Viscoelastic properties of physically crosslinked networks: Part 3. Time-dependent phenomena

Abstract

The initial value problem is solved for the transient network model of physically crosslinked gels. Stress relaxation following a sudden macrodeformation is calculated for several realistic models of the chain breakage rate β( r). It is shown that, on large time scales, stress decay obeys a power law when β( r) has significant r-dependence, the precise value of the power being dependent on the high stretching behaviour of β( r). For instance, the shear stress decays as ≈ t −5 n if β( r) is proportional to r n at high stretching. Although the Lodge-Meissner relation still holds, time-strain separability loses its physical background. Overshoot phenomena in shear and normal stress, which appear after steady flows are started at the initial equilibrium state, are also analyzed. It is found that the shear stress first shows a transient maximum, and then maxima of the first and second normal stress differences follow. Larger overshoot is expected for larger values of the shear rate γ, but the time at which the stress reaches its maximum is almost independent of γ The elongational stress is also obtained as a function of time.