives the desired accuracy is selected. A single hidden layer
was found to be sufficient for all the three cases.
4. RESULTS AND DISCUSSION
Two neural networks have been used in this research. In the first network, the ANN input
data is the mole fractions of liquid and vapor phases and the output is the activity coefficient
of binary system. The experimental data and the estimated results of the activity coefficient
are given in tables 3 and 4.
238
Table 3. experimental and estimated of the activity coefficient
for 2-ethyl hexanol+TBA Experimental ANN Experimental ANN
Experimental
4.7600
2.2834
2.1000
1.7121
1.2698
1.2800
ANN
4.7603
2.2528
2.2482
1.9400
1.2747
1.2753
Experimental
1.0000
1.1700
1.1900
1.3000
2.0600
2.7300
ANN
0.9980
1.1523
1.1965
1.3000
2.0603
2.7305
Table 4. experimental and estimated of the activity coefficient
for 2-ethyl hexanol+NBA Experimental ANN Experimental ANN
Experimental
4.5500
3.5700
2.8200
1.7700
1.3500
1.1220
1.0000
1.0000
ANN
4.5515
3.5767
2.8208
1.7724
1.3501
1.1220
1.0003
1.0000
Experimental
1.0000
1.1500
1.2499
1.4101
1.690
2.8200
3.5201
4.3000
ANN
0.9985
1.1471
1.2506
1.4101
1.6903
2.8204
3.9100
4.2982
6.00
Exp
Exp
ANN
ANN
activity coefficient
5.00
4.00
3.00
2.00
1.00
0.00
0.00
0.20
0.40
0.60
mole fraction of TBA
Figure 2. the activity coefficient of 2-ethyl hexanol+TBA.
0.80
1.00
239
In the figures 2 and 3, the experimental data and the ANN output have been compared.
Then, the activity coefficients, which are output of the first network together with the
atmospheric pressure, mole fraction of liquid and vapor phases, are given to the second
network. After the learning and training of ANN the output, which is temperature, generated.
Now, we can compare the experimental data with the output of ANN. Figures 4 and 5 show
this comparison. The output data of model is given in the tables 5 and 6. The average absolute
deviation for the temperature output was in range of 2-3.3% and for the activity coefficient
was less than 0.009%. If more experimental data are available for the present system, the
model could be improved to be applicable for a much wider range.
5.00
EXp
Exp
ANN
ANN
4.50
activity coefficient
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0.00
0.20
0.40
0.60
0.80
mole fraction of NBA
Figure 3. the activity coefficient of 2-ethyl hexanol+NBA.
480
exp
460
ANN
temperature/K
440
420
400
380
360
340
320
300
0.00
0.20
0.40
0.60
X or Y
0.80
1.00
1.00
240
Figure 4. Boiling temperature diagram (T) for the system of 2-ethyl-l-hexanol + TBA.
490
exp
Temperature /K
470
ANN
450
430
410
390
370
350
0.00
0.20
0.40
0.60
0.80
1.00
X or Y
Figure 5. Boiling temperature diagram (T) for the system of 2-ethyl-l-hexanol + NBA.
Table 5. boiling temperatures of 2-ethyl-l-hexanol + TBA
T (K)
459.5798
453.2555
441.3895
432.5254
425.7604
406.7601
385.5020
X1
0.0000
0.0025
0.0075
0.0125
0.0175
0.0549
0.1249
Y1
0.0005
0.1496
0.3870
0.5323
0.6280
0.7934
0.9371
T (K)
375.9545
370.7535
367.3869
365.4056
363.5585
361.0082
359.5574
X1
0.1949
0.2650
0.3700
0.4749
0.5799
0.7199
0.9676
Y1
0.9604
0.9698
0.9764
0.9808
0.9839
0.9879
0.9937
Table 6. boiling temperatures of 2-ethyl-l-hexanol + NBA
T (K)
458.0382
453.2278
447.3343
441.5815
4426.1870
411.9936
406.1795
X1
0.0000
0.0024
0.0080
0.0156
0.0550
0.1293
0.1993
Y1
0.0007
0.1501
0.3120
0.3613
0.5635
0.7707
0.8110
T (K)
403.7110
401.6450
400.0036
398.3105
396.9314
394.6240
392.6627
X1
0.2650
0.3200
0.3900
0.4750
0.5800
0.7550
0.8935
Y1
0.8398
0.8774
0.8978
0.9172
0.9234
0.9401
0.9668
5. CONCLUSION
Development of ANN model for estimating VLE is less cumbersome than methods based
on EOS. It does not require parameters such as the critical properties of the components or the
241
binary interaction parameters, nor the mixing rules as required by conventional methods.
Binary interaction parameters may not be linearly related to the temperature and hence
assumption of linear relation may lead to erroneous results. Once the ANN model is trained
estimation of VLE is a one step process. This considerably saves computational time. Hence,
it may be highly suitable to use it in place of conventional methods for real time process
control. Since ANN works like a black box, it can be applied to any type of binary mixture for
which the VLE data is available irrespective of the type of the system. However, the major
disadvantage of this technique is that it can be used only in the range in which it has been
trained, as it is empirical in nature. In this work, artificial neural network models have been
developed for the binary systems, tert-butanol+2-ethyl-1-hexanol and n-butanol+2-ethyl-1hexanol, to estimate the vapor liquid equilibrium in the temperature range of 353.2–458.2K
and the atmospheric pressure. The weights have been optimized so as to minimize the error
between the estimated and experimental VLE. The weights for the models have been
tabulated for all the binary systems that can be used for predicting the VLE at any
temperature. The models were able to estimate the vapor liquid equilibrium satisfactorily. The
percent deviation in estimating the vapor phase mole fraction was found to be similar to
experimental data in ANN model. The average absolute deviation for the boiling temperature
was in range of 2-3.3% and for the activity coefficient was less than 0.009%.The weights thus
optimized during the training period can be used in ANN models for predicting the VLE of
the binary systems at the boiling temperature in the range considered in this paper.
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[23] H. Ghanadzadeh, A. Ghanadzadeh, R. Sariri and A. Boshra, Fluid Phase Equilib.
233(2005) 123-128.
Chapter 18
LIQUID-LIQUID EQUILIBRIA OF THE MME
(METHYLCYCLOHEXANE + METHANOL +
ETHYLBENZENE ) SYSTEM
H. Ghanadzadeh and A. K.Haghi*
The university of Guilan, P O. Box 3756, Rasht, Iran
P.O .Box 3756 Rasht, Iran
ABSTRACT
The determination region of solubility of methanol with gasoline of high aromatic
content was investigated experimentally at temperature of 288.2 K. A type 1 liquid-liquid
phase diagram was obtained for this ternary system. These results were correlated
simultaneously by the UNIQUAC model. By application of this model and the
experimental data the values of the interaction parameters between each pair of
components in the system were determined. This revealed that the root mean square
deviation (RMSD) between the observed and calculated mole percents was 3.57% for
methylcyclohexane + methanol + ethylbenzene. The mutual solubility of
methylcyclohexane and ethylbenzene was also demostrated by the addition of methanol
at 288.2 K.
Keywords: liquid-liquid equilibria; phase equilibria; plait point; ternary system; UNIQUAC
model.
1. INTRODUCTION
The precise liquid-liquid equilibria (LLE) data is necessary to rational design of many
chemical processes and optimize extraction processes. Many researchers have investigated
various kinds of multi-component systems in order to understand and provide further
*
A.K.Haghi: Corresponding author e-mail: [email protected]
244
information about the phase behavior and the thermodynamic properties of such systems [18]. In order to be able to predict LLE in multi-component systems an adequate equilibrium
model. Earlier researchers reported the correlation of LLE systems with the solution model of
the UNIQUAC [9-10]. This model could depends on optimized interaction parameters
between each pair of components in the system, which can be carried out by experiments.By
optimizing the interaction parameter, the UNIQUAC equation can be best fitted to the
experimental composition.
In recent years, there has been increasing attraction in adding a range of oxygenated
compounds, mainly alcohols and ethers, to gasoline due to their octane enhancing [11]. Also,
by using oxygenated compounds instead of Lead in the gasoline the levels of contamination
can be remarkably reduced. In some countries, the oxygenated compounds such as, methyl
tert-butyl ether (MTBE), tert-amyl methyl ether (TAME) and ter-amyl alcohol (TAOH) have
been used. Methanol is one of the most appropriated oxygenated compounds for this purpose
because of its physical-chemical properties. Methanol can be easily produced from a variety
of organic materials [12], petroleum, and coal. However, phase separation and the high vapor
pressure of methanol in gasoline had been a restriction for achieving a wide application.
Therefore, thermodynamic studies and the precise liquid-liquid equilibria data for methanol
and representative compounds of the gasoline is necessary in order to the determine region of
solubility of methanol and plait point of the interest system.
Recently, Trejo et al. [13] have reported liquid-liquid equilibria measurements for
methanol and representative compounds of the gasoline, and their investigation were
somehow important in gasoline reformation with methanol. However, the present study is an
effort to show experimentally that methanol can be used as an appropriate oxygenated
compound in gasoline formulations. In view of this, the investigation included, the liquidliquid phase equilibria data for three different ternary systems: methylcyclohexane +
methanol +ethyl benzene at 288.2 K. Where the paraffin is methylcyclohexane a
representative component of the gasoline, methanol, is the oxygenated compound, and the
aromatic hydrocarbons are benzene, ethyl benzene. A high aromatic gasoline (35.4 vol %
aromatic, 60.4 vol % saturates, and 4.2 vol % olefins) having density of 0.738 gr/ml was used
in this study. The UNIQUAC model was used to correlate the experimental liquid-liquid
equilibria data. However, the values for the interaction parameters were observed for the
UNIQUAC model. The influence of aromatic compounds on mutual solubility of
methylcyclohexane and methanol was also investigated at 288.2 K.
2. EXPERIMENTAL
2.1. Materials
Methanol, toluene, methylcyclohexane and ethylbenzene were obtained from Merck at a
purity of about 99.5 % and were used without further purification. The purity of these
materials was checked by gas chromatography.
Liquid-Liquid Equilibria of the MME…
245
2.2. Apparatus and Procedure
The liquid-liquid phase equilibria measurements under ambient pressure and temperature
(288.2 K) were carried out using an apparatus of a 300 ml glass cell. The temperature of the
cell was controlled by a water jacket and measured with a copper-constantan thermocouple
and was estimated to be accurate within ± 0.1 K. A series of liquid-liquid equilibria
measurements were performed by changing the composition of the mixture.
The prepared mixtures were placed in the extraction vessel, and stirred for 2 h and then
left to settle for 4 h. Samples were taken by a syringe (Gaschromatographic’s Hamilton 0.4
μL) from both the upper (methylcyclohexane) phase and lower layers (aromatic phase). Both
phases were analyzed using Konik gas chromatography (GC) equipped with a thermal
conductivity detector (TCD) and Shimadzu C-R2AX integrator. A 2 m × 2 mm column was
used to separate the components
2.3. The UNIQUAC Model
At liquid-liquid equilibrium, the composition of the two phases (refined phase and
extracted phase ) can be determined from the following equations
(γixi ) 1= (γixi ) 2
(1)
Σ xi1 = Σ xi2 =1
(2)
Here γi1 and γi2 are the corresponding activity coefficients of component i in phase 1 and 2,
xi1, and xi2 are the mole fraction of components i in the system and in phase 1 and 2
respectively. The interaction parameters between methylcyclohexane , methanol and ethyl
benzene are used to estimate the activity coefficients from the UNIQUAC groups. Eqs. (1)
and (2) are solved for the mole fraction (x) of component i in the two liquid phase.The
UNIQUAC model (universal quasi –chemical model) is given by Abrams and prausnitz [8] as
c
c
θi
Φi z c
gE c
= ∑xi ln( ) + ∑qi xi ln( ) − ∑qi xi ln(∑θ jτ ji )
RT i=1
xi 2 i=1
Φi i=1
j =1
(3)
or
lnγi = lnγic+ lnγiR
(4)
where
⎛Φ
ln γ ic = ln ⎜⎜ i
⎝ xi
⎞ z
⎛θ
⎟⎟ + q i ln ⎜⎜ i
⎠ 2
⎝ Φi
⎞
φ
⎟⎟ + ιι − i
xi
⎠
c
∑xι
j =1
j j
(5)
246
⎡
⎛
⎜
⎢
c ⎜ θ τ
c
⎛
⎞
⎢
j ij
ln γ i R = qi ⎢1 − ln ⎜ ∑ θ jτ ji ⎟ − ∑ ⎜
c
⎜
⎟
⎢
⎝ j =1
⎠ j =1⎜ ∑ θ k τ kj
⎜
⎢
⎝ k =1
⎣
⎞⎤
⎟⎥
⎟⎥
⎟⎥
⎟⎥
⎟⎥
⎠⎦
(6 )
Here, γic is combinatorial parte of the activity coefficient, and γiR the residual part of the
activity coefficient. The variable τij the adjustable parameter in the UNIQUAC equation and
xi the equilibrium mole fraction of component i. The parameter Фi ( segment fraction ) and θi
( area fraction ) are given by the following equation:
Φ
=
i
x i ri
∑
x i ri
i=1
θ
i
=
x i ri
ij
(8 )
c
∑
i=1
τ
(7 )
c
xiq
i
( u ij − u
⎛
= exp ⎜⎜ −
RT
⎝
jj
⎞
⎟
⎟
⎠
(9 )
The parameter uij characterizes the interaction energy between compounds i and j and uij
equals uji.
⎛ z⎞
⎟ (ri − q i ) − (ri − 1 )
⎝2⎠
ιi = ⎜
(10 )
where z=10, is lattice coordination number, ri the number of segments per molecule, and qi
the relative surface area per molecule.
3. RESULTS AND DISCUSSION
Figures 1 compare graphically the observed and calculated phase behavior (liquid-liquid
equilibria data) for three ternary system: methylcyclohexane +methanol + ethylbenzene) at
temperature of 288.2 K.
