Long Range Interactions beyond first neighbour Intermolecular

The four cardinal interactions ( LRI )
Long Range Interactions beyond first neighbour
Dispersion plus electrostatic
( steric and entropy)
Intermolecular forces organizing complex fluids
…Laboratory experiments for challenging
predictive theories.
>>
« standard » PoissonBoltzmann-Lifshitz
•  Example 1: an hexapeptide as a vdW fluid
•  Example 2 : a reverse micelle as a vdW fluid
[email protected]
1
The van der Waals EOS
•  Hydration force: V. A. Parsegian and S. Marcelja ( 1974-1977)
2
•  Depletion mechanism : S Asakura and F Oosawa (1954)
EOS of a van der Waals fluid
Equilibrium between a dilute and a dense phase at same (P,T)
U sph (r) = −
•  Measure of concentration gap between phases in equilibrium :
givesluation of the strength of the interaction
3
Vg/Vl is relative concentration measures A : attraction
Ar
6d
2.
N-merisation in solution and octanol/water partitioning
a. Solutions in pure solvents. Peptide (1) is well soluble both
in water and octanol up to 20 mM (1.3% v/v) at 20 1C. Above
this critical concentration a phase separation occurs, leading
to the formation of a gel-like solid and a homogeneous
liquid phase.
Solutions of (1) in water or in octanol have been
investigated by means of light scattering. In water, dynamic
light scattering (DLS) produced a weak signal leading to an
apparent hydrodynamic diameter of about 1.5 nm. This
already indicated that the solution does not contain micelles
or larger colloidal aggregates. Moreover, molecular weight
determination by static light scattering (SLS) via the Debye
method gave an apparent molecular weight of 0.6 kDa,
confirming that the peptide solution in water is mainly made
of monomers, for concentrations below 20 mM. In pure
octanol, DLS gave similar results whereas the apparent
molecular weight determined by SLS was found to be
2 kDa, corresponding to dimers or trimers. We conclude that
this peptide does not self-assemble into micellar- or vesicular-like
structures contrary to what observed by other authors on
similar peptidic sequences.30–36 Aggregation in large assemblies is
not present in octanol: thus, we can consider monomers and
dimers as interacting globular colloids, since H-bonds between
solvent and peptide backbone are negligible even in the case of
octanol.37 Moreover, peptide self-association has already been
evidenced in other organic solvents like carbon tetrachloride
where polar interactions between peptide and solvent are
weaker compared to those observed in water.38
Coacervate as the simlest liquid-gas transition
The water-octanol « buyancy » effect
The hexapeptide chosen : Ac-Phe-Leu-Val-Pro-Ala-Ala
Dimers in water and in octanol
1000
304 nm
800
Intensity (a.u.)
400
200
« globules » plus
Dilute solution
coacervate
b. Partitioning between water and octanol. Peptide (1) was
then subjected to partitioning between equal volumes of water
octanol
0
250
275
300
325
350
375
400
Emission wavelength (nm)
73075 1uM dans H2O sat en C8OH
# 1 RT: 0.02
T: FTMS + p NSI Full ms [650.00-2000.00]
659.3757
100
AV: 1
water
NL: 3.31E5
95
90
659.3757
85
[M+H] +
80
75
70
676.4026
65
60
55
50
45
40
676.4026
[M+NH 4]+
[M+M+NH 4]+
35
1334.7714
30
25
1334.7714
20
15
10
c-Phe-Leu-Val-Pro-Ala-Ala peptide: molecular structure (left) with polar region circled by a dashed line;
ape of the amphipathic peptide.
Phys. Chem. Chem. Phys., 2011, 13, 6914–6924
697.3228
5
719.4435
808.4813
0
600
700
800
1317.7437
850.3668
914.1219
900
967.1215
1008.0354
1000
1127.5109
1100
1212.1560
1263.7355
1200
1300
dimer
1356.6942
1445.2869
1400
1500
6915
m/z
Peptides forming reversible « coacervates »
Dimer mass at zero concentration obtained from Light scattering
The octanol-water « buoyancy » of dimers
The water-octanol « buoyancy » effect
logP = log ( [peptide]octanol / [peptide]water )
-5
-5,5
-6
1,2
-6,5
octanol
1,0
water
0,9
ΔG w-->o (kJ/mol)
1,3
1,1
log P
2011
282 nm
600
Relative abundance
kages between amino-acids,
and it is difficult to design
ly in the form of micelles.13
minus (carboxylic acid and
head groups and bring a
re. A way to bring hydroremity of the peptide and to
side groups such as leucine
phenylalanine (Phe), etc.
