The sol–gel transition - Physical Gels from Biological and Synthetic Polymers - page 83

6

PDMS Gel point

t t c ~

+6

t - t c (min)

+2

-2

-6

4

t - t c A

2

-6 +2

-2 +1

0
+2

0

-1

+6 -2

0

0 5

ω a T

A + log

[rad s -1 ]

Reduced storage moduli for PDMS samples for which the reaction has been stopped at intermediate
states of conversion. t c is the instant of intersection of G 0 and G 00 . Curves are shifted horizontally to
avoid overlapping. Reproduced from Winter and Chambon ( 1986 ) with permission of the
American Institute of Physics for The Society of Rheology.

Figure 3.8

3.5.2 Experimental determination by the Winter - Chambon criteria

Nowadays it is accepted that rheological experiments are those most commonly
employed in both chemical and physical gelation studies. It is frustrating, however, to
appreciate that the most dif

cult task is understanding the evolution of viscosity or
elasticity with respect to the relevant cross-linking parameter, even for the case of
' flexible chains. Nor are dynamic

measurements of the whole spectrum of the sample easy to perform. However, this
approach, due to Winter and Chambon, has become much more familiar to scientists
working on gelation, and their criteria are considered by many a useful method of
determining when gelation occurs.
By stopping the chemical reaction of an end-linked PDMS reaction, Winter and
Chambon ( 1986 ) were able to measure the frequency spectrum over a very large region
(

point-like ' , randomly distributed cross-links between

(five orders of magnitude), as can be seen in Figure 3.8 . Within a window of time around
the point t reac = t c there is a full superposition of G 0 and G 00 spectra over the whole frequency
domain, and very shortly after, at t c + 2 min, G 0 exhibits a plateau at the lowest frequency
domain, related to a

finite relaxed modulus G eq . Within the accuracy of the experiments, the

de nition of the gelation point, whether from the power-law dependence of the spectra of

G 0 and G 00 using the Winter

Chambon criteria or using percolation theory and exploring
the low-frequency limit, seems to converge towards the same gelation time. Since this

-

rst

publication, the frequency power-law criteria for the moduli have been used to de ne the

connectivity transition in a number of cross-linking processes of polymer systems in
solution, and the formation of an in nite network has been assumed to correspond to the

-

Winter nition. These criteria have been applied, with varying success, in

processes of physical gelation, chemical gelation and inorganic gel formation.

Chambon de