247
toluene
0.5
0.5
0.6
EXP
Uniquac
0.4
0.7
0.3
0.8
0.2
0.9
0.1
1.0
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
methanol
0.9
1.0
methylcyclohexane
Figure 1. Experimental (⎯) and predicted UNIQUAC (---) LLE data at 288.2 K.
The liquid-liquid phase diagrams exhibit type 1 systems and as expected for these type of
systems, the diagrams present plait point (where the two phases in equilibrium become
experimentally miscible). Due to the variation of tie-line, the measuring of plait point is
slightly difficult. Meanwhile, the value of the plait point is important and it is a necessary
value to define the interval of solubility that present in components of a system. On other
hand, this point can define the appropriate quantity of oxygenated compound that can be
added to gasoline without phase separation. In view of the above, the plait points were
determined using a graphic method [14]. The values of the plait point for these systems are
presented in table 3
Table 1. The UNIQUAC binary interaction parameters (u12 and u21) optimized for the
system methylcyclohexane + methanol + ethylbenzene
Components
Methylcyclohexane
methanol
ethylbenzene
Methylcyclohexane
0.000
-112.337
9.17
methanol
425.760
0.000
135.369
ethylbenzene
32.675
-54.406
0.000
Table 2. The UNIQUAC structural parameters
Components
Ethybenzene
Methylcyclohexane
methanol
r
4.600
4.640
1.4311
q
3.510
3.550
1.4720
Table 3. Experimental and predicted values of the plait point
and the percentage of relative error
Components
Methylcyclohexane-methanolethylbenzene
Experimental
0.5996
Uniquac
0.6480
Relative error %
0.917
248
As it can be observed from figure 1, the ternary systems present a small region of partial
miscibility that limited by the plait point. This reveals that, methanol is totally miscible with
the gasoline in a wide interval. As illustrated in figure 1 and indicated in table 4. it is evident
that despite the representative compounds of the gasoline, the region of completely
miscibility and also the plait point values are nearly the same and independent of the type of
aromatic hydrocarbon. This provides an advantage as it can define the appropriate quantity of
oxygenated compound (methanol) that can be added to the gasoline.
The UNIQUAC model was successfully used to correlate the experimental liquid-liquid
equilibria data. As it can be seen from figure 1, the predicted tie lines (dashed lines) are in
good agreement with the experimental data (solid lines). In other words, the UNIQUAC
equations adequately fit the experimental data for this multi-component system.
The optimum UNIQUAC interaction parameters uij between methylcyclohexane,
methanol, and ethylbenzene were determined using the observed liquid-liquid data, where the
interaction parameters describe the interaction energy between molecules i and j or between
each pair of compounds. Table 4 show the calculated value of the UNIQUAC binary
interaction parameters for the mixture methanol + ethylbenzene using universal values for the
UNIQUAC structural parameters. The equilibrium model was optimized using an objective
function, which was developed by Sørensen [15].
Table 4. Experimental and predicted LLE for the ternary system
(methycyclohexane + methanol + ethylbenzene) at 288.2 K
Methylcyclohexane (upper phase)
Mole fraction
Mole fraction methanol
methylcyclohexane
Exp.
Uniquac
Exp.
Uniquac
0.8224
0.8386
0.1270
0.8810
0.7262
0.7600
0.1970
0.8659
0.6565
0.7229
0.2600
0.8360
0.5845
0.6621
0.3290
0.8040
0.5122
0.5586
0.3998
0.7699
0.4167
0.4049
0.4999
0.7070
0.3269
0.2801
0.5996
0.6480
RMSD%
4.83
4.40
Ethylbenzene (lower phase)
Mole fraction
methylcyclohexane
Exp.
Uniquac
0.2407
0.1102
0.2115
0.1181
0.1925
0.1371
0.1740
0.1591
0.1438
0.1851
0.1211
0.2328
0.1047
0.2801
2.40
Mole fraction methanol
Exp.
0.8698
0.8360
0.7930
0.7675
0.7420
0.7040
0.5996
Uniquac
0.8810
0.8659
0.8360
0.8040
0.7699
0.7070
0.6480
2.67
Moreover, the objective function obtained by minimizing the square of the difference
between the mole fractions calculated by UNIQUAC model and the experimental data.
Furthermore, he UNIQUAC structural parameters r and q were carried out from group
contribution data that has been previously reported [14-15]. The values of r and q used in the
UNIQUAC equation are presented in table 4. The goodness of fit, between the observed and
calculated mole fractions, was calculated in terms RMSD [1]. The RMSD values were
calculated according to the equation of percentage root mean square deviations (RMSD%):
⎡ 3 2
n ⎢ ∑∑
RMSD % = 100 ∑ ⎢ i j
k ⎢
⎢
⎣
(xi,exp − xi,calc) ⎤⎥
2
j
6n
⎥
⎥
⎥
⎦
(1)
249
Mole fraction of ethyle benzane
where n is the number of tie-lines, xexp indicates the experimental mole fraction, xcalc is the
calculated mole fraction, and the subscript i indexes components, j phases and k = 1,2,…n (
tie-lines ). The average (RMSD%) between the observed and calculated mole percents with a
reasonable error was 3.57% methylcyclohexane + methanol + ethylbenzene (see table 4). The
percentage of relative error between the experimental and predicted values of the plait point
for these systems have been also compiled in table 4.
The experimental result shows that the existence of aromatic compound(ethylbenzene) in
gasoline increases the solubility of methanol in methylcyclohexane.
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
0.00
0.20
0.40
0.60
0.80
1.00
Mole fraction of methanol
Figure 2.
1.00
0.90
Separation factor
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.1
0.15
0.2
0.25
0.3
mole fraction of methanol in mch phase
Figure 3.
0.35
250
4. CONCLUSION
An experimental investigation of equilibrium behavior of the systems composed of
methylcyclohexane + ethylbenzene + methanol was carried out at 288.2 K. The liquid-liquid
phase diagrams exhibit type 1 systems and indicate that methanol is totally miscible with the
gasoline in a wide interval. Therefore, methanol may be considered as a good candied in
gasoline formulations for vehicular fuels.
The optimum UNIQUAC interaction parameters between methyl cyclohexane, methanol
and ethylbenzene were determined using the experimental liquid-liquid data. The average
RMSD value between the observed and calculated mole percents with a reasonable error for
these system were methylcyclohexane + methanol + ethylbenzene. in the UNIQUAC model.
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Technical University of Denmark, Lyngby, Denmark, (1980).
N. Pesche, S. I. Sandler, J. Chem. Eng. Data, 40 (1995) 315.
Helinger, S. I. Sandler, J. Chem. Eng. data, 40 (1995) 321.
Chapter 19
SUGAR CARBAMIDES
J. A. Djamanbaev1, J. A. Abdurashitova and G. E. Zaikov2
1
Institute of Chemistry and Chemical Technology, Kyrgyz Academy of Sciences,
256 a, Chui Prospect, Bishkek 720071, Kyrgyzstan, e-mail: [email protected]
2
N.M. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, 4
Kosygin Str., Moscow 119334, Russia; E-mail: [email protected]
ABSTRACT
The results of experimental researches on the synthesis of sugars derivatives with
glycosylamide and thioamide bonds have been presented in this work. The possibility of
using their in the preparative chemistry of sugars, some fields of medicine and agriculture
has been shown.
Keywords: monosaccharides, glycosylisotiocyanates, glycosyltiocyanates, glycosylureas,
glycosylnitrozometylureas.
The study of the reactions with the participation of glycosyl bonds is important not only
for the theory of carbohydrates structure and reactional ability of carbohydrates. They
represent a significant interest and solution for a number of important problems of organic,
bioorganic chemistry, and molecular biology, fermentative catalysis, since the glycosyl bond
is one of the most important structural elements of many biologically active compounds.
The bioorganic chemistry laboratory of the Institute of Chemistry and Chemical
Technology under the National Academy of Science of the Kyrgyz Republic is conducting
studies in the area of kinetics, mechanisms of catalysis of carbohydrate reactions and
development of new methods of synthesis of the physiologically active compounds with the
N-glycosylamide bonds (derivatives of the sugar carbamides) for their application in
medicine and other industries. Among the practically important properties of this type of
derivatives of the sugar carbamides is the high hydrolytic stability as compared to the simple
N-glycosides of alkyl(aryl)amines. Chemical connection of sugars with the unprotected
hydrocsyl groups with the biologically active compounds at the account of stable N-
252
J. A. Djamanbaev, J. A. Abdurashitova and G. E. Zaikov
glycosylamide bonds will lead to the growth of solution in water, decrease of toxic and
change of selective action of the preparations [1, 2].
Two bases approaches are used in the synthesis of sugar carbamides: direct interaction of
carbohydrates with carbamides and their analogs in the conditions of acid catalysis (a) and
interaction of acetylation N-glycosylisothiocyanates with amines (b) or interaction of
acetylation N-glycosylamines with arylisothiocyanates (c) [3].
OH
O
OH
OH
+
H 2N
OH
NHR
NHR
O
+
OH
H 2O
a)
OH
OAc
O
OAc
N=C=O
+ H2N
NH C
OH
O
OH
OAc
O
OAc
C
H
OH
O
+
R/
OAc
NH C
H
N
R/
b)
O
OAc
OAc
OAc
O
OAc
OAc
OAc
OAc
OAc
O
NH2
+ C6H5NCO
OAc
NH C
O
H
N
C6H5
c)
OAc
OAc
The first direct approach requires a long stand of the reaction mixture under high
temperature. In the crystal form the product could be receive only after the fermentative
splitting of un-reacted glucose. In the further studies [4-6] the direct method was somewhere
improved and applied to other mono- and disaccharides, however, there were no principal
changes in the synthesis methods.
The second approach - amination glycosylisothiocyanates was suggested by E. Fisher
[3,7]. The method was widely used in the synthesis of analogs of glycoproteins and
nucleosides of pirimidine and geterocyclic derivatives of the carbohydrates [7-8].
The version of the isothiocyanates method of E. Fisher is based on the interaction
between alkyl- and arylisothiocyanates with glycosylamines, produced, for example, though
hydrogenezation glycosylazids [3].
These methods have many stages and require preliminary protection of the OH-groups,
followed by the removal of protective functions. The advantages of E. Fisher,s method
include its universality - the ability to introduce ureido (thioureido) fragments in any position
of the carbohydrate ring with the presence of amino group in this position.
The works of [9, 10] suggest a simplified isothiocyanates synthesis of glycosylureas.
According to this method, in the beginning they receive anomerical mixture of Nalkylglycosylamines, conduct the condensation with isocyanates and receive anomerical
mixture of N-alkylglycosylamines, conduct the condensation with isocyanates and receive
anomerical mixture of N-alkylglycopyranosylthioureas. After the processing of this mixture
with the ant acid the β-anomer of N-alkyl-N/-glycopyranosylthiourea is separated.
Sugar Carbamides
OH
O
OH
OH
OH
O
NH2R/
NHR/
OH
OH
253
OH
O
RNCO
OH
OH
O
C
NHR
O
OH
OH
H+
NH
OH
OH
OH
R/
R/
N
OH
OH
C
NHR
O
OH
The authors suggest a new more effective method of synthesis of N-glycosylcarbamides
with the use of N-arylglycozides [11, 12]. The kinetic studies have shown that the
replacement of the glycosyl hydrocsyl by N-arylaglycon leads to the growth of the reaction
properties of C1 in the reactions of nucleophilic addition and replacement, easing introduction
of aglycons with small basic in the conditions of acid catalysis.
OH
O
OH
O
OH
OH
+ NH2C6H4R
OH
- H2O
OH
NHC6H4R/
+
OH
OH
NH2CONHR//
-NH2C6H4R/
OH
OH
O HN
C
NH
R//
O
OH
OH
OH
/
R =H, CH3 , ì -NO2, ï
C
O
OH
R//=H, CH3, C2H5, C3H7, C4H9, C6H5, C6H4OCH3
To receive N-glycosylureas on the reaction of N-transglycosylation, it is enough to heat
the mixture of ureido derivatives and N-arylglycozides for a short period (10-30 min.) in an
alcohol environment with some small addition of mineral acid until the mixture becomes
homogenous.
The scheme shows that arylamine plays the role of nucleophilic catalyst reaction of direct
condensation of monosaccharide with the ureido derivatives. That is why in order to simplify
the synthesis of N-glycosylureas, one can go without N-arylglycozid and instead use the
catalyst additions of arylamine [13, 14].
When using the small basic m-nitroanilin as a catalyst, β-anomerical forms of
glucopyranosylureas are mostly formed. The stability of N-glycosylamid bond allows to
recommend these fragments as a connecting bridge between sugars and biologically active
compounds for the receiving sugar derivatives as drugs. The use of sugar carbamides is
limited mostly to N-glycosylureas, which are recommended for technical reasons. Currently,
a more important tendency is developing which leads to their applications in the area of
medical-biological problems. The sugar derivatives with N-nitrozo-N-alkylcarbamide
fragments deserve a special attention due to their important role in the chemical therapy of the
cancer diseases [15, 16].
254
J. A. Djamanbaev, J. A. Abdurashitova and G. E. Zaikov
The interest to compounds of this class arouse after the discovering of high antileucemia
activity of 1-methyl-1-nitrozourea [15]. Methods of synthesis of N-nitrozocarbamide
fragments in the carbohydrate rings were worked out to get select acting antitumour remedies
[17, 18, 19, 20].
Comparative methods of pharmaco-toxicological research help to ascertain [2, 19] that
adding of N-nitrozo-N-metylurea on the glycosyl center leads to the sharp lowering of toxic
activity of the antitumour preparation and to changing of spectrum of its activity to a number
of experimental swelling models. It is shown, that toxic and selective actions of carbohydrate
analogs of nitrozometylurea depend on the monosaccharide carrier of the cytosine agent.
N-nitrozo derivatives of N-glycosylureas attract attention to them not only as perspective
antitumour preparations also as compounds with high reactional ability on the bases of which
new methods of the carbohydrate derivative synthesis can be developed.
The authors in their works [21, 22] show that N-nitrozo derivative of carbohydrates can
easily come into the reaction of substitution on carbonil group of N-aglicon witch the help of
interaction of amines witch the development of sugar carbohydrate derivatives.
