A Particle Tracking Velocimetric Study of Stress Relaxation Behavior of Entangled Polystyrene Solutions after Stepwise Shear

Abstract

rheology 1−4 there have been numerous experimental studies performed to validate the model. The most well-known agreement between the theory and experiment in the nonlinear regime involves the stress relaxation behavior after stepwise shear. The tube model anticipates two-step relaxation dynamics for well-entangled polymers after a large step strain. Specifically, there would be a kink in the time dependence of the relaxing stress. 5 The sharp stress drop would occur quiescently around the Rouse relaxation time τR due to the chain retraction, which is assumed in the tube model to take place in a barrier-free manner. This ansatz of the tube model has the consequence that the chain orientation would relax on the time scale of reptation, decoupled from the fast dynamics associated with chain stretching. Thus, the structure of the tube model automatically insures that there would be time-strain separability, i.e., the relaxing stress would have the same time dependence beyond the Rouse time τR, independent of the magnitude of the applied step strain. In particular, the strain softening would take place, due to the assumed barrier-free chain retraction. In other words, the residual shear stress arises entirely from the surviving chain orientation σγ γ γ