Kinetic Network Model for Nonlinear Viscoelastic Properties of Entangled Monodisperse Polymers. I. Steady‐State Flow

Abstract

A molecular network theory is proposed to predict the nonlinear flow properties of entangled monodisperse polymers. The rate dependence of the viscosity and normal stress coefficients is attributed to the decrease in entanglement density with increasing shear rate. The probability for the existence of entanglements at a given shear rate is determined by equating the rates of two competing processes, i.e., entanglement creation and disengagement, which in steady flow are in a state of dynamic equilibrium. The entanglement creation process is driven by thermal diffusion and is assumed to be independent of shear rate. The entanglement loss process is caused primarily by the imposed shear and is assumed to be proportional to the shear rate to a power a, a parameter that accounts for the elasticity of the medium. The final equations are algebraically simple and can be easily adapted to most engineering calculations. The theory shows excellent agreement with experimental data on both melts and concentrated solutions.