part as the polar head group
ntial complexant properties
ll also be the only functional
uence the C-ter is kept free
o acids like alanines (Ala).
he rest of the molecule by a
nker. With a view to further
ng the Ala2 group, the linker
Gly) to avoid epimerization
g the hydrophobic part, we
etyl (non labile, bio-friendly
m the linker to the N-ter is
lky amino-acids, so that the
with a small head group and
eometry has been chosen to
ganic solvents by potentially
tes, like in the case of a well
sulfosuccinate (AOT) in isoructures designed for a large
the Hofmeister classification
ration have been selected:
d Ac-Phe-Leu-Val-Gly-Alane was decided to allow easy
y = -0,0932x + 20,349
R² = 0,968
-7
-7,5
-8
-8,5
-9
0,8
-9,5
0,7
0
10
20
30
40
50
Peptide total concentration (mM)
« hydrophibising » a peptide with temperature ?
60
-10
270
280
290
300
310
320
Temperature (K)
Salting-in and salting-out as Hofmeister discovered in 1880
8 2N ! 52d
8m
8
p,w /dT p .
w
This relation shows
the constra
ε. σ lipid to the
σ polymer solution inside the bag. During this pro519
It should be clear thattransition
what wetemperature
measure here
istransition
the des
and
cess, an optically clear monophasic domain may occur in the
V(r)=4ε.[(σ/r)12 - (σ/r)6]
Teflon cap
excess
entropy,
that
part
of the entropy
that contributes
the transitioto
temperature
T p at which
Sol-gel globule equilibrium : a liquid-gas equilibrium
: coexistence
of
dilute
andseal
« gelled » phase
reservoir,
showing
that the hemoglobin
lyotropic
liquid
crystal
hasthe
left
With O-ring
where r is the
distance
between
two particles,
σ
is
size,
and
ε
is
the
attractive
en
transition.
theattractive
coexistence
In this case, waterphase
or surfactant
has Stainless
to steelbyscrewchanges in the stress P p at transit
where r is the distance between two particles, σ is the size, and ε is the
energyregion.
at
condensed and a dilutedbephase.
of repulsiveand
van
der~ SWaals
The
transition
toLuciteosmotic-pressure
language is immedia
added We
to theconsider
reservoiraincombination
order
to recover
the
coexistence
cover with samplmg
2S
Serum cap
a 8opening,
a ! dT p 5 ~ V a 8 2V a ! dP p .
rubber stopper,
and positioning
notches
equilibrium
+function
globulesof the ratio
contact. A dimensional analysis shows that
ε is a simple
effected
by
recalling
that
a
volume
water V w is the n
plateau pressure.
For example,
at room
the function of theofratio
contact. A dimensional
analysis
shows
that εtemperature,
is a simple
N2 above
This
is
a
kind
of
compensation betw
Solutions
r7
interactions, part of this equilibrium
van der Waals
contribution
beingT500
counter-balanced
by
the
adsorption
concentration
of Dextran
was
2
N, inlet N
with stopcock
of water times the mola
ber ~Pharmacia!
of moles ~or
molecules!
w
Polyethylene
x = ρG / ρL
work-induced contributions to the diff
tubing
2661 wt. %. Therefore, the equilibrium
plateau pressure
is of water, v w ,
molecular!
volume
It can be rewritten to look like a Cla
5.660.1
x = ρion
/ on
ρdensity
Lucite carousel
G the
Lthe
Semi-permeable
determined
to be 10
Pa.membrane
of a chaotropic
peptide.
sample holder
where ρG and ρL are respectively the density
of the gas and
of the condensed
tion,
V w 5as
v waNreserThis new method, using the
diphasic sample
w or N w 5V w / v w .
