Chemistry Reference
In-Depth Information
because of the large surface of water as compared with that of the polymer segment,
making large g values and hence also large n values plausible [cf. (
24
)]. In view of
the pronounced chemical dissimilarities of water and PVME, this should lead to
large a values.
The phase diagram shown in Fig.
16
was calculated [
53
] choosing a combination
of a and n values inside the range of multiple critical points. For this modeling it
was (unrealistically but for the sake of simplicity) assumed that only a depends on
temperature and that this dependence can be formulated as:
¼
a
1
þ
a
2
T
ð
T
s
Þ
a
(64)
where a
1
, a
2
, and
T
s
are constants. From this graph it is clear that the central features
of the phase diagram observed for the water/PVME system can be adequately
modeled by the present approach.
An interesting result of the present modeling is an uncommon option to realize
theta conditions. Maintaining its definition in terms of
A
2
¼
0, leading to w
o
¼
0.5:
1
2
¼
w
o
;
y
¼
a
y
ðÞ
y
zl
(65)
it is obvious that this relation cannot only be fulfilled in the normal way, with z
y
¼
0
and a
y
0.5. For such
exceptional systems, the unperturbed state results from an exact compensation of an
uncommonly unfavorable contact formation between the components (a
¼
1
=
2, but also via an adequate combination of a and zl
6¼
>
0.5) by
an extraordinarily advantageous conformational response (zl
0). In the case of
H
2
O/PVME, the plausibility of large a values has already been mentioned. From
reports [
56
] on the formation of a complex between water and PVME and the fact
that the system exhibits LCST behavior, one can infer that large z values are caused
by the very favorable heat effects associated with that process.
340
Fig. 16 Spinodal area
calculated [
53
] according to
(
33
) and (
64
) for an
exothermal model system by
means of the parameters
listed. The
horizontal line
indicates the theta
temperature (w
o
0.5);
circle
normal critical point,
closed
square
stable anomalous
critical point,
open square
unstable anomalous critical
point
330
320
N
P
=1000
a
1
a
2
= 0.03 K
-1
= 2.9
T
s
= 300 K
n
= 0.40
zl
= 2.5
310
Q
0.0
0.2
0.4
0.6
0.8
1.0
j
