Chemistry Reference
In-Depth Information
As postulated by (
31
), the molecular weight dependence of
A
2
should not be
represented in double logarithmic plots, but as a function of
M
(1
a
)
, where
a
is the
exponent of the Kuhn Mark Houwink relation. In contrast to the customary evalu-
ation (in double logarithmic plots), this procedure does not in the general case lead
to zero
A
2
values; in most cases they are very small but, outside experimental
errors, different from zero.
The following example of the composition dependence of the Flory Huggins
interaction parameter pertains to the system cyclohexane/poly(vinyl methyl ether)
(CH/PVME) [
23
]. Except for w
o
,
obtained via osmometry, all data stem from vapor
pressure measurements [
40
]. This system does not fit into the normal scheme
because CH is a good solvent for PVME, despite uncommonly large w
o
values of
the order of 0.5. For good solvents, w
o
is usually considerable less than 0.5; for theta
solvents, w
o
is typically equal to 0.5 and it increases upon the approach of phase
separation. The curves combining the data points in Fig.
3
were calculated by
adjusting the parameters of (
32
). Within the scope of the present approach, the high
solvent quality results from fact that the w values decrease considerably as
'
increases so that they are favorable within the range of moderate polymer concen-
trations, where the system becomes very susceptible to phase separation.
The minima of w(
) shown in Fig.
3
represent a consequence of the dissimilar
contributions of the dilution in two steps, as demonstrated in Fig.
4
. The first term,
quantifying the effects of contact formation, is Gibbs energetically very unfavor-
able and increases with rising polymer concentration because of the parameter n.
By contrast, the second term, standing for the contributions of the conformational
relaxation, is highly favorable and the more so, the larger
'
'
becomes. The observed
minimum in w(
) is caused by the fact that the first summand increases more than
linearly, whereas the second decreases linearly.
Figure
4
also documents the general observation that the contributions of the two
terms of (
32
) to the measured functions w(
'
) are markedly larger than w itself; this
situation is very similar to the build up of the Gibbs energy from enthalpy and
entropy contributions. However, it is not permissible to interpret these terms in this
'
35 °C
1.25
1.00
45
55
0.75
Fig. 3 Composition
dependence of Flory
Huggins interaction
parameter for the CH/PVME
system at the indicated
temperatures [
40
]; the curves
are calculated according to
(
32
).
PVME 28
indicates
that the
M
w
of the PVME
is 28 kg/mol
65
0.50
0.25
0.00
0.0
0.2
0.4
0.6
0.8
1.0
j
CH
PVME 28
