Shear Banding in Simulations of Polymer Melts

TL;DR

This study compares polymer shear flow simulations with a coupled tube-entanglement model, predicting shear banding based on entanglement number and CCR parameter, with semi-quantitative agreement.

Contribution

It introduces a model linking Rolie-Poly dynamics to entanglement effects, predicting shear banding in polymers with high entanglement numbers.

Findings

Model predicts shear banding when entanglement number exceeds critical value.

Simulations semi-quantitatively agree with the model predictions.

Deviations are due to model approximations and limitations of tube models.

Abstract

Results from numerical simulations of polymers under shear flow are compared with predictions for shear banding based on a model coupling Rolie-Poly-like tube dynamics to the entanglement dynamics mediated by Convected Constraint Release (CCR). CCR is controlled by a parameter $\beta$, whose dependence on the bending stiffness $k_{\theta}$ is calculated from the simulations. The model predicts shear banding for polymers whose equilibrium entanglement number $Z$ exceeds a critical value $Z_{c}$ that depends on $\beta$. The simulations are in semi-quantitative agreement with the model, with deviations that are attributed to approximations inherent in the model, and the inadequacy of tube models to describe partially-disentangled liquids in strong flow. These results may help determine which physical polymers could undergo shear banding.