Concentrated
dextran
solution
phase. This function can be obtainedAby
fitting model
the values
from
accurate
voir,
thatis the
pressure
after potential
microphase
dP p potential
S a 8 2S of
a water
simple
ofρaGcalculated
Van
derρrecognizes
Waals
fluid
theosmotic
Lennard-Jones
(LJ)
V(r)chemical
described
asdensity
Changes
d mthe
are, con
by
where
and
are
respectively
the
density
of
gas
and
the
Hemoglobltn
L
w in the
5
. of the
solution
separation
is
fixed
at
the
coexistence
value
of
the
pressure,
dT
V
2V
71, 72
p
a
a
8
dP in osmotic pressure by
a
WA to /, changes
Magnetic
stirrer
simulations of the phase diagram
:
an intensive property independent of thenition,
amountrelated
of
material
V(r)=4ε.[(σ/r)12 - (σ/r)6]in the two lamellar phases @ L # and @ L # . These phases do iuc1teIn carousel
our notation, a 8 refers to the con
phase. This function can be obtained
the ! 52
values
calculated
from ! a
a8
a by
d mfitting
Invthe
case
of ! dP ~ energy/vol
~ vol/mol
ε = kBT / f(X)
w ~ energy/mol
holder w
dilute
~swollen! phase V a 8 2V a , the
have a macroscopic area of contact S. From previous micro- Sample
(top view) « release »e
associated
with condensation,
is alw
of water durring
agg.
2.3764
23.8121 scopic
where
r –is0.115163X
the distance
two particles,
is71,the
size, andof εthe
is the
energy
at
observations,
it is σknown
orderattractive
of Opening
with f(X) = 1.31 – 0.301026X / (1-0.443917X
) between
for
72that Ssoisthat
sample
tube prefer to think in terms of chem
2 phase
6
who
simulations 100
of the
diagram
:
m /g. The implicit assumption here is that the
interfaa
a8
Opening
Why does it « reverse »?
rive
relevant
N
2N
5for~ Vthe 2V
2
and X = (1-x) / (1+x).
~
a 8 ! dPClausius–Clapey
p.
cial energy
g .S is
negligible
compared
to theof
osmotic
work
w ratio
w ! d m p,w
gas equilibration a 8
contact. A dimensional analysis
shows
that
ε is a simple
function
the
Gibbs–Duhem
relation,
of creating the two phases. g is the surface energy per area
There
should
not be any confusion about the assignmen
ε = kBT / f(X)
In the Ch.
same
manner, the size is obtained from
MS Prouty,
AN. Schechter
and
VA Parsegian:
(0)
(b)Determination of the phase diagram of an
Déjugnat et al.. Phys Chem Chem Phys 2011;13:6914–24.
between the twoFigure
lamellar
phases.
Since
this
g
is
difficult
to
2sdT1
v d p2S
A
single
sample
of
protein
solution contained
in dialysis
ran i n
bei d m i 50.
x = ρG / ρL
1.
(a)
Test-tube
osmometer.
assembling protein (1985) and science (1992)
S a osmomet,er.
are,tubingalways,
entropy
S.
Entropies
S a 8 and
equilibrated
to
a
much
larger
volume
of
polymer
solution
of
known
osmotic
pressure.
(b) Carousel
Up to 6 the entropie
−1/ 3
measure,
the
inverse
osmotic
stress
approach
used
here
to
σ = g(Y) ρ L
separate sample solutions can be equilibrated to the 2.3764
same polymer osmotic pressure.
23.8121
Our measurements
at constant
phase
and
automatically
associated
with
any parh
measure
the
pressure of the
plateau had the
to be
independently
with
f(X)
=
1.31
–
0.301026X
/
(1-0.443917X
– not
0.115163X
) arearetwo
that
d
p[0.
There
component
where
ρ
and
ρ
are
respectively
the
density
of
the
gas
and
the
density
of
the
condensed
L
checked. In order
to do
have
cross-checked
thisbuffer
inlar Atcomponent.
Because
S about
is an
extensive
quantity,
with g(Y) = 0.314 + 0.477Y 1/3 + 0.2124Y − 0.01151Y 3/2G
with
to a concentration
loo,6 greater
than
operating
rangethis,
of thewe
Knauer
instrument.
these
that
the
G–D
relation
the expected equilibrium
value.
