Contour-Variable Model of Constitutive Equations for Polymer Melts

TL;DR

This paper introduces a new contour-variable constitutive model for polymer melts that accounts for non-uniform chain stretch and non-Gaussian statistics, improving understanding of their rheological behavior under shear.

Contribution

It presents a novel model incorporating non-uniform segmental stretch and non-Gaussian chain statistics, advancing the modeling of entangled polymer dynamics.

Findings

Orientation and stretch depend strongly on the chain contour variable at high shear rates.

Including non-uniform features has minimal impact compared to uniform models on rheological predictions.

The model successfully describes steady shear and start-up flow behaviors.

Abstract

Based on a modified expression of the rate of the convective constraint release, we present a new contour-variable model of constitutive equations in which the non-uniform segmental stretch and the non-Gaussian chain statistical treatment of the single chain are considered to describe the polymer chain dynamics and the rheological behavior of an entangled system composed of linear polymer chains. The constitutive equations are solved numerically in the cases of steady shear and transient start-up of steady shear. The results indicate that the orientation and stretch, as well as the tube survival probability, have strong dependence on the chain contour variable, especially in the high-shear-rate region. However, the inclusion of the non-uniform features in the constitutive models has little modification comparing with the uniform models in determining the rheological properties both qualitatively and quantitatively.