General properties of polymer networks - Physical Gels from Biological and Synthetic Polymers - page 107

swelling parameters, it can be more useful to consider swelling in terms of its overall
degree. For example, in many experiments what is actually determined is the mass m of
swollen gel relative to the mass m 0 of the initial un-swollen system, and the swelling ratio
q is simply m/m 0 . Depending on the speci c assumptions, a double logarithmic plot of

the modulus of the gel against the degree of swelling should have a slope of

1/3 for
an ideal Gaussian network. For chemical gels, however, any upward deviation from this
−

−

1/3 law at low swelling degrees can be interpreted in terms of constraints on the chain
motion becoming more signi

cant when the network volume fraction increases. For
physical gels, this becomes more complicated because the modulus has its own concen-
tration dependence, and the degree of swelling is nothing more than the reciprocal of the
volume fraction of gel in the network, i.e. effectively this concentration dependence.
Finally, we comment that the simple separability of the retractive and swelling force
terms is still a controversial topic. We will not discuss this further, but merely reiterate
that we have used this simple form of the swelling equations for the purpose of clarity.

4.3.1 Discontinuous swelling

The explanation of the swelling and de-swelling of polymer gels given above was
accepted until about 20 years ago (and remains true in the majority of cases). However,
Tanaka and co-workers then reported the behaviour of partly hydrolysed PAm gels
(Tanaka, 1981 ; Osada and Ross-Murphy, 1993 ). In a mixed solvent of good (water)
and poor (acetone) thermodynamic quality these are weakly polyelectrolytic in nature.
As small amounts of acetone are added to a PAm gel, the gel de-swells. Moreover,
for certain samples corresponding to certain amounts of alkaline hydrolysis, the swelling
become discontinuous: there is a sudden de-swelling over a very narrow range of
acetone n-

ity and electrolyte contributions (introduced above) produce, instead of a continuous
temperature (or acetone

- water compositions. This occurs because the net elastic, polymer - solvent af

- water composition) swelling ' phase diagram ' , one which is

discontinuous.
The explanation based on polymer

- solvent af nity and electrolyte terms neglects

speci c Donnan contributions. However, the higher the ionic concentration outside the

membrane (gel), the lower the concentration difference of mobile ions between the two
sides of the membrane. The concentration of mobile ions depends upon the ionic
strength, the polymer concentration and the effect of (Manning) counterion condensation
( Chapter 5 ). For example, Moe and co-workers (Moe et al., 1993 ) have shown that the
contribution of the Donnan term to the swelling of polyelectrolyte gels is actually the
most signi

cant one, and can lead to very high degrees of swelling (and de-swelling).
Whichever factor causes the gel collapse in the acetone

water system, the consequen-
ces are profound, since changes in swelling can be induced by appropriate changes in
temperature, pH, applied voltage etc., depending upon the precise chemical composition
of the gel

-

-

solvent system. Figure 4.4 illustrates the simple case of continuous swelling,
and contrasts this with the case of discontinuous swelling.
As mentioned above, so-called thermoresponsive gels can be formed by copolymer-
izing acrylamide and NIPAm. That this can be done is not in dispute, but whether this