Behavior at Very Long Times

In describing the mechanical response of gel networks at long times, it is necessary to distinguish between conditions where the cross-links are. stable and where they may be forming and dissociating during the period of the experiment. In the former case, the behavior may resemble that of permanently cross-linked networks as discussed in Section B4 of Chapter 14. The relaxation of stress beyond the pseudoequilibrium value, or the additional creep beyond the pseudoequilibrium compliance, is very slight, however. Some creep measurements have been fitted to an equation of the Andrade form, equation 28 of Chapter 13 (with infinite viscosity). 

on the other hand, cross-links are forming and dissociating while the measurements are in progress, phenomena similar to chemical stress relaxation (Section D of Chapter 14) may be encountered. The stress may drop nearly to zero in a stress relaxation process, whereas the shear modulus as measured in a moderately rapid 

Stress relaxation and reverse relaxation in a 5.9% aqueous gelatin gel at 20.2 . (For 

In such experiments, for a constant period of aging before the initial relaxation, the longer the period the initial relaxation the slower is the reverse relaxation the new bonds formed in the strained state have more time to anneal and develop resistance to dissociation. But when the period oi initial relaxation is kept constant and the period of aging preceding it is varied, a long aging period is followed by a rapid reverse relaxation. This is the result of 

In general, these results can he interpreted in terms of a complicated steady state of making and breaking of linkages, in which the longer a given linkage lasts without dissociation, the smaller its probability of dissociation becomes. 

---

Since it is the long-time behavior that is closely related to molecular structure, this is the information that is most interesting in the present context. For example, the zero-shear viscosity describes behavior in the limit of zero frequency and is very sensitive to molecular weight. However, for a material whose longest relaxation time is quite large, neither step-strain nor oscillatory shear experiments are useful to probe the behavior at very long times or very low frequencies. The main problem is that the stress is so small that it is not possible to measure it precisely. It is in this region that creep measurements are most useful. This is because it is possible to make a very precise measurement of a displacement, and it is also possible to apply a very small controlled stress. Controlled-torque (controlled-stress) rheometers are available from several manufacturers. 

---