OH
O
OH
NH C
N(NO)CH3
OH
O
NH2R
NH C
OH
O
H
N
R
+ CH3OH + N2
O
OH
OH
OH
OH
The described reaction opens great possibilities for the synthesis of different Nglycosylation derivatives witch carbamide bridges including such derivatives of sugar, the
synthesis of which by methods of direct interaction of nucleophilic agents with a glycoside
center, turns out to be difficult for poor reactional ability of the attack amino group.
The example of it can be shown by reaction of N-glycosylation semicarbazids [22].
OH
O
OH
NH C
N(NO)CH3
OH
O
NH2-NH2
OH
O
OH
NH C
O
H
N
NH2
+ CH3OH + N2
OH
OH
OH
The developed method of getting of glycosylation semicarbazids with N-glycosyl bond
and the final reactional amino group opens wide possibilities in the chemistry of semicarbazid
derivatives.
REFERENCES
[1]
[2]
[3]
V. A. Afanasjev, J. A. Djamanbaev, G.E. Zaikov // Progress in chemistry. V. 51. 1982.
p.661.
J. A. Djamanbaev, L. A. Ostrovskaja, V. A. Afanasjev // Chemical therapy of suellings
in the USSR. Issue 52. 1988. p. 145.
J. Goodman. Adv. Carbohydrate Chem.V.13. 198. p. 215.
Sugar Carbamides
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
255
Benn M.N., Jones A.S. J. Chem. Soc. V.82. 1960. p. 3837.
Badawi E. Jones A.S. Staseg M. Tetrahedron. 1966. p.281.
N. G. Shkantova, M. I. Dudkin, S.E. Grinshpun // J. Life of applied chemistry. V. 40.
1967. p. 164.
Zbigniew by ,Witczak J. Adv. Carbohydrate Chem. and biochem. V.44. 1986. p. 91.
Djamandaev J.A., Abdurashitova J.A., Sarimzakova R. K., Dermugin V.S.//Vestnic
KNU.-Bishkek.-2003.-Ser. 3.-V.-1.-p. 123.
Tsujihara K., Ozeki M., Morikawa T., Arai Y. Chem. pharm. Bull. V. 29. 1981. p.
2509.
Tsujihara K., Ozeki M., Morikawa T.,Kawamori M., Akaike Y., Arai Y.// J. Med.
Chem. V. 25. 1982. p. 441.
V. A. Afanasjev, J. A. Djamanbaev // Proceeding of the Academy of sciences of Kyrg
SSR. № 2. 1973. p. 64.
V. A. Afanasjev, J. A. Djamanbaev // Chemistry of natural compounds. № 2. 1974. p.
176.
V. A. Afanasjev, J. A. Djamanbaev // Proceeding of the Academy of sciences of Kyrg
SSR. № 2. 1982. p. 43.
V. A. Afanasjev, J. A. Djamanbaev, E. I. Kurmanalieva / Author, certificate USSR. №
772101. 1980.
N. M. Amanual, D.B. Korman, L. A. Ostrovskaja, L. B. Gorbacheva, N.P. Dementjeva.
Nitrozoalkylureas – a new class of antisuellig means. M: Science. 1977. 320 p.
Schein P.S., Heal J., Gveen D., Wolley P.V. Fudman. Cancer Chemotherapy. (Basel).
1978. B. 64.
Suami T., Machinami T. Bull. Chem. Soc. Japan. V. 43. 1970. p. 2953.
Panasci L.C., Fox P.A., Schein P.S. Cancer. Res. v. 37. 1974. p. 3321.
N. M. Amanual, D.B. Korman, L. A. Ostrovskaja. From the collection of conferences.
Actual problems of the swelling experimental chemical therapy. Chernogolovka. 1980.
p. 126.
V. A. Afanasjev, J. A. Djamanbaev . Patent of the USA. № 4.656.259. 1987.
J. A. Djamanbaev, V. A. Afanasjev, Z. А. Djamanbaeva / Collection. Carbohydrates
and carbohydrate plants of Kyrgyzstan. Publishing house: Ilim. Frunze. 1984. p. 3.
J. A. Djamanbaev, Z. А. Djamanbaeva, V. A. Afanasjev. Rospatent. № 2027721. 1995.
Chapter 20
IMPACT OF CHAIN-END STRUCTURE, BASIC
COMONOMER INCORPORATION AND PENDANT
STRUCTURE ON THE STABILITY OF VINYLIDENE
CHLORIDE BARRIER POLYMERS
Bob A. Howell*, Adeyinka O. Odelana
and Douglas E. Beyer
Center for Applications in Polymer Science
Central Michigan University
INTRODUCTION
Vinylidene chloride copolymers occupy a place of prominence in the barrier plastic
packaging industry. The homopolymer, poly(vinylidene chloride) (PVDC), is not
commercially important because it undergoes catastrophic decomposition at its melt
temperature. Rather, it is the copolymers with vinyl chloride, alkyl acrylates, acrylonitrile,
and alkyl methacrylates that are commercially viable.[1-8] The vinylidene chloride
copolymers contain low levels of unsaturation due to thermal dehydrochlorination during
polymerization. Copolymerization with one or more comonomers (≤ 15 wt %) decreases melt
temperature and increases solubility. Often one copolymer is introduced to improve
processability or solubility of the polymer, while another is introduced to provide specific use
properties. A vinylidene chloride (VDC) copolymer containing high VDC content acts as
excellent barrier to the transport of small molecules, principally oxygen, (to prevent food
spoilage) as well as excellent barrier to the transport of flavor and aroma constituents (to
prevent flavor scalping on the store shelf).[9-11] These copolymers occupy a place of
prominence in the barrier plastics packaging industry. They have been used as wraps for meat
and diary products, and as components of rigid multilayer structures such as bottles, jars,
tubs, etc. Packages are important for good appearance, taste and shelf life. Modern packaging
*
Bob A. Howell: Mt. Pleasant, MI 48859-0001; [email protected]
258
Bob A. Howell, Adeyinka O. Odelana and Douglas E. Beyer
represents a sophisticated technology rooted deeply in fundamental polymer science. Plastics
represent a large percentage of new packaging materials. Plastics have many advantages over
conventional packaging materials for many applications. These advantages include:
•
•
•
•
Plastics can be used over a wide range of temperature.
Some plastics, principally VDC copolymers, provide an excellent barrier to the
transport of small molecules such as oxygen, water, and carbon dioxide.
Providing good moisture barrier thus preventing dehydration of food items.
Providing an aroma barrier to help retain flavor in foods and to prevent the
absorption of undesirable flavors or aroma.
Copolymerization results in regular structure, high density, and high crystallinity. These
polymers are generally free of the defect sites characteristic of similar vinyl polymers, i.e.,
they are regular head- to-tail, unbranched and highly crystalline polymers. While these
outstanding characteristics have made them commercial successes, high VDC content
copolymers undergo thermally-induced degradative dehydrochlorination at process
temperatures. The thermal instability of VDC and its copolymers has been of interest for
several decades.[12,13] The dehydrochlorination occurs at modest temperatures (120 – 200
°C) and is a typical chain process involving initiation, propagation, and termination phases
(figure 1), often enhanced by defects in the polymer mainchain.[14-16] Defect structures,
arising from internal unsaturation (allylic dichloromethylene groups), serve as initiation sites
for the degradation.[17] Sequential dehydrohalogenation can lead to the formation of
conjugated polyene sequences along the polymer mainchain.
Figure 1. Hydrogen Chloride Evolution for the Thermal Degradation of a Typical Vinylidene Chloride
Polymer.
This is the primary degradation process accompanying processing of the polymer. The
early stage of the dehydrochlorination process is uncomplicated by interfering processes. The
only product observed by evolved gas analysis is hydrogen chloride (scheme 1). The sample
Impact of Chain-End Structure, Basic Comonomer Incorporation…
259
weight loss is directly reflective of the extent of degradation.[18, 19] Hence, the degradation
of vinylidene polymers presents an ideal reaction that can be studied using thermogravimetric
techniques.[20, 21]
CH2
Fast
CCl2
CH
n
CCl
n
+
n HCl
Scheme 1. The Principal Step Involved in the Thermal Degradation of Vinylidene Chloride Polymers.
These copolymers must, therefore, be processed with care at relatively low temperatures
(150 – 170 °C) in specially designed equipment. If appreciable, the degradation can lead to
discoloration of the materials thereby making them unsuitable for packaging.
Scheme 2. Mode of Degradation of Vinylidene Chloride Polymers.
Thermal homolysis of an allylic carbon – chlorine bond generates a tight carbon, chlorine
radical pair. The chlorine atom abstracts an adjacent hydrogen atom to extend the
unsaturation by one unit. Allylic dichloromethylene units are regenerated in the polymer
mainchain and serve as initiation sites for degradation and so propagate the
dehydrochlorination reaction (scheme 2).[14] Another consequence of this degradation is the
evolution of hydrogen chloride. The vinylidene chloride repeat unit loses a mole of hydrogen
chloride which can react with the walls of process equipment, commonly stainless steel, to
form iron(III) chloride which is a strong Lewis acid catalyst, strong enough to promote further
dehydrohalogenation of the vinylidene repeat units at process temperatures (120 – 200 °C).
Hence, this problem must be overcome or at least controlled to permit the commercial
260
exploitation of these materials. One way is to scavenge the hydrogen chloride as it is formed
during thermal degradation. This will prevent reaction with the walls of the processing
equipment and the subsequent formation of metal halides. Attempts to stabilize VDC systems
have often resulted in decreased stability as a result of E2 elimination reactions which
introduce initiation sites (unsaturation) for the thermal degradation. Presently, passive bases
such as magnesium oxide, or tetrasodium pyrophosphate which are capable of absorbing
hydrogen chloride, are introduced into the polymer melt during processing to partially
overcome this problem.[22] However, the presence of these inorganic bases may negatively
impact clarity of finished items, particularly for film applications. For this reason organic
bases which would be compatible with the polymer, and would effectively absorb evolved
hydrogen chloride, and would not actively promote the dehydrochlorination reaction have
been sought.[23] Amines, even highly hindered amines, have been found to be too basic to
function as satisfactory stabilizing additives.[24,25] In this case, an amine has been
incorporated as a comonomer into a vinylidene chloride copolymer. Vinylidene chloride
copolymers containing a constant five mole percent methyl acrylate and small but varying
amounts (0.1 – 3.0 mole percent) of 4-vinylpyridine have been subjected to thermogravimetry
to assess thermal stability. In addition, some limited studies of the impact of initiator used for
polymerization and the nature of acrylate comonomer on the thermal stability of vinylidene
chloride polymers have been initiated using thermogravimetric techniques.
The thermal degradation of the vinylidene chloride /methyl acrylate copolymer at modest
temperatures (120 – 200 °C) corresponds to the first order loss of hydrogen chloride from the
vinylidene chloride repeat units in the polymer. Since hydrogen chloride has been shown to
be the only volatile product of the degradation at these temperatures, the degradation reaction
can be easily studied by thermogravimetry.[14-16, 18-21] Hence, the rate of change of sample
mass is a measure of the rate of degradation. It has also been found that the thermal
degradation is a typical chain process involving initiation, propagation, and termination
phases (figure 2), often enhanced by defects in the polymer mainchain.[14] The degradation
becomes prominent in the vicinity of 190 °C and occurs smoothly to reflect the loss of one
mole of hydrogen chloride from each vinylidene chloride repeat unit in the polymer chain
(figure 2).
Both initiation and propagation phases of degradation are obvious in the plot of weight
loss versus time (figure 2). However, this becomes more apparent in the plot of ln{(w∞- wo) /
w∞ - wt)} versus time (figure 3) , where w∞ is the weight of the sample at infinite time (t∞)
taken as that weight which would remain after 37.62% of the initial vinylidene chloride
component weight had been lost (corresponding to the loss of one mole of hydrogen chloride
from the vinylidene chloride repeat units in the polymer); wt is the sample weight at any time,
t, during the experiment; and wo is the sample weight at time zero (to), i.e., the time at which
the first point was recorded.
261
Figure 2. Degradation of a Vinylidene Chloride/Methyl Acrylate (Five Mole percent)/ 4-Vinylpyridine (0.1
Mole Percent) Terpolymer at 170 °C.
0.07
ln(W ∞-W o /W ∞-W t)
0.06
0.05
0.04
0.03
0.02
0.01
0
0
500
1000
1500
2000
2500
Time (sec)
Figure 3. Thermal Degradation of a Vinylidene Chloride/Methyl Acrylate (Five Mole Percent)/ 4Vinylpyridine (0.1 Mole Percent) Terpolymer at 170 °C.
The initiation degradation reaction is apparent in the initial portion of the weight loss
versus time plot while the propagation reaction is dominant at long reaction time. Thus rate
constants for both processes may be extracted from the data presented in this plot. Data from
the appropriate portions of this plot are replotted in figures 4 and 5. Figure 4 represents a plot
of ln mass change versus time for the early portion of the degradation in which initiation is
occurring. An excellent linear plot is obtained for which the slope reflects the rate constant, ki,
for the initiation of degradation. Similarly, the corresponding plot (figure 5) of data at long
reaction time allows the extraction of kp, the rate constant for propagation of the degradation
262
ln (w∞ - wo/w∞ -
reaction. Multiple determinations were carried out at three different temperatures to obtain
reliable rate constants for the determination of activation parameters. In all cases excellent
reproducibility was observed. The rate constants for the degradation at 170, 180, and 190 °C
are tabulated in table 1.
Figure 4. Initiation Rate Constant (ki) for the Thermal Degradation of a Vinylidene Chloride/Methyl Acrylate
(Five Mole Percent)/ 4-Vinylpyridine (0.1 Mole Percent) Terpolymer at 170 °C.
Figure 5. Propagation Rate Constant (kp) for the Thermal Degradation of a Vinylidene Chloride/Methyl
Acrylate (Five Mole Percent)/ 4-Vinylpyridine (0.1 Mole Percent) Terpolymer at 170 °C.
