Concentrated Polymer Solutions

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Concentrated Polymer Solutions
Up to now we were dealing mainly with the dilute
polymer solutions, i.e. with single chain
properties (except for the chapter on the
viscosity of entangled polymer systems). Now we
consider more systematically the equilibrium
properties of concentrated polymer solutions of
over-lapping coils.
It is to be reminded that the overlap
concentration of monomer units is
The corresponding volume fraction
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Since , the overlap occurs already at
very low polymer concentration. There is a wide
concentration region where (i) coils are
overlapping and strongly entangled and (ii)
. Such solutions are called semidilute.
The existence of the regime of the semi-dilute
polymer solutions is a specific polymer feature,
for low-molecular solutions such regime does not
exist. The crossover volume fraction between the
two regimes is
for -solvents (ideal coils)
for good solvents (swollen coil)
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Two sites with excluded volume repel each other
In the liquid of dimers two sites normally
exclude 8 possible dimers positions
If these sites are nearest neighbors, they
exclude 7 dimer positions additional attraction
In the liquid of polymers (multimers) this effect
becomes even larger and leads to the complete
screening of excluded volume.
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Polymer coil dimensions in semidilute solutions
example of scaling arguments
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Step 1.
Step 2.
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Step 3.
The exponent n is chosen from additional physical
arguments. In our case we know at

(Flory theorem). Thus
Therefore, for semidilute solutions, i.e. in the
range we get the following
relation
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Behavior of Polymer Solutions in Poor Solvents
In poor solvent (below the - point) the
attraction between monomer units prevails. Single
chains (or chain in dilute enough solutions)
collapse and form a globule. However, in
concentrated solutions the macroscopic phase
separation can take place as well (a kind of
intermolecular collapse).
Supernatant phase
Precipitant phase
What are the conditions for macroscopic phase
separation? To answer this question it is
necessary to write down the free energy of
polymer solution. This problem was first solved
independently by Flory and Huggins (1941-1942)
for the lattice model of polymer solution.
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Polymer chains are represented as random walks on
the lattice without self-intersections and with
the energy corresponding to each close
contact of two non-neighboring along the chain
units. In the Flory-Huggins theory the number of
conformations is counted and the entropy is
derived as a logarithm of this number. The energy
is calculated from the average number of close
contacting monomer units ( ), where n
is the total number of chains and N is the
number of units in each chain.
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Flory and Huggins obtained
where is the total number of lattice sites
and is the so-called Flory
para-meter corresponds to
(only excluded volume very good solvent).
This term describes translatio-nal entropy of
coils (free energy of ideal gas of coils)
Term responsible for exclu-ded volume interaction
Term responsible for the attraction of monomer
units
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With the increase of the quality of
solvent becomes poorer. Which value of ?
corresponds to the - point? The expansion of
F in the power of
Ideal gas term
Binary interactions, second virial coefficient B
Ternary interactions, third virial coefficient C
At - point
corres-ponds to .
- good solvent region
- poor solvent region
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Macroscopic Phase Separation
This dependence contains both convex and concave
parts.
Convex part of the function F(?) no macroscopic
phase separation. Free energy of the solution
separated into two phases with and
Free energy of homogeneous solution at
F
Concave part of the depen-dence F(?) macroscopic
phase separation into two phases.
?
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Conditions for the phase separation (minimum
possible free energy) are determined from common
tangent straight line - binodal curve.
Condi-tions for the absolute stability of
homo-geneous phase at a given concentration are
determined from the positions of inflexion points
( ) - spinodal
curve. Spinodal at
or
This dependence is shown in the figure
?
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Phase diagram with binodal and spinodal
Spinodal
Single globules
Binodal
?
Conclusions

• The critical point for macroscopic phase
  separation corresponds to the dilute enough
  solution.

• The region of isolated globules in solu-tion
  corresponds to very low polymer concentrations,
  especially at the values of ?
  significantly larger than .

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• The precipitant phase close enough to the
  - point is very diluted.

• For different values of N the binodal curves
  (boundaries of the phase separa-tion region) have
  the form

With the increase of N the critical tempe-rature
becomes closer to the - point, and the
critical concentration becomes lower.
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• What is the connection of the Flory-Huggins
  parameter and the temperatu-re T ? Within
  the framework of the lattice model in the
  experi-mental variables T, c the phase diagram
  has the form shown in the figure, i.e. the poor
  solvent region corresponds to

Such situation is called upper critical solution
temperature (UCST) - critical point is on the
top of the phase separa-tion region. Examples
poly(styrene) in cyclohexane (around ),
poly(isobutylene) in benzene, acetylcellulose in
chlorophorm.
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However, due to the complicated renormalization
of polymer-polymer interactions due to the
solvent, sometimes increases with the
increase of T. Then the T, c phase diagram has
the form shown in the figure below, i.e. the poor
solvent region corresponds to .
Such situation is called lower critical solution
temperature (LCST)-critical point is on the
bottom of the phase separation region.
T
c
Examples poly(oxyethylene) in water,
methylcellulose in water, in general - most of
the water-based solutions. The reason increase
of the so-called hydrophobic interactions with
the temperature (organic polymers contaminate
network of hydrogen in water and water molecules
become less mobile (solvated), i.e. they lose
entropy - this unfavorable entropic factor for
polymer- water contacts is more important at high
temperatures).
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• Suppose that the polymer with UCST is glassy
  without solvent in this range of temperatures.
  Then the situation is similar to that shown in
  the figure below

Upon the temperature jump to the region of
macroscopic phase separation, the separation
begins, but it cannot be completed, because of
the formation of the glassy nuclei which freeze
the system. As a result, microporous system is
formed, and this is one of the methods of
preparation of microporous chromatogra-phic
columns.