Chemistry Reference
In-Depth Information
and block copolymers of different architecture; the phase equilibria encompass
liquid/gas, liquid/liquid and liquid/solid. The only aspects that are excluded are the
coexistence of three liquid phases and the demixing of mixed solvent.
This theoretical section is followed (Sect.
3
) by a recap of the measuring
techniques used for the determination of the thermodynamic properties discussed
here. The subsequent main part of the article (Sect.
4
) outlines the modeling of
experimental observations and investigates the predictive power of the extended
Flory Huggins theory. Throughout this contribution, particular attention is paid to
phenomena that cannot be rationalized on the basis of the original Flory Huggins
theory, like anomalous influences of molar mass on thermodynamic properties or
the existence of two critical points (liquid/liquid phase separation) for binary
systems. In fact, it was the literature reports on such experimental findings that
have prompted the present theoretical considerations.
2 Extension of the Flory-Huggins Theory
2.1 Binary Systems
2.1.1 Polymer Solutions
Organic Solvents/Linear Homopolymers
The basis for a better understanding of the particularities of polymer-containing
mixtures as compared with mixtures of low molecular weight compounds was laid
more than half a century ago [
13 17
], in the form of the well-known Flory Huggins
interaction equation. By contrast to the form used for low molecular wei
gh
t
mixtures, this relation is usually not stated in terms of the
molar
Gibbs energy
G
;
for polymer-containing systems one chooses one mole of segments as the basis (in
order to keep the amount of matter under consideration
of
the same order of
magnitude) and introduces the
segment molar
Gibbs energy
G
. For polymer solu-
tions, where the molar volume of the solvent normally defines the size of a segment,
this relation reads:
D
G
RT
¼
Þ
N
ln
ð
1
'
Þ
ln 1
ð
'
' þ
g
'
ð
1
'
Þ
(1)
D
G
stands for the segment molar Gibbs energy of mixing. The number
N
of
segments that form the polymer is calculated by dividing the molar volume of the
macromolecule by the molar volume of the solvent. The composition variable
,
representing the segment molar fraction of the polymer, is in most cases approxi-
mated by its volume fraction (neglecting nonzero volumes of mixing), and
g
stands
for the integral Flory Huggins interaction parameter. In the case of polymer
'