263
Table 1. Rate Constants for the Thermal Degradation of Vinylidene Chloride/Methyl
Acrylate (Five Mole Percent)/4-Vinylpyridine (Variable Content) Terpolymers.
4-Vinylpyridine
(Mole %)
0
0
0
0.1
0.1
0.1
0.3
0.3
0.3
0.5
0.5
0.5
1
ki x 105
(sec-1)a,c
1.54 ± 0.02
3.31 ± 0.03
6.27 ± 0.02
1.86 ± 0.01
3.65 ± 0.05
6.62 ± 0.01
20.2 ± 0.10
30.3 ± 0.10
38.8 ± 0.10
46.4 ± 0.30
57.1 ± 0.10
65.5 ± 0.20
kp x 105
(sec-1)b,c
2.07 ± 0.04
4.27 ± 0.01
8.97 ± 0.02
2.26 ± 0.01
4.76 ± 0.01
9.28 ± 0.01
25.3 ± 0.20
32.1 ± 0.10
44.8 ± 0.40
54.6 ± 0.10
62.3 ± 0.10
72.9 ± 0.11
204.0 ± 3.00
Temperature
(°C)
170
180
190
170
180
190
170
180
190
170
180
190
170
a. Rate constant for the initiation of degradation.
b. Rate constant for the propagation of degradation.
c. Average of three determinations accompanied by the average deviation.
It may be noted that the rate constants for degradation of the vinylidene chloride/methyl
acrylate (five mole percent) copolymer containing no 4-vinylpyridine (ki = 1.54 x 10-5 sec-1 ; kp
-5
-1
-5
-1
= 2.07 x 10 sec ) are virtually identical to those previously reported; (ki = 1.55 x 10 sec ; kp
-5
-1
= 2.09 x 10 sec ).[1]
To demonstrate the impact of the increasing incorporation of 4-vinylpyridine into the
polymer in a consistent manner, data from table 1 reflecting degradation at a single
temperature (170 °C) are collected in table 2.
Table 2. Rate Constants for the Thermal Degradation of Vinylidene Chloride/Methyl
Acrylate (Five Mole Percent)/ 4-Vinylpyridine (Variable Content)
Terpolymers at 170 °C
4-Vinylpyridine
(Mole %)
0
0.1
ki x 105
(sec-1)a,c
1.54 ± 0.02
1.86 ± 0.01
kp x 105
(sec-1)b,c
2.07 ± 0.04
2.26 ± 0.01
0.3
20.15 ± 0.10
25.25 ± 0.2
0.5
1
46.44 ± 0.3
-
54.60 ± 0.10
240.03 ± 3.00
a. Rate constant for the initiation of degradation.
b. Rate constant for the propagation of degradation.
c. Average of three determinations accompanied by the average deviation.
The initiation and propagation rate constants for the degradation of the 4-vinylpyridine
copolymers obtained at several temperatures may be used to determine both the activation
264
energy (Ea) and the enthalpy of activation (ΔH‡) for the two processes. This is illustrated for
the determination of the Arrhenius activation energy for the initiation of degradation of a
vinylidene chloride/methyl acrylate (five mole percent)/4-vinylpyridine (0.1 mole percent)
copolymer. A plot of ln ki versus 1/T for the reaction is shown in figure 8. The slope of this
plot is given by -13037 and is equal to - Ea/R where R, the gas constant, is 1.9872
cal/mol·deg. The value of the Arrhenius activation energy, Ea, for the initiation process is then
equal to - (-13037) x (1.9872 cal/mol·deg), i.e., 25.91 kcal/mol.
Similarly, from a plot of ln (k/T) versus 1/T, the enthalpy of activation for each process
may be obtained. This is also illustrated for the determination of the activation enthalpy for
the propagation of degradation of a vinylidene chloride/methyl acrylate (five mole percent)/4vinylpyridine (0.1 mole percent) copolymer in figure 7. The slope of the plot of ln (kp/T)
versus 1/T (figure 7) is given by -ΔH‡/R and the enthalpy of activation, ΔH‡, for the
propagation reaction is calculated to be equal to 27.92 kcal/mol. The activation parameters for
both the initiation and propagation reactions are recorded in table 3.
Figure 6. Arrhenius Activation Energy for the Initiation of Degradation of a Vinylidene Chloride/ Methyl
Acrylate (Five Mole percent)/ 4-Vinylpyridine (0.1 Mole Percent) Terpolymer.
265
Figure 7. Activation Enthalpy for Propagation of the Thermal Degradation of a Vinylidene Chloride/ Methyl
Acrylate (Five Mole Percent)/ 4-Vinylpyridine (0.1 Mole Percent) Terpolymer.
Table 3. Activation Parameters for the Initiation and Propagation Reactions for the
Thermal Degradation of Vinylidene Chloride/ Methyl Acrylate (Five Mole Percent)/ 4Vinylpyridine (Variable Content) Terpolymers.
4-Vinylpyridine
(Mole %)
0
0
0.1
0.1
0.3
0.3
0.5
0.5
Enthalpy of
Activation, ΔH‡,
(kcal/mol)a
27.76
29.01
25.01
27.92
10.78
12.43
4.96
6.17
Arrhenius
Activation Energy,
Ea, (kcal/mol)a
28.66
29.91
25.91
28.82
11.68
13.33
5.86
7.07
Entropy of
Activation, ΔS‡,
(cal/mol·deg; 190°C)b
-9.42
-7.7
-12.35
-8.86
-25.9
-24.26
-31.73
-30.53
Process
Initiation
Propagation
Initiation
Propagation
Initiation
Propagation
Initiation
Propagation
a. Based on the uncertainty in the values for rate constants and the temperature control (± 0.02 ºC)
possible with the TGA unit, the estimated uncertainty in activation values is less than 0.1 kcal/mol.
b. Calculated from the expression: ΔS±/R = ln k-23.760 – ln T – ΔH‡/RT.
The degradation onset and the temperatures of maximum degradation were determined
from the derivative plot of weight loss versus temperature (as illustrated in figure 8) and are
displayed in table 4. A composite plot for the degradation of the 4-vinylpyridine containing
polymers is displayed in figure 9.
266
Figure 8. Derivative Plot of Weight Loss versus Temperature for the Thermal Degradation of a Vinylidene
Chloride/Methyl Acrylate (Five Mole Percent) / 4-Vinylpyridine (0.5 Mole Percent) Terpolymer at 170 °C.
Table 4. Thermal Degradation of Vinylidene Chloride /Methyl Acrylate (Five Mole
Percent) / 4-Vinylpyridine (Variable Content) Terpolymers.
4Vinylpyridine
(Mole %)
0
0.1
0.3
0.5
Degradation
Onset a
(°C)
202
200
194
184
Temperature of Maximum
Degradation Rate. b
(°C)
241
231
222
215
a. Extrapolated onset temperatures from the derivative plot of weight loss versus temperature; the
reproducibility for multiple determinations is ± 0.2 ºC.
b. Maximum in the derivative plot of weight loss versus temperature; the reproducibility for multiple
determinations is ± 0.1 ºC.
267
Figure 9. Composite Plot of Weight Loss versus Temperature (°C) for the Thermal Degradation of
Vinylidene Chloride/ Methyl Acrylate (Five Mole Percent)/ 4-Vinylpyridine (Variable Content) Terpolymers.
From a composite plot of weight loss versus temperature (°C) for the thermal degradation
of vinylidene chloride/methyl acrylate (five mole percent) /4-vinylpyridine (variable content)
terpolymers shown in figure 9, it is observed that the incorporation of low levels of 4vinylpyridine (0.1-3 mole percent) into the copolymer has a great impact on stability. All
vinylpyridine copolymers are less stable than the standard vinylidene chloride/methyl acrylate
polymer containing no 4-vinylpyridine. The instability increases as the mole percent of the 4vinylpyridine in the polymer increases. The polymer containing 3% 4-vinylpyridine is
dramatically less stable. These qualitative observations are also supported by the rate
constants presented in table 1 and the activation parameters recorded in table 3. Both the
initiation and the propagation rate constants for the degradation of the polymers increase as
the levels of 4-vinylpyridine in the copolymer increase. Similar conclusions can be drawn
from a consideration of the temperatures for the onset of degradation compiled in table 4. The
extrapolated onset temperatures decrease as the mole percent of the 4-vinylpyridine increases.
The copolymer containing three mole percent 4-vinylpyridine has an extrapolated onset
temperature for degradation of approximately 130 °C! These results are fully consistant with
the conclusions from an NMR study of thermal aging of these polymers.[26]
The stability of vinylidene chloride copolymers generated using different polymerization
initiators has also been examined. The two common types of initiators for radical
polymerization are azo compounds and peroxides. A common azo initiator is
azoisobutronitrile or AIBN. The initiation of vinylidene chloride polymerization using AIBN
is illustrated in scheme 3.
268
Scheme 3. Initiation of Vinylidene Chloride Polymerization Using AIBN as Initiator.
It can be seen that the initiator fragment to chain end linkage is a carbon-carbon bond. In
contrast for initiation using a peroxide the initiator fragment to chain end linkage is a carbonoxygen bond (see scheme 4).
Scheme 4. Initiation of Vinylidene Chloride Polymerization Using Di-t- butyl Peroxide (TBPO) as Initiator.
It has sometimes been observed that vinylidene chloride polymers generated using
peroxide initiators are less stable than similar polymers generated using azo initiators. What is
the origin of this difference in stability? Could it arise as a consequence of differences in
chain-end structure? To explore this possibility the thermal stability of two polymers
generated using azo initiators (similar in structure to AIBN) and another produced using di-tbutylperoxide (TBPO) as initiator has been examined using thermogravimetry. A direct
comparison of the thermal degradation characteristic of these polymers is provided in figure
10.
269
Figure 10. Composite Plot of Weight Loss versus Temperature (°C) for the Thermal Degradation of
Vinylidene Chloride/ Methyl Acrylate (Five Mole Percent) Copolymers Generated Using Different Initiators.
This comparison suggests that there is little difference in the thermal stability of the three
polymers. This is supported by the extrapolated onset temperatures (see table 5) for the
degradation obtained from the derivative plots of weight loss versus temperature.
Table 5. Thermal Stability of Vinylidene Chloride /Methyl Acrylate
(Five Mole Percent) Copolymers Generated Using Different Initiators
Initiator Type
Azo
Azo
Peroxide (TBPO)
Initiation
Temperature
(°C)
34
86
86
Degradation
Onset (°C)a
208
202
202
Temperature of
Maximum
Degradation Rate. (°C)b
234
238
237
reproducibility for multiple determinations is ± 0.2 ºC.
determinations is ± 0.1 ºC.
The onset temperature for degradation is virtually identical for the three polymers. This
would suggest that any thermal instability observed for vinylidene chloride polymers
generated using peroxide initiators must arise elsewhere, perhaps from residual initiator in the
finished polymer.
270
It has been suggested that vinylidene chloride copolymers containing alkyl pendants
display stability greater than that of the corresponding polymer with no alkyl side-groups.[27]
The pendant alkyl groups presumably serve as sources of hydrogen atoms which may be
abstracted by reactive species (chlorine atoms, carbon radicals) formed by degradation along
the mainchain. This has been tested for with vinylidene chloride/ butyl acrylate
copolymers.[20] A most probable mode of stabilization is outlined in scheme 5. Chlorine
atoms formed from thermolysis of a carbon-chlorine bond may abstract a hydrogen atom
from the alkyl pendant rather than the mainchain which would introduce unsaturation. The
most probable hydrogen atom to be abstracted is that adjacent to the oxygen atom since the
resulting carbon radical would be conjugatively stabilized. It was shown that this process was
not competitive with hydrogen abstraction from the mainchain.[20] Figure 11 presents a
direct comparison of the thermal degradation characteristics of these polymers.
The fate of the radicals formed in the potential stabilization process is illustrated in
scheme 6.
Scheme 5. Proposed Mode of Stabilization of Vinylidene Chloride Copolymers Containing Pendant Butyl
Ester Groups.
271
Scheme 6. Proposed Fates of Radicals Formed by Butyl Ester Sidechain Scavenging of Chlorine Atoms
Generated During the Degradative Dehydrochlorination of Vinylidene Chloride/ Butyl Acrylate Copolymers.
In this instance the thermal stability of vinylidene chloride /alkyl acrylate copolymers in
which the alkyl groups are isomeric butyl units has been examined by thermogravimetry. The
butyl ester comonomers incorporated are shown below (scheme 7).
Scheme 7. Structures of Butyl Ester Comonomers Incorporated Into Vinylidene Chloride Polymers.
272
A composite plot of weight loss versus temperature for the degradation of vinylidene
chloride copolymers containing five mole percent of an isomeric butyl acrylate comonomer is
displayed in figure 11. From this plot it is apparent that there is little difference in the
degradation behavior of these polymers. This is even more apparent from the degradation
onset data presented in table 6. As may be seen the onset temperature for degradation is
essentially identical independent of the nature of the butyl group. This is somewhat
surprising, particularly for the case of the sec-butyl ester. The potential stabilization as a
consequence of the presence of the sec-butyl acrylate comonomer is illustrated in scheme 8.
As shown in this scheme, the radical formed by hydrogen atom abstraction would be both
fully substituted and alpha to oxygen, and therefore, should be considerably more stable than
the corresponding radicals formed in the case of the other esters.
Figure 11. Composite Plot of Weight Loss versus Temperature (°C) for the Thermal Stability of Vinylidene
Chloride / Butyl Acrylate Ester (Five Mole Percent) Copolymers.
273
Figure 12. Composite Plot of Weight Loss versus Temperature (°C) for Vinylidene Chloride/ Butyl Acrylate
Ester (Five Mole Percent) Copolymers and for Comparison a Vinylidene Chloride/ Methyl Acrylate (Five
Mole Percent) Copolymer.
A composite plot of weight loss versus temperature for vinylidene chloride/ butyl acrylate
ester (five mole percent) copolymers and for comparison a vinylidene chloride/methyl
acrylate (five mole percent) copolymer is displayed in figure 12. The figure shows that the
stability of the copolymers containing butyl acrylate was no greater than that of the polymer
containing methyl acrylate as comonomer. This observation is supported by the extrapolated
onset temperatures (see table 6) for the degradation obtained from the derivative plots of
weight loss versus temperature.
