Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 44

Glassy region

G '

Cross-over

Plateau region

G ”

Terminal zone

slope = 2

log ω

Figure 2.16 Mechanical spectrum of a polymer solution - viscoelastic liquid.

2.5.1.3 Frequency and strain dependence

Polymer solutions
The mechanical spectrum of a polymer solution (a viscoelastic liquid) has the general
form illustrated in Figure 2.16 (Ross-Murphy, 1994 ; Kavanagh and Ross-Murphy, 1998 ).
At low frequencies (note the double log scale) G 00 is greater than G 0 , but as the oscillatory
frequency increase, G 0

increases more rapidly than G 00

log
representation, compared to a slope of 1 for G 00 ), and at some frequency there is a cross-
over. After this, both G 0 and G 00 become much less frequency-dependent

(with a slope ~2 in the log -

- the so-called

' region.

Whether the cross-over region is reached in the frequency window of conventional
oscillatory measurements depends upon polymer concentration, relative molecular mass
(M) and chain

rubbery plateau '

flexibility. At the same time, the mechanical spectrum measured will be
essentially independent of the amount of shear strain, out to, say, 100% in

'
(i.e. a strain, in terms of the geometry of deformation, of unity). Rheologists may express
this by saying that the linear viscoelastic (LV) strain extends out to c.100%.

' strain units

Polymer gels
The mechanical spectrum of a viscoelastic solid will have a nite G 0 , with a value usually

50 times) that of G 00 at all frequencies, as in Figure 2.17 (Clark and
Ross-Murphy, 1987 ; te Nijenhuis, 1997 ). In this respect it shows some similarities with
the plateau region of the solution mentioned above; such a plateau is often referred to,
somewhat imprecisely, as gel-like, for exactly this reason.
The strain-dependent behaviour, for polymer gels is more dif

well above (say 5 -

cult to generalize,
although the LV strain is rarely as great as 100% (some gelatin gels may be the exception
here), and may be extremely low - say 0.1% or less. At values just greater than the LV