Chemistry Reference
In-Depth Information
These are interactions between the polymer molecule and the solvent, chain branching, conformational
factors arising from polarity, restricted rotation due to resonance, and the bulk of substituents.
The above, of course, assumes that the polymer molecules are fully separated from each other.
2.6.2 The Thermodynamics of Polymer Solutions
Solutions of polymers deviate to a great extent from Raoult's law, except at extreme dilution. In
extremely dilute solutions the ideal behavior is approached as an asymptotic limit. These deviations
arise largely from small entropies of mixing. That is mostly due to the large difference in size between
the solute and the solvent. The change in the
entropy of mixing
, according to
Flory-Huggins theory
of polymer solutions [
63
] is:
DS ¼kðN
1
ln
v
1
þ N
2
ln
v
2
Þ
where subscript 1 denotes the solvent and subscript 2 the solute.
v
1
and
v
2
are
volume fractions
. They
are defined as follows
v
1
¼ N
1
=ðN
1
þ xN
2
Þ
v
2
¼ xN
2
=ðN
1
þ xN
2
Þ
where
is the heat of mixing. The change in the heat content of mixing of polymer solutions is similar
to that of other solutions
x
DH ¼ x
1
kTN
1
v
2
where
x
1
characterizes the internal energy per solvent molecule. The change in free energy of mixing,
according to Flory-Huggins [
63
], is
DF ¼ kTðN
1
ln
v
1
þ N
2
ln
v
2
þ x
1
N
1
v
2
Þ
The Flory-Huggins treatment overlooks the fact that dilute solutions of polymers consist of domains
or clusters of polymeric chains that are separated by regions of pure solvent that is free from the solute.
Flory-Krigbaum
treatment assumes a model of dilute polymeric solutions where the polymeric
clusters are approximately spherical and their density reaches a maximum at their centers and decreases
in an approximately Gaussian function away from the center. The volume that is occupied by the
segments of each molecule excludes the volumes of all other molecules. Long range intramole-
cular interactions take place within such excluded volumes. The thermodynamic functions of such
interactions can be derived, such as the free energy change, the enthalpy change, and the entropy change:
DF
1
¼ kTðk
1
C
1
Þv
2
2
DH
1
¼ kTk
1
v
2
2
DS
1
¼ kC
1
v
2
2
where
C
is an entropy parameter and can be expressed as,