Table 6. Thermal Stability of Vinylidene Chloride/ Butyl Acrylate Ester
(Five Mole Percent) Copolymers and a Vinylidene Chloride/ Methyl
Acrylate (Five Mole Percent) Copolymer
VDC Copolymer
Degradation Onset
(°C)
VDC / MA
VDC / BA
VDC / IBA
VDC / SBA
200
204
205
207
Temperature of
Maximum
Degradation Rate(°C)
241
241
244
243
reproducibility for multiple determinations is ± 0.2° C.
determinations is ± 0.1° C.
274
Scheme 8. Possible Mode of Stabilization of a Vinylidene Chloride Copolymer Containing Pendant secButyl Ester Groups.
From the data presented here it is clear that little stabilization is provided by the presence
of pendant buytl groups of any structure despite the fact that abstractable hydrogen atoms,
particularly in the case of the sec-butyl acrylate copolymer, are available. This stands in
contrast to an earlier observation that the presence of aliphatic pendant groups afforded
stability for vinylidene chloride copolymers.[43] It may be that the size of the pendant groups
in this case is too small, i.e., that the availability of abstractable hydrogen atoms is not great.
Further work will be required to resolve this issue.
Both methyl acrylate and butyl acrylate have been used to prepare vinylidene chloride
copolymers with sufficient stability to permit thermal processing. The presence of alkyl
acrylate units in the polymer mainchain limits the size of vinylidene chloride sequences and
thus the propagation of degradative dehydrochlorination. More importantly it lowers the melt
275
temperature such that processing can be accomplished at a temperature at which thermal
dehydrochlorination is not prominent. In an attempt to determine whether or not one
comonomer is more suitable for the purpose of generating relatively stable vinylidene
chloride copolymers, copolymers containing five mole percent methyl acrylate, butyl
acrylate, and 2.5 mole percent of each methyl acrylate and butyl acrylate have been
investigated using thermogravimetry. A composite plot of weight loss versus temperature for
the degradation of the three polymers is shown in figure 13.
Figure 13. Thermal Degradation of Vinylidene Chloride/ Alkyl Acrylate Copolymers.
It is apparent that there is little difference in the stability of the three polymers. This is
supported by the degradation onset data presented in table 7. The onset temperature for
degradation is virtually identical for the three polymers. Based upon this very limited
exploration it would appear that the presence of either monomer in the copolymer has
effectively the same impact on stability.
Table 7. Thermal Stability of VDC/ Alkyl Acrylate (Five Mole Percent) Copolymers
VDC Copolymer
VDC / MA
VDC/BA
VDC / MA / BA
Degradation Onset (°C)a
200
204
204
Temperature of Maximum
Degradation Rate. (°C)b
241
241
240
reproducibility for multiple determinations is ± 0.2 °C.
determinations is ± 0.1 °C.
276
CONCLUSION
The kinetics of the thermally-induced degradative dehydrochlorination of vinylidene
chloride copolymers are well suited for study using thermogravimetry. The degradation
corresponds to a well defined process – the first order elimination of hydrogen chloride- such
that the mass loss as a function of time provides a direct reflection of the extent of
degradation. Degradation may be studied in two ways; degradation as a function of
temperature (dynamic) and degradation at constant temperature as a finction of time
(isothermal). Initiation and propagation rate constants of the dehydrochlorination reaction can
be obtained from isothermal thermogravimetric data. For the dynamic method, samples were
subjected to increasing temperature at a rate of 5 °C/min. over a range of 25 to 350 °C.
Polymers containing even small levels of 4-vinylpyridine undergo facile thermally-promoted
degradative dehydrochlorination. All the polymers containing 4-vinylpyridine are less stable
than the standard vinylidene chloride/methyl acrylate (five mole percent) copolymer. The
polymer containing three mole percent 4-vinylpyridine is dramatically less stable with
degradation onset at about 130 °C. This demonstrates that the pyridine moiety is sufficiently
basic so as to actively strip hydrogen chloride from vinylidene chloride units, promoting E2
elimination in vinylidene sequences to generate initiation sites (internal unsaturation; allylic
dichloromethylene units) for the thermal dehydrochlorination reaction.
Limited studies suggest that the nature of the initiator, azo versus peroxide, used for the
preparation of vinylidene chloride copolymers has little influence on the stability of the
resulting polymers. The nature of the comonomer incorporated, methyl versus butyl acrylate,
also seems to have little impact on the stability of the copolymers generated. The
incorporation of isomeric butyl acrylate esters into vinylidene chloride copolymers also
displays little impact on the stability of the resulting polymer, beyond that obtained by
incorporation of any comonomer, independent of butyl structure.
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INDEX
A
accelerator, 90
access, 53, 202
acclimatization, 130
accuracy, 3, 5, 237
acetic acid, 105, 116, 117
acetone, 53, 66, 67, 113, 118, 119
acetophenone, 37
acid, 38, 39, 42, 43, 46, 74, 82, 84, 112, 116, 117,
120, 133, 134, 135, 136, 137, 138, 141, 142, 146,
147, 153, 178, 181, 182, 201, 207, 227, 252, 253,
259
acrylate, 260, 263, 264, 267, 270, 271, 272, 273,
274, 276
acrylic acid, 108, 112, 113, 118, 136
acrylonitrile, 115, 117, 257
actinic keratosis, 148
activation, 62, 66, 67, 86, 115, 117, 119, 122, 145,
153, 167, 180, 262, 264, 265, 267
activation energy, 62, 86, 115, 117, 119, 122, 145,
167, 264
activation enthalpy, 264
activation parameters, 262, 264, 267
active radicals, 93
actuators, 133
additives, 30, 120, 132, 146, 174, 260
adenine, 74
adenosine, 74
adenosine triphosphate, 74
adhesion, 112, 144, 147, 155
adhesives, 144
adiabatic, x, 1, 10, 17, 18, 21
adsorption, 36, 45, 46, 120, 131, 136, 140, 152, 156
aerosols, 142, 157
age, ix, 101
ageing, 101
agent, 105, 106, 111, 113, 114, 117, 134, 135, 145,
148, 153, 154, 155, 170, 182, 254
aggregation, 109
aging, 178, 182
agriculture, xiii, 148, 251
AIBN, 267, 268
air pollution, 156
albumin, 144, 150, 151
alcohol(s), 37, 42, 43, 45, 103, 108, 109, 111, 112,
113, 115, 116, 118, 120, 121, 122, 127, 128, 132,
134, 135, 136, 137, 140, 141, 146, 147, 151, 154,
157, 158, 160, 169, 170, 233, 244, 253
aldehydes, 117, 122
algorithm, 14
alkyl methacrylates, 257
alloys, 200
allylamine, 111, 114, 118, 150
alternative(s), 107, 120, 128, 133, 134, 234
amendments, 38
amines, 38, 42, 43, 251, 252, 254, 260
amino acid, 90
amino-groups, 141
ammonia, 53, 150, 234
amorphous phases, 175
anhydrase, 156
aniline, 108, 109
animals, 106, 144
anion, 82, 84, 191, 199
annealing, 112, 135, 169
anticancer drug, 149
apoptosis, 143
apparel, 106
applied research, 174
aqueous solutions, 106, 108, 109, 113, 114, 116, 147
argon, 218
aromatic compounds, 244
aromatic hydrocarbons, 244
articular cartilage, 140, 147, 148
ascorbic acid, 138
280
Index
ash, 41
assessment, 69, 70, 71, 149, 171, 187, 188
assignment, xii, 173, 174, 181, 184, 185
assimilation, 85, 86
assumptions, 37, 38, 70, 95
asthma, 139
asymptotics, 26
atmospheric pressure, xiii, 233, 234, 236, 239, 241
atomic orbitals, 84, 95
atoms, 38, 56, 59, 74, 76, 78, 79, 81, 82, 84, 86, 90,
92, 93, 94, 95, 96, 98, 99, 100, 178, 188, 189,
190, 191, 197, 198, 199, 270, 274
ATP, 82, 83, 86, 87
attachment, 72, 125
attention, 24, 31, 52, 133, 136, 137, 141, 152, 155,
157, 218, 253, 254
autodeceleration, 202, 207
availability, 120, 274
B
barriers, 157
basicity, xi, 35, 41, 42, 43, 45, 47, 66
beams, 105, 144
behavior, 39, 113, 135, 144, 148, 202, 228, 244, 246,
250, 272
bending, 135, 136
benign, 133
benzene, xi, 46, 51, 53, 55, 63, 67, 119, 120, 121,
234, 244, 245
benzoyl peroxide, 65
binding, xii, 52, 62, 93, 106, 125, 128, 130, 136, 148,
199
bioaccumulation, 130
bioavailability, 142
biocatalysts, 153
biocompatibility, 112, 132, 140, 148, 157
biodegradability, 106, 130, 148, 149, 157
biological processes, 90
biological stability, 131
biological systems, 24
biologically active compounds, 251, 253
biomass, 112, 130
biomaterials, 139, 140, 142, 148, 154
biomedical applications, 105, 140, 147
biomolecules, 98, 137
biosensors, 133, 137, 138
biosorption, 130
blend films, 123, 136
blends, 107, 112, 113, 114, 116, 118, 119, 120, 123,
129, 130, 134, 140, 148, 154, 156, 158
blocks, 15, 93
blood, 138, 139, 140, 142, 151
bloodstream, 142
body fluid, 149
body weight, 106
bonding, 48, 121, 128, 141
bonds, xiii, 36, 37, 43, 62, 74, 75, 81, 86, 93, 98,
137, 177, 178, 179, 181, 182, 192, 199, 251
boric acid, 136, 162
branching, 36, 169, 170
breakdown, 69, 169
Brownian motion, 226
Bulgaria, 177
butadiene, 177, 180, 181, 185
butyl ether, 244
by-products, 122
C
Ca2+, 150
calibration, 139
cancer, 127, 139, 142, 253
candidates, 125, 140, 141
capillary, 128, 176
carbamide, xii, 173, 174, 175, 254
carbides, 196
carbohydrate(s), 74, 251, 252, 254, 255
carbon, xii, 37, 41, 52, 74, 82, 86, 93, 96, 98, 99,
120, 121, 138, 187, 193, 197, 198, 199, 200, 234,
258, 259, 268, 270
carbon atoms, 86, 199
carbon dioxide, 234, 258
carbon monoxide, 120
carbon nanotubes, 199
carcinoma, 148
carrier, 128, 141, 218, 254
cartilage, 148
cast, 112, 116, 135
casting, 113, 116, 117, 120, 123, 128
catalysis, 67, 106, 201, 225, 251, 252, 253
catalyst(s), xiii, 53, 54, 113, 117, 120, 128, 133, 151,
152, 157, 174, 202, 217, 218, 219, 220, 222, 253,
259
catalytic activity, 217, 227
catalytic hydrogenation, 120
catalytic system, 152
cation, 191, 199
cell, 2, 3, 130, 133, 134, 135, 143, 147, 148, 153,
245
cell adhesion, 147
cell culture, 153
cell culture method, 153
cell cycle, 148
cell death, 143
cell growth, 147
cell line, 147
cell organization, 147
Index
cellulose, 114, 131, 132, 137, 144
cellulose diacetate, 137
ceramic(s), 106, 139, 147
certificate, 255
chains conformation, 21
channels, 109, 134, 212, 213
characteristic viscosity, 71
chemical bonds, x, 1, 74, 86, 87, 95, 176
chemical energy, 74
chemical interaction, 36, 136, 226
chemical kinetics, ix
chemical properties, xi, 35, 100, 200, 244
chemical reactions, 90, 154, 203, 225
chemical stability, 140
chitin, 148
chlorine, 65, 67, 259, 270
chlorophyll, 74, 81
chromatography, 130, 244, 245
chronic diseases, 127
circulation, 141
classes, 192
clean energy, 112
clean technology, 107
cleaning, 130
clusters, 38, 197, 199, 210
C-N, 93
CO2, 80, 83, 155, 156
coagulation, 133
coal, xi, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47,
48, 244
coatings, 142, 149
cohesion, 36, 37, 40, 41, 42, 45, 65, 66, 67
collagen, 147
colon, 148
combined effect, 145
compatibility, 123, 137, 141, 151, 177
compensation, 136
compliance, xii, 86, 89, 142
complications, 41