Gelled
samples
were firstreduces to
concentrations, the osmotic pressure of dextran is also
Apparent Hamaker varies in water, NaCl and other salts ? verse osmotic pressure
Winsor
of microemulsions
method
using aclassification
cumbersome
but
preit per
molefrom
~ordialysis
molecule!
of DDAB
cooled or oxygenated
upon removal
sacs in
virtually independent of buffer used, and choose
of temperature.to normalize
and function
X = (1-x)
/ (1+x).
order to permit
good accurate
volume measurement
before
For speed
of equilibration,
thethe
use of values
lower molecular
and Y = 1.31− kBT /ε .
phase. This
can
be obtained
by
fitting
calculated
from
cise
extrapolation
method.
2sdT2n
dwere
m wtransition
2n
m DDAB
osmotic
pressure
P p of(1wthe
dilution. Solutions
of sodium
dithionite
made DDABrdplateau
weight dextran or of polyethylene giyeol would If
give the
the
1,50
up withdedegassed buffer and used within 10 min of
advantage of lower
concentrationsThis
and viscosity
for the
b. The extrapolation
method:
method
requires
temperature,
then the entropy
S a 8 the
of amo
the
preparation.
same osmotic pressure; but “tighter” creases
semipermeablewith
With this approach we have calculated the apparent Hamaker constanttermination
A = ε and theof72
interWe normalize
entropy and
Hemoglobin concentrations were measured by dilution
membranes
might distance
be necessary,D *
thusfor
slowing
down
different
volume
the
repeat
simulations
thesame
phasemanner,
diagram 71,the
: size
In of
the
isDextran
obtained
1,45
a portion is
in KCN
buffer
(Van
Assendelft,
1970)
and
equilibration.
solutions werefrom
made up and
less
than
S
of
the
dilute
L
phas
densed
L a 8 ofphase
mole ~or molecule!
a absorbanceof atDDABr,
a
fractions
pureby collapsed
phase buffer
L a 8 ofatthefixed
measurement of cyanomethemoglobin
weight using degassed
same temperapeptide distance in the condensed phase for each case. Results are reported
in Table in
3. thediluted
540 nm.
The solubility
of the stock solution
for each
run
composition (including dithionite)
as the
hemoglobin
P
decreases
with
temperature,
then
creation
of
the
p exponential
1,40
ture. A monotonic
close
a simple
was reladetermined
at the S5s/n
appropriate DDABr
temperature
solution curve,
against which
theytowere
to be dialyzed.
Equal
and byN w 5n w /n DDA
neat,negative
ε
=
k
BT / f(X)
−1/
3
ultracentrifugation
as
described
by
Hofrichter
et
al.
of permeant species was
preset. Cona 8 from the dilute phase must involve an
densed
phase
charge
Then,of the
coexisting
periodicities
σ = g(Y ) ρ L tion is obtained.concentrations
centrations
dextran two
solutions
were determined
after
(1976). are
1,35
This normalization gives
final equilibration
by measuring refractivecrease
index, using
in entropy.
measured usinganaAbbe
biphasic
sample.
The periodicity
Refractometer.
The refractive index increment.
2.3764
23.8121of the L a 8
(e) Lysozymr
with
f(X)
=
1.31
–
0.301026X
/
(1-0.443917X
–
0.115163X
)
in each buffer system
usedawas
determined
byshallcorreH2O
phase, when it for
is dextran
in equilibrium
with
swollen
Wephase
use the convention
that
quantity
1,30
dthe
mobtained
m DDABr50
w 2d
Egg-white lysozyme (22SdT2N
x crystallized) w
was
measurements
on carefully prepared and diluted samples.
1/3
3/2
NaCl
When
dithionite
had
been
added
to
the
solution,
a
from
Worthington
Biochemical
Co.,
Freehold,
1\;J.
sponds
to
a
graphically
extrapolated
pressure
of
the
plateau
with
g(Y)
=
0.314
+
0.477Y
+
0.2124Y
−
0.01151Y
competitive,
correction was made in the measured refractive index.
Measurements were or
in 0.10 M-sodium acetate
1,25
LiCl
”S0.5a 8carried
2S aoutchloride,
a!(pH
a 84.70),
and X = (1-x) / (1+x).
buffer
M-sodium
conditions chosen
as shown in Fig. 4. Winsor
This procedure
is time DS5DS
consuming,
besalt,and,peptide,
I
:
solubilisation
failure;
«
solute
»
in
excess
to maintain lysozyme in monomeric form and achieve
NaNO3
hydration
(d) Hemoglobin samples
cause
it
requires
determination
of
a
full
set
of
pressures
for
moderate
solubility.
