Chemistry Reference
In-Depth Information
2
1
0
-1
-2
-2
-1
0
1
2
a
Fig. 22 Interrelation between the parameters zl and a [the
vertical line
at a 0.5 is drawn
according to (
34
)]. The data for solutions of several typical polymers in organic solvents are almost
exclusively located in the first quadrant (
open symbols
); they only extend into the third quadrant
for systems close to their demixing. Data for anomalous systems (
half closed symbols
), where the
first step of dilution represents the main driving force to homogeneity, are entirely located in the
third quadrant
particularly suited for modeling of interaction parameters on the basis of critical
conditions.
The modeling presented here still uses the expression for the integral interaction
parameter as formulated for polymer
solutions
(
26
), which leads to the critical
conditions specified in (
36
) and (
37
). According to the extension of the approach to
polymer
blends
(which had not yet been carried out when this study was per-
formed), (
49
) should have been used for that purpose because it accounts for the
fact that the polymer coils A are accessible to the segments of polymer B and vice
versa. Both expressions employ a linear dependence of the parameter z on the
composition of the mixture; the differences between polymer solution and polymer
blends only lie in the numerical values of the constants.
Figure
23
shows how the molar masses of the blend components influence the
experimentally obtained critical compositions of the mixture. The two curves
shown in this graph were obtained by adjusting five parameters, namely n and l
(which were considered to be temperature independent), plus two parameters for
the temperature dependence of a. The fifth parameter concerns z, which was either
kept constant (variant 1) or set proportional to a (variant 2). Both assumptions
model the experimental data with comparable accuracy. In view of the expectation
that all system-specific parameters should depend on temperature, the quality of the
description with only five parameter is surprising. It must, however, be kept in mind
that a naive molecular interpretation of the system-specific parameters is not
permissible in the present case.
Despite the similarity of the two variants of modeling presented in Fig.
23,
the detailed phase diagrams calculated from the two sets of parameters differ
