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(liquid/gas equilibrium), matches the observed swelling behavior (liquid/liquid
equilibrium) reasonably well. Above all, it correctly models the observed
diminution
of the two-phase region with rising molar mass of the cellulose. The lack of
quantitative agreement should not be overestimated because of the sensitivity of
the calculated swelling with respect to the exact value of the central parameter a;a
reduction of a by less than 3% would suffice for quantitative matching.
In an attempt to rationalize this unique behavior, we recall that the w
o
values of
the present system are about ten times larger than normal, which means that the
tendency to form dilute solutions is practically nil. When adding increasing
amounts of water to pure cellulose, the extent of chain overlap (stabilizing the
homogenous state) will surpass a critical value below which a cellulose molecule
can no longer evade the formation of extremely adverse contacts between its
segments and water. At this point, the segregation of a second phase consisting of
practically pure water sets in. From simple considerations concerning the chain-
length dependence of the size of polymer coils, one can conclude that this critical
overlap will be reached at higher dilution by larger molecular weight samples than
by smaller molecular weight samples, thus explaining the anomalous swelling
behavior of cellulose in water.
The last two examples have dealt with systems for which the first step is
uncommonly unfavorable and goes along with a favorable second step. For the
mixtures described in the next section, the opposite is the case: here a very
favorable first step is followed by a correspondingly adverse second step.
Aqueous Solutions of Pullulan and Dextran
These systems exhibit a common feature, which becomes noticeable in the primary
data, i.e., in the composition dependence of the vapor pressures. Unlike normal
polymer solutions,
p
(
) shows a point of inflection in the region of high polymer
contents, as demonstrated in Fig.
19
. This peculiarity and the necessity to introduce
an additional term in the expression for the integral interaction parameter
g
[cf.
(
42
)] is interpreted in terms of hydrogen bonds between the monomer units of the
polymer, on one hand, and between water and the monomers, on the other hand.
The opening of intersegmental contacts a prerequisite for the dilution of t
he
mixture is Gibbs energetically adverse and modeled in terms of positive
o
parameters. The subsequent insertion of solvent molecules between these polymer
segments is, in contrast, very favorable and quantified by negative a values. The
reason why the total contribution of the first step of dilution cannot be modeled by a
single common parameter lies in the different composition dependencies of the
effects of opening and of insertion.
According to the details of the dilution process discussed above, the point of
inflection in the vapor pressure curve shown in Fig.
19
can be given an illustrative
meaning: In the region of low polymer concentration it is practically only “bulk”
water that it transferred into the vapor phase. This situation changes, however, as
'
'
approaches unity; under these conditions the vapor is increasingly made up of
solvent molecules taken from the “bound” water (located between two polymer
