Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 47

G '

η

G ”

G eq

Gelation time Gelation time

Time Time

(a) Time growth of equilibrium gel modulus. G eq rises very rapidly, even on a log scale, at or
just after the gelation time, before reaching a final asymptotic level. (b) Because of the finite
frequency effect and the contribution of non-ideal network assembly contributions, both G 0 and G 00
will tend to rise before the true gelation point.

Figure 2.18

commonly for frequencies greater than, say, 30 rad s − 1 . The measuring strain may also
have to be a compromise so suf cient signal can be detected pre-gel, but with sensitive

modern instruments this is less of a problem.

Gelation time measurement
There are a number of approaches to the determination of, say, gelation time, but rst we

consider the expected self-assembly time pro le. For the equilibrium gel modulus, the ideal

pro le is shown in Figure 2.18a . Initially there is no response, but then G eq rises very

rapidly, even on a log scale, at or just after the gelation time, before reaching a

final
asymptotic level. Such behaviour is a simple consequence of the positive-order kinetics of
self-assembly (cross-linking) and the requirement of a minimum number of cross-links per
' at the gel point. We note that some phenomenological models have neglected the

pre-gel behaviour and simply

chain '

tted the G eq (>0) versus t behaviour to an n-order kinetic

model. From the data- tting viewpoint this is quite acceptable, provided it is appreciated

that the underlying physics of self-assembly has been perverted.
The above scenario is, of course, complicated by the consideration that what is being
evaluated by the instrument is not G eq but G 0 and G 00 . Both of these are finite even for a

solution, although the respective moduli values may be very low. However, because of
the

finite frequency effect and the contribution of non-ideal network assembly contribu-
tions, both G 0 and G 00 will tend to rise before the true gelation point, and something akin
to Figure 2.18b is usually seen. The flattening off of G 00 is not something predicted from

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indeed some would expect a pronounced maximum in G 00 after gelation

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theory but

this is rarely observed for physical gels, except for some low-concentration gelatin
systems. This asymptotic level G 00 behaviour has been associated with the ' stiffness ' of