Force-Based Theory of the Shear Rheology of Entangled Polymer Melts

We qualitatively extend the reptation-tube theory for the stress-strain curve and chain stretch dynamics under continuous startup shear deformation. New theoretical aspects include a dynamic tension blob scaling model for predicting the interchain grip force that causes stretching, a delayed onset of chain retraction, a distribution of entanglement spacings and grip loss strains, and shear-rate-dependent accelerated stretch relaxation for fast deformations (Rouse Wi_R>1). The convective constraint release idea is modified to be consistent with delayed retraction guided by the physical idea the overshoot is an elastic-viscous crossover. Calculations are performed for the stress-strain response, chain stretch dynamics, and orientational stress and relaxation time. For Wi_R>1, qualitatively different results are predicted compared to existing tube models for the shear rate dependence of the overshoot stress and strain, degree of chain stretch at the overshoot and in the steady state, and the long time stress. Connections between nonlinear dynamics at the overshoot and in the steady state suggest common underlying physics. Very good agreement is found between theory and experiments and simulations.