Chemistry Reference
In-Depth Information
(a) Parameters describing the feed polymer
(b) Parameters describing the selected solvent + nonsolvent system
(c) Parameters describing the operative conditions
The feed polymer can be characterized by a two-dimensional distribution func-
tion, (
15
)or(
16
). Typical values for parameters of these distribution functions are:
r
N
¼
100
k
¼
1
e
¼
0
:
25
y
W
¼
0
:
5
a
¼
b
¼
4
:
(57)
¼
b in (
16
) means that the distribution function with respect to the
chemical heterogeneity is symmetrical. The parameters describing the selected
solvent + nonsolvent system occur in the
G
E
model [i.e., (
5
)]. For the model
calculation, the following parameter were chosen:
Setting a
r
A
¼
1
w
AP
¼
150 K
p
A
¼
0
g
A
¼
0
:
5
r
B
¼
1
w
BP
¼
250 K
p
B
¼
0
g
B
¼
1
(58)
w
AB
¼
500 K
:
The low-molecular weight component A should act as solvent. The parameter
w
AP
is selected in a way that no demixing with the copolymer occur. The low
molecular weight component B takes over the role of the nonsolvent and, hence, the
parameter w
BP
leads to a miscibility gap with the polymer. The selected operative
conditions are:
X
F
01
Z
F
¼
0
:
¼
0
:
2
T
¼
350 K
:
(59)
The asymmetry of the distribution with respect to the chemical composition has
a large impact on the phase equilibria of copolymers [
6
]. First the influence of the
feed distribution (
16
), especially the symmetry, is studied. At constant mass-
average chemical composition, the maxima of the distribution according to the
chemical composition are shifted to higher values if the distribution become
unsymmetric (a
2). The distribution
W
(100,
y
) in the sol and gel
phases are plotted in Fig.
9
. The symmetry of the feed copolymer has a large impact
on the theoretical fractionation results. Caused by the shift of the maxima in the
feed distribution, the maxima in the fractions shift also to higher values. Moreover,
in the case of a symmetric feed distribution (solid lines in Fig.
9
) more polymer
molecules will be in the sol phase in comparison with an unsymmetric feed
distribution (broken lines in Fig.
9
). If a modified version of (
16
) is used, namely
ignoring the polydispersity with respect to the molecular weight, the ratio between
the amounts of sol and gel phases does not change if the parameter b is changed
from b
¼
4 and b
¼
2 (unsymmetrical case). This finding indi-
cates the complex interactions of both polydispersities.
¼
4 (symmetrical case) to b
¼
