The sol–gel transition - Physical Gels from Biological and Synthetic Polymers - page 94

second dif culty is establishing the mechanism of macromolecular self-assembly, with

respect to temperature, concentration variation or time, for instance. In this case there is
no way of diluting the samples to characterize the clusters. The characterization has to be
done in situ in the course of aggregation. For a kinetic process, the time is limited. When
examining changes in rheological properties, it is not possible to explore any window of
frequency; frequency has to be adapted to the time dependence of the gelation parameter,
which is supposed to remain constant during any one experimental run.
Rheological methods have become among the most important and widely used for
investigation of gelation processes. The use of the power-law criteria became very popular
on this type of systems, albeit over a limited range of frequencies. In many but not all cases,
these lead, at some

, to parallelism of G 0 and G 00 versus frequency in a double
logarithmic scale. However, many cases reported correspond to a de

' reaction time '

nition of the ' gel

where G 00 >G 0 over the whole range of frequencies investigated. Clearly, this point
should not be identi

point '

nite network; the next-
closest step (one more link added to the largest cluster) should indeed correspond to a
connected network, with an equilibrium modulus at low frequency. Sometimes this is the
case, but in other cases it seems that the medium is not close to reaching a permanent
modulus, and a larger concentration or a lower temperature must be used to step into the gel
solid-like phase. We shall discuss these points further in the next chapters.
Despite this, percolation models and the Winter

ed as the last step before formation of the in

-

Chambon criteria both seem to

converge towards the same de nition of the gel point, although how closely they agree

is still a matter for debate. Certainly the Winter

nition of the gel point is
open to criticism on a number of grounds: that it neglects the effect of topologically
'

- Chambon de

entanglements; that it assumes linear viscoelasticity even for extremely tenuous
physical gels when the linear viscoelastic strain may tend to zero at the gel point; that
systems are known that generate a Winter

trapped '

- Chambon type of mechanical spectrum even

though they are patently not gels.

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