The sol–gel transition - Physical Gels from Biological and Synthetic Polymers - page 80

3.5 Experimental investigations of gelation transitions

3.5.1 Percolation exponents

A large number of experimental investigations have been devoted solely to exploration of
the vicinity of the gel point, in order to examine if either the classical or the percolation
model is valid. As we have already hinted, experimental dif culties and the potential

differences between behaviours of various chemical systems make the exercise delicate.
For example, Patton and co-workers (Patton et al., 1989 ) investigated the bulk
condensation polymerization of a neopentyl glycol-dimethyl terephthalate based poly-
ester to probe the applicability of the scaling approach. They applied an effective
quenching of the reactions which allowed the time evolution of the molecular mass
distribution and other parameters below the gel point to be determined during the
chemical reaction. The samples were diluted and characterized by dynamic and static
light scattering and intrinsic viscosity measurements. The authors were able to evaluate
several critical exponents, through various combinations of their experimental data. They

first established the correlation between M w and the extent of reaction p and found
( Tables 3.2 and 3.3 ) the exponent

= 1.8 ± 0.3, in good agreement with the d =3
percolation prediction. The relation between the radius of gyration R g and molecular
mass M w of the branched molecules, or between intrinsic viscosity

γ

and M w , are
predicted to follow power laws and this is indeed what the authors found, the exper-
imentally determined exponents being much closer to critical percolation than to classical
theory. Interestingly, the scaling relationships also applied experimentally over a broader
range of extent of the reaction than was expected.
Colby and co-workers (Colby et al., 1992 ) continued the analysis beyond the gel point,
for the same reaction. Samples were separated into a sol and a gel fraction, the sol being
constituted by the clusters which are not yet connected to the gel network. The models
predict a scaling law between the gel fraction and the average molecular mass M w of the
independent clusters. The swelling ratio of the gel is also expected to vary with the gel
fraction: near the threshold p > p c , swelling is very important, but it decreases rapidly
when the reaction proceeds towards a totally cross-linked network (p = 1). These very
careful investigations established that the measured exponents were intermediate
between percolation and classical theories, but also suggest that the distance to the gel
point was not close enough and measurements exhibited a crossover between the two
limiting theories. Indeed measurements do not appear to have been made within the
Ginzburg region, as delineated above. Moreover, the chemical system employed in the
two studies can be criticized since, compared for example with the BTA

η

-

DMG system

( Section 3.1 ), it is potentially much more susceptible to cyclization, ' wastage ' and other

non-idealities (Stepto, 1998 ).
Following this work, the same group (Lusignan et al., 1995 ) re-examined this point
and designed a system with a very low degree of polymerization between cross-links, in
an attempt to approach the ideal percolation case, and the Ginzburg limit. They per-
formed similar experiments in an attempt to determine the relation between scaling