The
concentration
of lysozyme
2d m DDABrin
5SdT1N
. d
1,20
Winsor II : excessiswater:
extraction
w d m wthe
the entropy
change
experienced
going
from
solutions
after
equilibration
was determined
by
Hemoglobin S was prepared from blood of individuals
Y
=
1.31−
k
T
/
ε
and
.
monophasic
samples.
Within
the
final
accuracy,
measuring
the
absorbance
of
a
portion
at
280
nm.
homozygous
or
heterozygous
for
HbS
by
ion-exchange
In the same manner, the concentrated
size Bis obtained
from
Winsor
III : three phase
phase situation
phase.lamellar-phase equilibrium, t
During
chromatography
on DEAE-Sephacel.
HbAS usedto(athe condensed
1,15
typically 20% in
pressure
approximately
0.1blood
in the logphase
P
mixture
of Hba or
and IV:
HbS) optimisation
was a lysate from
Winosr
withput
separation
(
) Procedure
of f DDABr
are equal,
obtained by exchange transfusion. Hemoglobin samples
units on the graphs,
the inverse
osmoticbuffer
pressure
corresponds
−1/ 3
were dialyzed
into 0.15
M-phosphate
(pH
7.4),
and
Osmometer assembly
for deoxygenated
hemoglobins
Translation
in
phase
diagram
?
1,10
With
this
approach
we
have
calculated
the
apparent
Hamaker
constant
A = ε and th
σ
=
g(Y)
ρ
RESULTS
was carried out in a “glove
box” in aa nitrogen
concentrated by vacuum filtration
andIV.
ultrafiltration.
L330
a
250
260
270
280
290
300
310
320
340
350 to the value obtained from the extrapolation method.
8 by an
atmosphere.
Oxygen
pressure
was
monitored
For osmotic stress experiments, samples were diluted
m
5
m
DDABr
DDABr
15
Temperature,(K)
8
!/~ Nw
~ S the2S
ing equilibration,
water is transferred to or from
reservoir
A simple model of a Van der Waals fluid is the Lennard-Jones
V(r)=4(LJ)[(potential
/r)12V(r)
- (described
/r)6]as
DeoxyhemogEobin
S Polymerization
90
Temperature (°C)
70
SOLID
H2O
NaCl
LiCl
NaNO3
50
30
SOLUTION
10
-10
0
5
10
15
20
25
30
35
40
Peptide concentration (mM)
A/kT
M)
Wesolubilisation
examine two
•  PA Winsor
andbinary
related didodecyldimethylammon
1/3
3/2 : Hydrotropy,
Because
this necessary
equality3.
of
with g(Y) peptide
= 0.314 +distance
0.477Y
+in
0.2124Y
− 0.01151Y
the condensed
phase
for
each
case.
Results
are ofreported
in Table
III. COMPUTATION
OF
ENTROPY
FROM
THE
emulsification processes
( 1948…)
systems,I…XII
DDABr
and DDACl,
differing
only
in Gibbs–D
the cou
can
take
a
difference
of
the
OSMOTIC STRESS AND WATER VOLUME CHANGE
ion. These differences appeara clearly a in thea compara
and Y = 1.31− kBT /ε . AT TRANSITION
m DDABr
dT1N w dofm wthe l
phase diagrams, shown in2d
Fig.
3 as5Sfunctions
Ch. Déjugnat et al.. Phys Chem Chem Phys 2011;13:6914–24.
12
sol is readily obtained as a clear solution. This is possibly true in certain
of Schulman's experiments with sodium oleate.B In all cases yet examined
S, and S , are isotropic. In all cases yet examined S, and S, are isotropic
while G shows birefringence of greater or less intensity.
A diagrammatic
representation
of phases
the passage
Type I to Type I1
In reality:
lyotropic
plusfrom
microphase
system via the S, G and S, stages of a Type IV system is illustrated in
separation stability
Fig. 2 in which I? has the significance explained in a later section.
-
Type I
S,
(S,+ excess organic liquid)
R < I
S,
+G
G
G
(R=
4
I)
+ S,
f
-
w/o small aggregets as a vdW fluid
Basis of liquid-liquid extraction water<>oil<>water
-
S , Type I1
(S,+ excess aqueous liquid)
R > I
FIG.2.
