Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 48

the network strands. The gelation time can then be estimated from the cross-over of G 0
and G 00 (if seen, although this is not always the case), the time where there is a sudden
increase in G 0 or by back-extrapolation of the G 0 versus time curve. In practice the results
are not very different, as discussed elsewhere (Tobitani and Ross-Murphy, 1997 ).

2.5.1.7 Range of viscoelastic linearity

Yet another aspect of gel time measurement, and arguably one of greater signi

cance, is

the effect of finite strain on the tenuous mechanical system close to gelation (Ross-

Murphy, 2005 ). In performing the kinetic gelation experiment it is usual practice to
employ the smallest strain consistent with obtaining reliable data. In principle this can be
checked to be within the linear viscoelastic region both before and after gelation by
stopping the experiment and performing a so-called strain sweep. However, as we
discussed above, many experiments are performed using controlled-stress instruments
in their pseudo-controlled-strain mode, and such instruments do have more problems
measuring a gelling system when the properties are changing quite rapidly within the
oscillatory cycle, especially when using the

strain mode. This is because one
might expect that the linear viscoelastic strain of the gelling system, rather than being
constant, would tend to change during the gelation process, and would be a minimum just
at the gel point (Rodd et al., 2001 ).

' controlled '

2.5.1.8 Failure of the Cox Merz rule

In the introductory chapter a rheological de

-

nition of a gel as a viscoelastic solid
was given (Ferry, 1980 ). However, as this chapter makes clear, systems such as sur-
factant based ' shower gels ' fail the rst de nition. Many of these are what rheologists

refer to as ' structured liquids ' , although sometimes - misleadingly - these have been

called .

For many polymer solutions and almost all melts, the shear-rate dependence of
viscosity shows the expected

' weak gels '

behaviour, in which the viscosity becomes
increasingly shear-rate dependent at high deformation rates but at low enough rates is
constant (so-called Newtonian behaviour). For the same class of materials, the frequency
dependence of

' pseudoplastic '

η

* and the shear-rate dependence of

η are observed to be closely super-

imposable, when the same numerical values of ω and γ are compared. This empirical

correlation, often called the Cox Merz rule (Ferry, 1980 ), has been observed for many

solutions, but within the perspective of the present volume there are a number of
exceptions. In these cases, useful information may be extracted from the comparison of
(

-

les.
A number of these materials, particularly at low strains, have a gel-like frequency
spectrum but with very pronounced strain dependence. In this case, if subjected to a
steady (shear) deformation, they will apparently

η , γ ) and ( η

* ,

ω ) pro

flow rather than fracture. More signifi- -

- η ω

cantly, such systems do not obey the Cox Merz rule; in fact

* (

), measured in the small-

strain limit, tends to lie above ), except at high frequencies when the curves may

appear to converge (Richardson et al., 1987 ; Ross-Murphy et al., 1993 ). Such behaviour
is usually associated with a tendency to form aggregated structures or dispersions, which
are then broken down under the applied strain.

η ( γ