components, xiii, 3, 36, 41, 75, 79, 81, 82, 90, 91,
93, 94, 95, 106, 107, 113, 116, 118, 119, 121,
122, 125, 126, 130, 149, 175, 176, 234, 240, 243,
244, 245, 247, 249, 257
composites, xii, 52, 62, 107, 114, 147, 158
composition, xi, 27, 30, 41, 51, 53, 55, 62, 108, 111,
113, 115, 116, 117, 118, 119, 120, 122, 128, 130,
133, 134, 135, 154, 155, 156, 173, 178, 182, 192,
209, 234, 244, 245
compost, 106
compounds, 54, 64, 74, 82, 86, 90, 93, 105, 107, 126,
127, 128, 140, 149, 157, 174, 192, 200, 225, 234,
244, 246, 248, 251, 254, 255, 267
compressibility, 29, 30, 32, 234
281
computation, xii, 67, 187
concentration, x, xi, 1, 2, 11, 21, 23, 24, 25, 26, 27,
28, 29, 30, 31, 32, 36, 105, 114, 115, 116, 118,
119, 121, 123, 124, 126, 130, 131, 135, 136, 137,
138, 139, 140, 154, 156, 168, 169, 174, 178, 179,
181, 208, 218, 219, 220, 221, 222, 227
conception, xii, 207, 211, 214
concrete, 32, 228
condensation, 107, 109, 111, 116, 252, 253
conducting polymer composites, 63
conductivity, 63, 109, 133, 134, 135, 137, 245
Congress, iv
connectivity, 209, 226, 227
constant rate, 142
consumption, 86, 167, 177
contamination, 244
control, 107, 109, 112, 125, 146, 149, 155, 157, 178,
182, 234, 265
conversion, xii, 54, 117, 120, 201, 202, 203, 204,
206, 207, 208, 219, 227, 229
conversion rate, 117
cooling, 52
copolymers, 107, 114, 140, 257, 258, 259, 260, 264,
267, 270, 271, 272, 273, 274, 276
copper, 126, 245
cornea, 147
correlation(s), 25, 32, 40, 41, 42, 44, 56, 65, 66, 67,
95, 189, 198, 244
correlation analysis, 67
correlation coefficient, 41, 56, 66
corrosion, 154, 156
cosmetics, 148
coupling, 142
covalent bond, 98, 152, 197, 199
covalent bonding, 152
creatine, 138
creatinine, 138, 148, 149
critical analysis, 38
critical density, 11
critical value, 16
crystalline, 93, 96, 120, 188, 189, 192, 194, 199, 258
crystallinity, 121, 147, 154, 210, 258
crystallites, 105
crystallization, 169, 200
crystals, 191
culture, 147
curing, 111, 113, 114, 117, 118, 139, 181
curing process, 181
cycles, 105, 113, 144, 147, 197
cyclodextrins, 123, 128
cyclohexanone, 37
cytocompatibility, 153
cytosine, 254
282
Index
cytotoxicity, 141, 153
D
data analysis, 65
death, 106
decay, 219, 220, 221, 222
decomposition, 24, 65, 169, 170, 176, 257
defects, 258, 260
deficiency, 25, 218
definition, xiii, 175, 203, 207, 214, 230
deformation, x, 1, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 28, 33, 72, 133, 154, 169, 170,
171, 181
degenerate, 169
degradation, 169, 258, 259, 260, 261, 263, 264, 265,
267, 269, 270, 272, 273, 275, 276
degradation process, 258
degree of crystallinity, 154
dehydrate, 118
dehydration, 107, 108, 109, 111, 112, 113, 114, 116,
117, 118, 213, 258
dehydrochlorination, 257, 258, 259, 274, 276
dehydrocondensation, 59
delivery, 106, 130, 140, 141, 142, 143, 145, 146
demand, 142
demulcent, 106
denaturation, 150
Denmark, 250
density, 6, 9, 11, 36, 38, 39, 42, 65, 79, 92, 93, 111,
125, 134, 138, 178, 182, 202, 234, 244, 258
dependent variable, 234
deposition, 149
depreciation, 154
depression, 170
derivatives, xi, xiii, 23, 32, 114, 137, 146, 152, 154,
157, 204, 228, 236, 237, 251, 252, 253, 254
dermatoses, 148
desorption, 145, 146
destruction, xii, 41, 62, 69, 70, 71, 72, 167, 168, 169,
171, 176
destruction processes, xii, 71, 72, 167, 171
destructive process, 69
detection, 135, 138, 176
detergents, 131
deviation, xiii, 37, 43, 233, 239, 241, 243, 263
diabetes, 139, 150
dialysis, 130, 138, 139
diamines, 141
diet, 101
differential scanning, 52
differential scanning calorimeter, 52
diffraction, 135
diffusion, xii, xiii, 40, 75, 91, 107, 117, 121, 124,
128, 129, 134, 136, 146, 152, 153, 170, 207, 208,
212, 214, 217, 221, 222, 225, 226, 230
diffusivity, 112
diluent, 106
dimensionality, 14, 28
dimer, 81
dimethylformamide, 37, 43
diphenylolpropane, 47
dipole moment, 234
discrimination, 125
disinfection, 142
disorder, 210
dispersion, 109
displacement, 5, 9, 39, 228
dissociation, 98, 99, 135
distillation, 107, 112, 118, 120, 122
distribution, xiii, 2, 3, 4, 5, 6, 40, 72, 121, 130, 131,
169, 170, 202, 209, 217, 220, 221, 222, 228
distribution function, 228
division, 66, 220
DMA analysis, 147
DNA, 131, 141
dopants, 109
doping, 109
dosing, 142
double bonds, 84
double logarithmic coordinates, 208
dream, x
dressing material, 144
dressings, 145
Drosophila, 101
drug delivery, 106, 107, 140, 141, 142, 144
drug delivery systems, 141
drug release, 146
drugs, 140, 142, 144, 145, 157, 253
drying, 41, 138
DSC, 52, 59, 61
DTA curve, 175, 176
durability, 117, 132
duration, xiii, 142, 202, 203, 204, 207, 208, 217,
220, 221, 222, 225, 227, 231
E
Education, 161
effective spectral dimension, 209
effluent, 120
elaboration, 52
elasticity, x, 1, 2, 21, 114, 144
elastomers, 52
electrical conductivity, 109
electricity, 142
electrocatalyst, 137
Index
electrodes, 137, 138
electrolysis, 109
electrolyte, 129, 133, 134, 140
electromagnetic, 74
electromigration, 136
electron(s), 48, 66, 73, 74, 75, 76, 78, 79, 81, 82, 87,
90, 91, 92, 93, 94, 96, 97, 98, 99, 105, 128, 138,
144, 188, 198, 199, 200
electron density, 79, 92, 93, 128, 188, 198, 199
electron pairs, 128
electrophoresis, 128
electroporation, 142
electrostatic interactions, 141
elongation, 121, 132, 181
emission, 155
enantiomers, 128
encapsulation, 144, 164
endothelial cells, 147
endothermic, 41, 52, 59, 176
energetic excitation, 211
energetic parameters, 59
energy, x, xi, xii, 1, 8, 9, 21, 23, 28, 32, 36, 37, 39,
40, 41, 42, 45, 62, 65, 67, 73, 74, 75, 76, 78, 79,
81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94,
95, 96, 99, 100, 101, 107, 117, 118, 120, 127,
133, 143, 156, 168, 187, 188, 189, 190, 191, 194,
196, 197, 198, 199, 210, 212, 246, 248, 264
energy characteristics, xii, 73, 75, 78, 85, 89, 91,
100, 188
energy density, 42, 67, 133
energy parameters, 93
England, 158
enthalpy of activation, 264
entrapment, 136, 137, 143, 153
entropy, x, 1, 9, 15, 16, 21, 27, 32
environment, 111, 131, 140, 144, 152, 253
environmental conditions, 130
environmental impact, 106
environmental protection, 127
environmental stimuli, 141
enzymatic activity, 131
enzyme immobilization, 152
enzymes, 128, 137, 138, 141, 151, 152, 157
epoxy groups, 63
equality, 81, 82, 188, 189, 191, 197, 198, 226
equating, 16
equilibrium, x, xiii, 1, 6, 8, 10, 12, 13, 15, 16, 21, 38,
39, 40, 41, 44, 47, 136, 148, 233, 234, 241, 244,
245, 246, 247, 248, 250
equipment, 259
ester, 137, 142, 271, 272, 273
estimating, 234, 240
ethanol, 112, 113, 114, 115, 116, 119, 137, 142, 244
283
ethers, 169, 244
ethyl acetate, 65
ethyl alcohol, 122
ethylene, 117, 141, 154
ethylene glycol, 117
ethylene oxide, 141
Euclidean space, 202, 221, 227, 228
evaporation, 40, 107, 113, 117, 120, 123, 129
evolution, xii, 201, 203, 206, 259
excitation, 74
exclusion, 38, 41, 42, 43, 44, 45, 65, 66, 67, 129, 138
excretion, 141
exercise, 145
exothermic peaks, 52
exploitation, 260
exposure, 109, 111
extracellular matrix, 151
extraction, xi, 35, 36, 37, 38, 46, 47, 48, 105, 106,
125, 126, 130, 142, 174, 243, 245, 262
extraction process, 38, 105, 125, 243
extrusion, 71, 72, 142, 156
F
fabric, 106
fabrication, 132, 138
family, 134
fat, 148
fatigue, 4
FDA, 106
FEMA, 117
fermentation, 112, 122
fermentation broth, 122
fibers, 105, 117
fibroblasts, 146
fillers, 109, 146
film(s), 105, 108, 112, 113, 118, 128, 133, 137, 144,
145, 146, 154, 155, 157, 169, 260
film formation, 157
filtration, 106, 132, 153
fish, 127
fixation, 147, 148
flavor, 257, 258
flexibility, 111, 114, 156
Flory theory, 38
fluctuations, xiii, 217, 220, 221, 222
fluid, 130, 151
food, 106, 131, 152, 154, 257, 258
food industry, 131, 152
food safety, 131
Ford, 185
formaldehyde, xii, 133, 137, 148, 173, 174, 175, 182
fouling, 131, 132, 133, 138
fractal analysis, xii, 201, 202, 206
284
Index
fractal dimension, 203, 228
fractal kinetics, 203
fractal objects, 202
fractal space, 202, 209, 227
fractal structure, 225
France, 33
free energy, x, xi, 1, 7, 8, 9, 21, 23, 24, 26, 27, 28,
29, 31, 32, 36, 39, 41, 47, 74, 84
free radicals, xii, 73, 89, 90, 98, 99, 100
free volume, xii, 24, 111, 116, 121, 207, 210, 211,
212, 213, 214
freezing, 105, 113, 126, 134, 144
FTIR, 201, 202
fuel, 36, 62, 120, 133, 135, 156, 157
fuel efficiency, 134
fullerene, 200
G
gas phase, 130
gases, 40, 157
gasoline, xiii, 120, 156, 243, 244, 247, 248, 249, 250
gastrointestinal tract, 106
gel, 105, 106, 112, 125, 132, 136, 137, 140, 141,
142, 144, 146, 152, 157
gelation, 105, 203
generalization, xi, 35, 39, 40, 41, 42, 43, 46, 47, 65
generation, 106, 144, 145, 167, 168
Georgia, 51, 64
gerontology, 101
glass, 59, 210, 211, 245
glass transition, 59, 210, 211
glass transition temperature, 59, 210
glucose, 128, 137, 139, 144, 151, 252
glucose oxidase, 137, 139
glutamate, 138
glycerin, 74
glycerol, 152
glycoproteins, 252
glycoside, 254
glycosylation, 254
goals, 107
government, 155
grades, 144
graphite, xii, 52, 62, 120, 121, 199, 200
grouping, 84
groups, 38, 39, 41, 42, 43, 46, 52, 53, 54, 55, 59, 61,
62, 74, 85, 90, 108, 109, 111, 114, 127, 128, 133,
134, 135, 137, 140, 141, 142, 157, 170, 177, 185,
245, 251, 258, 270, 271, 274
growth, 24, 36, 130, 144, 146, 169, 200, 209, 218,
252, 253
growth factor, 146
H
halogen, 192
hardness, 179, 181
harmful effects, 153
HDPE, 155, 156
healing, 144, 145, 146
health, 138
health care, 138
heat, 10, 11, 17, 59, 117, 120, 253
heating, 176
heating rate, 176
helium, 218
hepatocytes, 149, 150
hepatoma, 149
heptane, 67
heterogeneity, xii, 207, 208, 211, 212, 213, 214, 219
heterogeneous systems, 75
hexane, 142, 234
high density polyethylene, 155, 156
hip, 208, 227
homogeneity, 209, 212
homopolymerization, 55
Honda, 47
hospitals, 106
host, 128, 137, 147
host tissue, 147
human brain, 235
humidity, 99, 154, 234
hybrid, 109, 111, 112, 116, 120, 121, 147, 149
hybridization, 82, 87, 96, 101, 112, 198
hydrocarbons, 37, 156
hydrogels, 104, 105, 106, 113, 125, 126, 127, 128,
135, 140, 142, 143, 144, 146, 147, 148, 151, 157,
160, 164
hydrogen, 37, 38, 41, 42, 43, 46, 48, 54, 59, 81, 82,
96, 121, 128, 138, 141, 258, 259, 260, 270, 272,
274, 276
hydrogen abstraction, 270
hydrogen atoms, 81, 82, 128, 270, 274
hydrogen bonds, 38, 41, 42, 43
hydrogen chloride, 258, 259, 260, 276
hydrolysis, 52, 62, 103, 104, 111, 116, 131, 132,
133, 140, 144, 152, 153, 154, 157
hydrolytic stability, 251
hydroperoxides, 167
hydrophilicity, 108, 112, 114, 132, 137
hydrophobic interactions, 131
hydrophobicity, 112, 134
hydrosilylation, 55, 56, 58
hydroxide, 136, 174, 176
hydroxyapatite, 147
hydroxyl, 81, 103, 105, 109, 128, 132, 133
Index
hydroxyl groups, 105, 109, 128, 132, 133
hygiene, 106
I
identity, 203
imidization, xii, 201, 202, 203, 204, 205, 206, 207,
208, 209, 210, 211, 212, 213, 214
immersion, 131, 144, 218
immobilization, 128, 136, 137, 145, 151, 152, 153
immune system, 149, 151
immunoglobulin, 151
implants, 141
impregnation, 125, 136