Lyotropic crystals: viscosity and birefringence
S , , G, S2 Changes in Aqueous Amphiphile Solutions in Absence of 6.
-In the Micro-phase
above two examples
the effect
an amphiphile
on equal volumes
separation
: lowofinterfacial
tension….
of water (or aqueous salt solution) and organic liquid has been described,
but the same sequence of changes can be distinguished over very wide
Translation
diagram
n fact the
whole?sequence
(probably all) volume
ratios. inI phase
+
+
+
S, +- ( S ,
G) += G + (G
S,) --f S, -+ ( S ,
-4q)
•  PA Winsor : Hydrotropy, solubilisation and related
has been emulsification
observed in the
absenceI…XII
of any
organic liquid when a 1 213yo
processes
( 1948…)
aqueous solution of a mixture of C,,-C,, sodium secondary alkyl sulphates
(containing 3-5yo sodium sulphate) was converted t o a solution of cyclohexylammonium alkyl sulphates by gradual addition of cyclohexylammonium chloride. Also it has been found that the hydrophilic character
Phasedecreases
diagramm
: generic
(I) tetradecan -3,
of the molecule apparently
in the
series sodium
Text here
Schulman, Trans. Faraday SOC.1946, QB, 165.
.
Phase diagramm : reality with some electrolyte
present (II)
Terahedron :
oil
Toil
2Φ
2Φ
Text
3Φ
2Φ
water/HNO3
14
Acid/ metal salt
oil
Toil
Text
•  Th.Z et al: Recycling metals by controlled transfer of ionic
species between complex fluids (2014)
1Φ
.
2Φ
extractant
1Φ
water
C. Bauer et al: Liq/liq metal extraction: Phase diagram topology resulting
from molecular interactions between extractant, ion, oil and water (2012) 15
extractant
C. Bauer et al: Li/liqmetal extraction: Phase diagram topology resulting
from molecular interactions between extractant, ion, oil and water (2012) 16
Phase diagramm cut to show : liquid-liquid phase
separation (III)
Text here
+A-
H+A-
(b)
Allows determination of the effective step of attraction
potential
H+A-
(c)
3φ
3φ
o
o
o
Scattering decomposed in P(q) and S(q)
TExt.
Toil
Toil
2φ
TExt.
2φ
1φ
Ext.
w
Ext.
w
Ext.
!
Erlinger, C: Attractive Interactions between Reverse Aggregates and Phase
Separation in Concentrated Malonamide Extractant Solutions (1999)
17
ThZ et al. :Recycling metals by controlled transfer of ionic species
18
between complex fluids: en route to “ienaics” (2014)
Assume incompressible globular aggregates
measured and expected phase diagramm
Origin of the difference: Hamaker and/or coalescence?
Combining steric, depletion, dispersion for the
determination of the effective step of attraction potential:
[DMDBTDMA] (M)
1,6
Limite de 3ème phase expérimentale (dans le Dodécane)
Limite de 3ème phase théorique
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1,2
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2 phases
0,8
3 phases
Rc Rsd
δ"
"
fluctuation de 10 % du taux de collage
0,4
r
0
0
1
2
3
[HNO3]org / [DMDBTDMA]
Usage of the « Baxter » model (1964) : valid when potential is less than 1/10 of
19
D ; gives analytic expressions for S(q) and phase stability
•  Polarisability variation ?
(a)!
!
!
(b)!
! 20
Reverse micelles and molecular dynamics
What we have learnt :
Without specific key-lock vdW fluid is a good guess for
globular colloids when attraction is dominant
Dimers of hexapeptides : « hydrophilicity » is an illdefined concept : « octanol-waries » varies by up to an
order of magnitude when salt is added
Water-poor microemulsions
Alias « reverse » micelles
More or less organized aggregates
Interface difficult to
Define consitently
•  Ph. Guilbaud et ThZ: Depletion of water-in-oil aggregates from poor
solvents: transition from weak aggregates towards reverse micelles (2014)
Small reverse micelles in the « Winsor II » regime : vdW
attraction governed by content of polar cores and givern
liquid-liquid phase separation when no coalesence
happens.
21
22