Random walk model for viscoelastic response of glassy polymers

Abstract

Both theory and experiment suggest that reptation plays a minor role in the viscoelastic response of polymers in the glassy state. The time for reptation is so long that the entanglement network can be considered to be permanent, at least for deformation far below T g. We have developed a network picture of a glassy polymer in which mechanical stresses and strains in the solid are represented in terms of forces and displacement in a harmonic lattice with nearest-neighbor interactions. The intermittent character of segmental motion in the glassy state is modelled in terms of the behavior of a two-state continuous time random walk, one state of which refers to mobilized segments and the second to immobilized segments. The pausing time density for segments in an immobilized state is taken to be negative exponential, and for mobile segments it has an asymptotic stable law form ψ( t)∼ t -( α+1) , where 0<α<1. We show that the quantity needed to calculate the mechanical response of the network is a fourth-order correlation function which is readily found for a harmonic model. A comparison of the theoretical prediction will be made to experimental data on stress relaxation and recovery of glassy polycarbonate.