Shear Banding in Simulations of Polymer Melts

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 $β$, whose dependence on the bending stiffness $k_θ$ 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 $β$. 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.