Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 45

G '

Equilibrium modulus slope ~ 0

G ”

log ω

Figure 2.17 Mechanical spectrum of a viscoelastic solid.

strain, G 0 and G 00 may show an apparent increase with strain. This is, of course, largely an
artefact of the experiment, since G 0 and G 00 are only de

ned within the LV region. This is
then followed by a dramatic decrease, caused by failure, either by rupture or fracture,
sometimes macroscopic - but more often failure occurs at the geometry interface.

2.5.1.4 Creep and stress relaxation

Although there are limitations to using a controlled-stress instrument in pseudo-controlled-
strain mode, such controlled-stress instruments are ideal for time domain experiments, in
which a small fixed stress is applied to a gelled sample and the strain ( ' creep ' )ismonitored

over time. In creep, the static compliance J is de ned as the ratio of strain to stress, and so is

simply the reciprocal of the ideal (or Hookean) elastic shear modulus G. For a viscoelastic
sample, however, the value of time-dependent compliance J(t), at the time given by t=1/

ω ,

is not simply equal to the reciprocal of dynamic modulus 1/|G * (

)|, although the two can be
related by appropriate transforms. However, it is just as useful to use the time domain
expression, and to evaluate J as a function of time as the sample

ω

.
The long-time behaviour of J(t) is particularly valuable, since it can help us to under-
stand the behaviour of physically cross-linked gels. As a rule of thumb, for times shorter
than, say, 100 s (corresponding radial frequency

' creeps '

6x10 - 2 rad s − 1 ) the
oscillatory strain experiment is the best, whereas for longer times (and for time stationary
systems) the creep experiment has advantages. The disadvantage in a long-time stress-
relaxation experiment is that the detectable stress signal decays to zero with time (rather
than increasing monotonically as does the strain in creep), and tends to disappear into the
zero-signal background of the rheometer.

ω >2 π /100 ≈

2.5.1.5 Temperature dependence

Many polymer gels show so-called behaviour at high enough frequencies or low

enough temperatures, and the study of gels under these conditions, perhaps induced by

' glassy '