impurities, 177, 200
in situ, 109, 121
in vitro, 146, 153
in vivo, 141, 151
inclusion, 126, 128, 146
incompatibility, 156
independence, 26, 31, 32
independent variable, 16, 17
index numbers, 55
indicators, 136, 137
indomethacin, 144
induction peroid, 169, 170
industrial application, 107, 152
industry, 106, 116, 139, 152, 257
infection, 144
infinite, 260
information processing, 235
inhibition, 153
inhibitor, 146
initial state, 188
initiation, 235, 258, 259, 260, 261, 263, 264, 267,
268, 276
injections, 141
input, 234, 235, 236, 237
insertion, 130
instability, 258, 267, 269
insulin, 144, 151
integration, 19, 29, 30, 70
intensity, 69, 71, 72, 177
interaction(s), xii, xiii, 9, 24, 25, 36, 37, 38, 39, 40,
41, 46, 48, 52, 53, 59, 61, 65, 73, 74, 75, 79, 80,
81, 82, 84, 87, 89, 90, 91, 92, 93, 94, 95, 96, 98,
100, 120, 121, 126, 128, 130, 135, 138, 139, 141,
146, 170, 182, 188, 189, 192, 197, 198, 199, 234,
240, 243, 244, 245, 246, 247, 248, 250, 252, 254
interface, 136, 153, 155
interference, 93, 138
intermetallic compounds, 192
intermolecular interactions, 141
internal reconstruction, 95
285
interpretation, 37, 40
interval, 10, 62, 142, 176, 221, 228, 247, 248, 250
inversion, 133
iodine, 126
ion exchangers, 127
ionization, 87, 189, 190
ions, 84, 95, 121, 126, 128, 130, 135, 136, 138, 202,
208
IR, xi, xii, 39, 51, 52, 53, 54, 55, 59, 173, 176, 202,
208
Iran, 233, 243
iron, 86, 259
irradiation, 105, 153
irreversible aggregation, 202
IR-spectra, 52, 53, 55, 59, 202, 208
IR-spectroscopy, xii, 173, 176
isobutylene, 120
isolation, 74, 81
isomers, 123, 124, 125, 128
isoprene, 17, 177, 178, 179, 180, 185
isothermal, x, 1, 17, 21, 276
isotropic media, x, 1
J
Japan, 33, 47, 255
K
K+, 80, 138
KBr, 52, 202, 208
ketones, 38, 169
kidney, 138, 151
kidney dialysis, 138
kidney failure, 138
kinetic curves, 54, 202, 207, 208, 218, 219, 220, 227
kinetic parameters, 75, 91
kinetic studies, 218, 253
kinetics, ix, xi, xii, xiii, 44, 51, 67, 136, 167, 168,
170, 171, 181, 182, 183, 184, 201, 202, 207, 208,
217, 218, 219, 222, 225, 227, 251, 276
knees, 148
Kyrgyzstan, 251, 255
L
lamellae, 154, 155
laminar, 154, 156
lamination, 106
landfills, 106
lateral meniscus, 148
laws, x, 1
learning, 239
lending, 128
lesions, 149
286
Index
life expectancy, 138
life span, 101
linear dependence, 218
linear function, 28, 29
linear macromolecule, 33
linear molecules, 131
linkage, 137, 152, 268
links, 2, 3, 9, 24, 25, 26, 31, 37, 170
lipase(s), 152, 153
liquid interfaces, 125
liquid phase, xiii, 36, 39, 40, 41, 42, 120, 125, 234,
243, 244, 245, 247, 250
liquids, xi, 35, 37, 39, 40, 41, 46, 47, 48, 53, 54, 109,
122, 144
liver, 150
living conditions, 150
local order, 210
localization, 210, 212
location, 3
low temperatures, 131, 259
low-molecular substances, 230
LTD, 158
luminescence, 136
lying, 5, 27
lysine, 138
M
macromolecular chains, 70
macromolecular coil, xii, 201, 202, 203, 205, 206
macromolecular coil fractal dimension, xii, 201, 206
macromolecules, xi, 23, 24, 26, 27, 28, 29, 30, 31,
32, 59, 61, 70, 100, 168, 169
magnesium, 81, 181, 260
mammalian cells, 138
management, 133
manganese, 81
manufacturing, 53, 122, 139
market, 157
mass loss, 276
matrix, 105, 109, 113, 121, 126, 130, 137, 138, 140,
142, 143, 145, 147, 150, 151, 152, 153, 177, 185,
210, 217
mean-field theory, 219
measurement, 136
meat, 257
mechanical properties, 47, 114, 121, 134, 148, 173
media, 40, 65, 75, 109, 127, 131
medicine, x, xii, xiii, 139, 148, 157, 251
melt(s), 1, 2, 9, 11, 17, 21, 33, 69, 71, 72, 155, 167,
168, 171, 202, 257, 260, 274
melting, 176, 209
melting temperature, 176, 209
membrane separation processes, 151
membranes, 104, 107, 108, 109, 111, 112, 114, 115,
116, 117, 118, 119, 120, 121, 123, 124, 125, 126,
128, 129, 130, 131, 132, 133, 134, 135, 137, 138,
140, 142, 148, 149, 150, 151, 152, 153, 154, 156,
157
memory, 228
Mendeleev, 94
metabolism, 138, 142
metabolites, 141
metal carbides, 192
metallurgy, 200
metals, 139, 151, 192, 200
methacrylic acid, 117
methane, 234
methanol, xiii, 105, 118, 120, 133, 135, 137, 156,
243, 244, 245, 246, 247, 248, 249, 250
Mexico, 201
Mg2+, 80, 85
mice, 101
micrometer, 152
microorganism, 130
microscopy, xii, 173, 175
microspheres, 104, 141
microstructure, 225
microvoid, 211, 212, 213
migration, 125, 147
minerals, 36
miniaturization, 133
missions, 120
mixing, x, 1, 4, 9, 15, 16, 21, 36, 38, 113, 116, 234,
240
model system, xi, 51, 54, 57, 59, 217
modeling, xiii, 177, 178, 179, 180, 181, 182, 183,
184, 197, 233
models, xiii, 87, 128, 233, 234, 235, 241, 254
modules, x, 1, 2, 21, 92, 151
moisture, 53, 62, 90, 176, 258
moisture content, 90
molar volume, xi, 26, 30, 31, 35, 36, 37, 40, 41, 42,
43, 44, 45, 46, 47
molasses, 122
mole, xiii, 17, 28, 37, 46, 53, 67, 83, 86, 125, 131,
167, 169, 174, 234, 236, 237, 239, 241, 243, 245,
246, 248, 249, 250, 259, 260, 263, 264, 267, 272,
273, 275, 276
molecular biology, 251
molecular mass, 38, 69, 70, 72, 144, 169
molecular orbitals, 199
molecular structure, 74, 98, 99, 137
molecular weight, 37, 38, 70, 105, 108, 131, 132,
140, 143, 146, 234
molecules, xii, 24, 27, 36, 41, 42, 46, 74, 78, 80, 81,
82, 83, 84, 86, 89, 90, 94, 98, 99, 100, 101, 109,
Index
121, 123, 128, 130, 131, 136, 141, 153, 169, 200,
226, 230, 248, 257, 258
monomer(s), xi, 51, 52, 54, 103, 109, 113, 117, 157,
275
monosaccharide, 253, 254
Moon, 159, 161, 165
morphology, 146, 147, 154, 155, 184
motion, 209
moulding, 217
movement, 75, 91
mucosa, 140
multi-component systems, 243
multiplicity, 7, 8, 16, 19, 20, 21, 28
multiplier, 3
N
Na+, 80, 129, 138, 143, 201, 202, 204, 205, 207, 208,
211
NaCl, 117, 191, 194
nanocomposites, 201, 202, 208
nanoparticles, 109, 126, 141, 200
nanostructures, xii, 187, 193, 198, 200
nanotube(s), 199, 200
natural environment, 106
natural polymers, 36
neglect, 27, 38
negotiation, 41
Netherlands, 63, 87, 101, 200
network, xiii, 15, 121, 128, 135, 140, 178, 179, 182,
207, 212, 214, 234, 235, 236, 237, 239
neural network(s), xiii, 233, 234, 235, 236, 237, 241
Neural Network Model, 236
neurons, 235, 237
neutrons, 90
nicotine, 74
nitric acid, 130
nitric oxide, 90, 146
nitrile rubber, 181
nitrogen, 39, 59, 81, 111, 177
NMR, xi, 51, 52, 54, 55, 59, 267
nonlocality, 228
non-metals, 192
nontoxicity, 148
North America, 277
nucleus, 73, 75, 76, 81, 89, 91, 92, 188
numerical analysis, 17
numerical tool, 234
nutrients, 149
O
observations, 37, 170, 267
occlusion, 139
287
octane, 244
OH-groups, 252
oil(s), 122, 152, 218
olefins, 244
oligomers, 61, 62, 64
olive oil, 153
operator, 228
optical chemical sensors, 136
optical fiber, 117
optical properties, 157
optimization, 59, 111, 114, 138
ores, 174
organ, 149
organic compounds, 107, 118, 135, 198
organic polymers, 52
organic solvent(s), 36, 40, 41, 53, 54, 106, 107, 111,
114, 118, 126, 152
organism, 149, 153
organization, 7, 27
orientation, 221, 226
oscillation, 92
osmosis, 108
osmotic pressure, xi, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 36, 135
ossification, 148
osteoporosis, 139
output, xiii, 136, 233, 234, 235, 236, 237, 239
oxidability, 170
oxidation, 65, 67, 108, 110, 138, 167, 169, 170
oxidation rate, 167, 169, 170
oxides, 151
oxygen, 38, 42, 53, 74, 81, 82, 84, 86, 90, 96, 98, 99,
128, 143, 149, 154, 155, 168, 169, 170, 257, 258,
268, 270, 272
P
PAA, 108, 111, 114, 115, 118, 119, 201, 202, 203,
204, 205, 207, 208, 209, 211, 212, 213, 214
packaging, 257, 259
pain, 144, 145
paints, 117
palladium, 138
palm oil, 152
PAN, 115, 118
pancreas, 149, 150, 151
parameter, xii, 2, 5, 11, 16, 24, 31, 36, 37, 38, 40, 41,
42, 43, 44, 46, 47, 62, 65, 66, 73, 74, 75, 76, 79,
81, 82, 84, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96,
98, 100, 169, 170, 179, 182, 184, 187, 188, 189,
197, 198, 201, 205, 206, 209, 222, 228, 236, 244,
246
particles, 79, 92, 93, 109, 121, 130, 146, 147, 152,
154, 155, 174, 175, 177, 184, 185, 221, 227, 228
288
Index
passive, 109, 130, 260
PCR, 131
peat, 36
peptides, 140
perception, 236
percolation, xiii, 207, 210, 212, 213, 214
peritoneal cavity, 149
permeability, 107, 113, 118, 121, 125, 129, 131, 134,
135, 137, 145, 149, 151, 154, 155, 156
permeation, 107, 112, 114, 115, 116, 117, 121, 122,
124, 132, 133, 156
permit, 259, 274
peroxide, 177, 181, 183, 184, 185, 268, 269, 276
pH, 113, 126, 131, 132, 135, 136, 137, 140, 141,
147, 174
phase inversion, 133, 152
phenol, 39, 43, 108, 136, 137, 182
phenolphthalein, 137
philosophers, ix
phosphorous, 82, 84
phosphorus, 82
phosphorylation, 82, 84
photolithography, 138
photopolymerization, 137
photosynthesis, xii, 73, 74, 81, 82, 83, 84, 86, 87, 89,
90, 95
physical and mechanical properties, 62, 63
physical chemistry, ix, 65
physical properties, 105, 140, 151
physical-mechanical properties, 180, 181, 185
physics, ix, 65, 73, 87, 89, 187, 211
plants, 87, 127, 255
plasma, 111, 112, 138, 142
plasma levels, 142
plasmapheresis, 140
plastics, 257, 258
platelets, 139
Plato, ix
PMMA, 150
poison, 133
Poland, 178
polar groups, 108
polarity, 39, 43, 46, 65, 66
polarizability, 42, 66, 67
polarization, 39, 41, 152, 199
pollutants, 125, 126
pollution, 130, 156
poly(vinylpyrrolidone), 134
polyacrylamide, 116, 153
polyamides, 201
polycarbonate, 52
polycondensation, 174, 228
polydispersity, 227
polyesters, 217, 225
polyimide(s), 208, 209, 210
polyisoprene, 17
polymer(s), xi, xii, 2, 24, 25, 26, 31, 36, 37, 39, 40,
41, 44, 51, 52, 54, 55, 56, 59, 60, 61, 62, 69, 70,
71, 72, 103, 104, 105, 106, 107, 108, 109, 111,
112, 113, 114, 115, 118, 121, 124, 125, 127, 128,
130, 131, 132, 133, 134, 135, 137, 138, 139, 140,
141, 142, 144, 145, 147, 148, 152, 153, 154, 156,
157, 158, 169, 170, 173, 180, 202, 210, 211, 217,
257, 258, 259, 260, 263, 265, 267, 269, 270, 272,
273, 274, 275, 276
polymer blends, 134, 154
polymer chains, 109
polymer composites, xii, 51, 62, 217
polymer destruction, 69
polymer materials, 112, 141
polymer matrix, 109, 128, 130, 137
polymer melts, 69
polymer mixing, 113
polymer networks, 113, 140, 148
polymer solutions, 25
polymer structure, 107, 210, 211
polymeric blends, 140
polymeric chains, x, xi, 1, 2, 13, 21, 23, 25, 26, 27
polymeric materials, 140
polymeric membranes, 40, 118, 121, 128
polymerization, 24, 54, 103, 108, 109, 113, 144, 153,
201, 207, 257, 260, 267
polymerization mechanism, 109
polymerization process, 153
polyolefins, 154
polyorganocarbosiloxanes, xi, 51
polypropylene, xii, 69, 71, 72, 155, 167, 168, 171
polyurethane, 39, 142
polyvinyl alcohol, 137, 138, 147, 148, 152
poor, 108, 117, 133, 134, 140, 141, 142, 148, 155,
156, 254
population, 127
porosity, 129, 131, 132, 147
porphyrins, 127, 142, 143, 144, 160
Portugal, x, 103
potassium, 96
potential energy, 73, 75, 89, 91
power, xi, 23, 32, 84, 86, 133, 177
precipitation, 130, 150
preference, 144
pressure, x, xi, 1, 9, 10, 13, 14, 21, 23, 31, 63, 107,
111, 118, 130, 132, 135, 169, 218, 234, 244, 245
