Nonlinear rheology of highly entangled polymer liquids: Step shear damping function

Abstract

Nonlinear step shear relaxation moduli G(t,γ)=σ(t,γ)/γ in a series of entangled polystyrene/diethylphthalate solutions are studied using mechanical rheometry and birefringence polarimetry measurements. We pose the question: Is the step shear damping function h(γ)=G(t,γ)/G(t) universal for fluids in the class entangled liquids? The experimental results provide a clear answer in the negative, and in fact show that the damping functions in entangled polymer liquids continuously vary with polymer molecular weight and concentration. In weak to moderately entangled solutions, N/Ne=Mw¯φ1.3/Me0⩽11, experimental h(γ) results are in accord with the Doi–Edwards theoretical prediction, hDE-IA (type A damping). At higher entanglement densities, however, damping functions become progressively softer than hDE-IA, particularly at low strains (type C damping). The transition from type A to type C damping behavior is accompanied by the appearance of a complex time-dependent crossing pattern in experimental G(t,γ)h(γ)−1 plots at variable shear strain. Using a simple tube model analysis, we show that both experimental observations can be explained in terms of coupled relaxation of polymer segment orientation and tube equilibration following step shear.