Polymer Physics

This parameter has been called Flory-Huggins interaction parameter. Therefore,

DUm¼kTwN 1 f 2 (8.21)

With the assumption of incompressible mixing in the lattice space, the mixing heat
corresponds to the mixing enthalpy, and the Helmhotz free energy is equivalent to the
Gibbs free energy.
Merging the mixing entropy and the mixing heat into the mixing free energy, one
can obtain

DFm

NkT

¼f 1 lnf 1 þ

f 2

r

lnf 2 þwf 1 f 2 (8.22)

This equation is the well-knownFlory-Huggins Equation. The power of a theory
is reflected by its capability for further applications in various situations. In the next
section, we will introduce how the assumptions of Flory-Huggins theory can be
amended for its broad applications.

8.3 Developments of Flory-Huggins Theory

8.3.1 Simple Additions

8.3.1.1 Polydisperse Polymer Solutions

The mixing free energy can be linearly integrated by the contributions according to
the volume fraction of polymers with each molecular weight, i.e.

DFm

kT

¼N 1 lnf 1 þ

X

i> 1

NilnfiþwN 1

X

i> 1

fi (8.23)

8.3.1.2 Binary Blends

The binary blends are the mixture of two species of polymers. In the mixing free
energy, the term for small solvent molecules can be substituted by the term
for another specie of polymers with chain lengthr 1 (Scott 1949 ; Tompa 1949 ), as
given by

DFm

NkT

¼

f 1

r 1

lnf 1 þ

f 2

r 2

lnf 2 þwf 1 f 2 (8.24)

156 8 Statistical Thermodynamics of Polymer Solutions