priming, 167, 170
probability, xi, 2, 3, 4, 5, 7, 51, 57
process control, 241
production, 90, 122, 138, 157
Index
prognosis, 148
proliferation, 147, 153
propagation, 237, 258, 260, 261, 263, 264, 267, 274,
276
proportionality, 27, 45, 71
propylene, 141
prosthesis, 147, 165
proteins, 81, 87, 131, 137, 140, 141, 149, 150
proteolytic enzyme, 145
protons, 55, 81, 82, 133, 136
PTFE, 152
pure water, 129
purification, 127, 128, 131, 156, 157, 244
PVA, vi, 103, 104, 105, 106, 107, 108, 109, 111,
112, 113, 114, 115, 116, 117, 118, 119, 120, 121,
122, 123, 124, 125, 126, 127, 128, 129, 130, 131,
132, 133, 134, 135, 136, 137, 138, 139, 140, 141,
142, 143, 144, 145, 146, 147, 148, 149, 150, 151,
152, 153, 154, 156, 157, 160, 162
PVA films, 146, 154
PVAc, 103, 104
PVP, 134, 140
pyromellitic dianhydride, 202
pyrophosphate, 260
Q
qualitative differences, 218
quartz, 135
R
radiation, 81, 82, 101, 105, 147, 153, 169
radical polymerization, 153, 267
radius, x, 1, 2, 6, 12, 21, 24, 25, 28, 73, 76, 79, 81,
90, 91, 96, 191, 202, 212
random walk, x, 1, 2, 4, 7, 21, 26, 33, 228
range, xiii, 24, 27, 38, 42, 52, 54, 55, 86, 93, 98, 106,
112, 113, 121, 130, 132, 133, 135, 137, 138, 139,
151, 175, 176, 177, 201, 208, 233, 234, 236, 239,
241, 244, 258, 276
reactant(s), 151, 152
reaction center, 74, 81
reaction medium, 151
reaction order, 54
reaction rate, 39, 54, 56, 57, 58, 65, 75, 91, 153, 201,
204, 208, 218, 219
reaction rate constants, 54, 56, 57, 58
reaction time, 220, 221, 261
reactivity, 48, 56, 90, 98, 154
reagents, xiii, 100, 153, 157, 202, 213, 219, 220,
221, 225, 226, 230
real time, xiii, 225, 228, 230, 231, 234, 241
reality, 37, 38, 228
289
reception, 174
recognition, 106, 128, 142, 147
recombination, xiii, 170, 217, 219, 220, 221, 222
reconstruction, 81, 86, 140, 200
recovery, 120, 128, 131, 152
rectum, 148
recycling, 174
redistribution, 79, 93
reduction, 52, 74, 82, 83, 85, 86, 111, 116, 136, 142,
174, 182, 202, 207, 211, 226, 230
reflection, 276
refractory, 200
regenerated cellulose, 132
regeneration, 130
regulation(s), 87, 131, 188
rejection, 118, 226
relationship(s), 43, 177, 203, 204, 205, 207, 208,
209, 211, 213, 218, 219, 220, 221, 226, 228, 229,
234
reliability, 188
repair, 148
replacement, 95, 148, 156, 180, 181, 182, 184, 188,
253
reproduction, 106
Republican, 64
resection, 148
residuals, 153
residues, 105, 137
resilience, 181
resins, xii, 51, 52
resistance, 114, 128, 140, 149, 153, 156, 157, 182
response time, 136, 137
retention, 127, 130, 131, 132, 133
rings, 254
RNA, 131
rods, 104
rolling, 199
Romania, 103, 160
room temperature, 41, 123, 135
root-mean-square, 228
rubber(s), xi, xii, 2, 10, 15, 17, 18, 19, 20, 21, 39, 52,
173, 174, 177, 178, 179, 180, 181, 182, 183, 184,
185
rubber compounds, 178
Russia, x, 23, 35, 51, 64, 65, 73, 89, 187, 207, 217,
225, 251
S
safety, 106, 144, 156
sales, 157
salt(s), 109, 117, 118, 121, 122, 131, 135, 144, 145,
174
290
Index
sample, 36, 41, 42, 43, 129, 136, 154, 176, 179, 258,
260
saturation, 41, 43, 236
scaling, xi, xiii, 23, 31, 32, 208, 217, 221, 222, 227
scaling approach, xiii, 217, 221, 222
scaling relations, 208, 227
search, 109, 217, 225
searching, 90, 100, 168
second virial coefficient, 24
sedimentation, 113
seeding, 147
segregation, 151
selecting, 71, 218
selectivity, 107, 108, 109, 111, 112, 114, 116, 118,
119, 120, 121, 125, 128, 156
selenium, 90, 98, 99, 100
self-control, 149
self-organization, 225
semiconductor, 138, 139
sensitivity, 135, 136, 137, 138, 157
sensors, 133, 135, 136, 137, 157
separation, 42, 59, 95, 103, 106, 107, 108, 111, 112,
114, 115, 116, 117, 118, 119, 120, 121, 122, 123,
124, 125, 128, 129, 130, 131, 140, 148, 151, 152,
156, 157, 161, 233, 244, 247
series, 31, 36, 58, 86, 198, 245, 277
serum, 132, 133
serum albumin, 132, 133
shape, 2, 94, 104, 128, 130, 131, 133, 140, 197, 202,
207, 208, 210, 234
shape-memory, 140
shear, 131, 167, 171
shear deformation, 171
shock, 147
Si3N4, 137
Siberia, 38
side effects, 141, 142, 149
sign(s), 3, 8, 10, 12, 13, 15, 66, 234
signals, 55, 59
silicon, 52, 56, 59, 135, 136
similarity, 79, 82, 94, 147, 175, 176
simulation, 211
SiO2, 137
sites, 13, 258, 259, 276
skin, 140, 142, 144
skin diseases, 142
social problems, ix
society, 157
sodium, 117, 128, 129, 145, 156, 227
sodium hydroxide, 227
soil, 106
sol-gel, 112, 121
solid phase, xii, 202, 207, 208, 214
solid solutions, 188
solid state, 200, 208, 209, 210, 211, 212, 213, 214
solubility, xiii, 36, 37, 38, 40, 47, 48, 55, 66, 75, 79,
93, 106, 112, 116, 120, 140, 144, 153, 170, 187,
188, 200, 243, 244, 247, 249, 257
solvation, 38, 39, 40, 41, 42, 43, 45, 46, 47, 66
solvents, xi, 2, 24, 35, 36, 37, 38, 39, 40, 41, 42, 43,
44, 45, 46, 47, 53, 65, 66, 67, 113, 128, 132, 156
sorption, 38, 48, 117, 124, 127, 130, 134, 143, 144,
146
Spain, 250
species, 107, 128, 130, 131, 138, 226, 270
specificity, 225
spectral dimension, 208, 227
spectrum, 39, 176, 254
speed, 178, 181
spin, 131, 138, 202, 208
stability, xi, 15, 51, 61, 104, 108, 111, 114, 118, 132,
134, 136, 137, 138, 140, 141, 152, 156, 169, 170,
192, 197, 198, 253, 260, 267, 268, 270, 273, 274,
275, 276
stabilization, xii, 187, 188, 191, 194, 198, 199, 270,
272, 274
stages, xii, 44, 67, 73, 74, 82, 86, 87, 89, 169, 252
standard deviation, 5, 45
statistics, x, 1, 2, 21, 24, 26, 33
steel, 259
stock, 144
storage, 137
strain, 69, 71
strength, xi, 2, 72, 105, 114, 117, 118, 132, 137, 179,
182, 183, 235
stretching, 12, 15, 16, 18, 20
strong interaction, 109
structural characteristics, 140
structural formation, 82, 86
structure formation, 184, 187, 189
styrene, 128
substitution, 8, 12, 70, 86, 254
substrates, 52, 136, 137
sucrose, 122
suffering, 139
sugar, 122, 251, 252, 253, 254
sulfur, 87, 90, 98, 99, 100, 177, 178, 180, 181, 183,
184, 185
sulfuric acid, 105
sulphur, 41, 177, 227
Sun, 159, 160, 165
supported liquid membrane, 125
suppression, 47
surface area, 246
surface modification, 109, 112
surface properties, 112
Index
surface region, 109
survival, 101, 150, 151
susceptibility, 109
swelling, xi, 24, 25, 35, 36, 37, 38, 40, 41, 42, 43,
44, 45, 46, 47, 48, 104, 105, 106, 109, 112, 113,
114, 116, 122, 124, 129, 134, 135, 136, 141, 144,
146, 147, 148, 153, 254, 255
swelling process(es), xi, 35, 36, 38, 40, 41, 42, 43,
46, 47, 136
synergistic effect, 121
synthesis, xii, xiii, 52, 63, 74, 81, 87, 105, 107, 109,
112, 120, 131, 139, 150, 151, 152, 157, 173, 174,
202, 208, 225, 228, 251, 252, 253, 254
synthetic polymers, 37, 38, 40, 140, 144, 153
systems, xi, xii, xiii, 10, 12, 13, 51, 59, 90, 92, 93,
94, 95, 106, 128, 130, 140, 141, 142, 145, 148,
149, 151, 154, 173, 174, 177, 180, 181, 182, 183,
184, 185, 187, 188, 192, 199, 200, 217, 233, 234,
236, 241, 244, 247, 248, 249, 250, 260
T
tacticity, 140, 157
technology, xii, 106, 107, 125, 131, 141, 142, 157,
173, 258
temperature, xiii, 10, 32, 37, 43, 54, 56, 57, 61, 71,
105, 108, 111, 113, 114, 115, 116, 118, 119, 120,
122, 133, 135, 140, 141, 152, 154, 155, 167, 168,
169, 174, 176, 192, 201, 210, 211, 218, 233, 234,
236, 237, 239, 240, 241, 243, 245, 246, 252, 257,
258, 263, 265, 266, 267, 269, 272, 273, 275, 276
temperature dependence, 167, 168
tensile strength, x, 1, 16, 21, 114, 144, 153, 181
tension, 13, 14, 15, 21
TEOS, 111, 112, 116
tetraethoxysilane, 112
textiles, 106
TGA, 61, 62, 265
theory, xi, 35, 36, 37, 38, 46, 47, 184, 192, 200, 205,
234, 251
therapy, 127, 142, 253, 254, 255
thermal aging, 179, 267
thermal analysis, xii, 173, 175
thermal decomposition, 169
thermal degradation, 260, 267, 268, 270
thermal energy, 211
thermal resistance, 132, 140
thermal stability, 131, 132, 134, 175, 260, 268, 269,
271
thermal treatment, 113
thermodestruction, 176
thermodynamic properties, 234, 244
thermodynamics, x, 1, 2, 10, 21, 26, 40
thermogravimetric technique, 259, 260
291
thermogravimetry, 260, 268, 271, 275, 276
thermolysis, 270
thermooxidation, xi, 51, 61
thermoplastics, 217
three-dimensional space, 221
threshold, 212
thyroid, 138
time, 36, 38, 40, 41, 43, 55, 56, 57, 59, 66, 67, 69,
79, 86, 94, 98, 105, 128, 129, 136, 144, 145, 146,
147, 152, 174, 176, 181, 182, 185, 189, 197, 207,
213, 218, 219, 221, 225, 228, 229, 230, 241, 260,
261, 276
tissue, 106, 142, 143, 147, 148, 150, 151
toluene, 53, 54, 56, 57, 119, 120, 154, 155, 244
total energy, 78, 92
toxic effect, 153
toxic metals, 130
toxicity, 105, 106, 130, 140, 157
trade, 118
training, 237, 239, 241
trajectory, 3, 4, 5, 6, 226
transformation(s), xi, xii, 36, 51, 70, 72, 201, 202,
203, 206, 208, 235, 236
transistor, 137
transition(s), xi, 16, 23, 44, 52, 79, 82, 93, 141, 176,
184, 199, 210, 211, 213, 226
transition temperature, 52
translation, 21
transmission, 149, 154
transplantation, 151
transport, 82, 87, 107, 117, 121, 136, 142, 148, 226,
227, 228, 229, 230, 250, 257, 258
transport processes, 226, 227, 230
transportation, 133
trifluoroethyl methacrylate, 117
trypsin, 146
tumor, 148
tumor cells, 148
turbulence, 228
U
UK, 166
Ukraine, x, 1, 23, 35, 65, 173, 200
uncertainty, 265
uniform, 142
UNIQUAC, xiii, 243, 244, 245, 246, 247, 248, 250
unit cost, 139
United States, 165
universality, 95, 252
urea, 138
urethane, 141, 142
uric acid, 138, 148, 149
USSR, 254, 255
292
Index
UV, 113, 146
UV irradiation, 113
vulcanization, xii, 15, 173, 174, 177, 178, 179, 180,
181, 182, 183, 184, 185
V
W
vacuum, 41, 75, 91, 107, 123, 202, 208, 218
valence, 75, 76, 78, 79, 82, 86, 91, 92, 93, 94, 96, 98,
170, 188, 198
validity, 141
values, xii, xiii, 5, 8, 10, 12, 13, 17, 19, 21, 24, 25,
32, 37, 38, 40, 41, 42, 43, 44, 45, 46, 56, 66, 67,
70, 71, 72, 73, 76, 78, 81, 82, 84, 85, 86, 92, 95,
96, 98, 99, 117, 126, 135, 136, 146, 167, 168,
169, 170, 188, 189, 191, 192, 197, 198, 204, 209,
236, 243, 244, 247, 248, 249, 265
vanadium, 137
vanadium pentoxide, 137
vapor, 48, 153, 154, 156, 157, 233, 234, 236, 237,
239, 241, 244
variable(s), 5, 6, 10, 19, 71, 130, 246, 267
variation, 136, 202, 210, 230, 247
vehicles, 144, 146
vein, 147
velocity, 52, 75, 91
vessels, 41
vinyl chloride, 257
vinylidene chloride, 257, 259, 260, 263, 264, 267,
268, 269, 270, 271, 272, 273, 274, 276
viscosity, 63, 69, 71, 72, 145, 155, 234
visual area, 53
vitamin B1, 148, 149
vitamin B12, 148, 149
volatile substances, 41
vulcanizates, 178, 179, 180, 181, 184
walking, 6
washing procedures, 153
wastewater, 106, 125, 126, 130, 131, 144, 157, 160
wastewater treatment, 106, 126, 131
water absorption, 134
water diffusion, 117
water evaporation, 123
water sorption, 146
water vapor, 146
weakness, 116, 136
wear, 148
weight loss, 176, 259, 260, 261, 265, 266, 267, 269,
272, 273, 275
weight ratio, 113
wetting, 138
writing, 32
Y
yield, 37, 54, 56, 57, 152
Z
zinc, 174, 175, 177, 178, 180, 181, 182, 183, 184
zinc oxide, 174, 175, 177, 178, 180, 181, 182, 183,
184
ZnO, 174, 178, 179, 182, 183, 184

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