Shear Banding in Polymer Melt Simulations Depends on Convective Constraint Release

Steady-state shear banding, in which a uniformly-sheared fluid becomes unstable and separates into layers at different shear rates, has been seen in a number of simulations of entangled polymer melts, dependent upon the length and stiffness of the polymers and the applied shear rate. We examine this behavior from a theoretical standpoint by considering nonmonotonic constitutive curves, one of the simplest instabilities which can lead to banding. We consider the constitutive curves predicted by a model coupling Rolie-Poly-like tube dynamics to the entanglement dynamics mediated by Convected Constraint Release (CCR), and find that the best predictors for non-monotonicity are large entanglement numbers $Z$, weak CCR, and strong anisotropy from a Giesekus-like term in the model related to the ratio of the normal stress differences. Comparing the resulting predictions to the presence or absence of banding in non-equilibrium MD simulations of bead-spring polymers, we find semi-quantitative agreement with the model. We also find substantially stronger CCR in more detailed united-atom polyethylene simulations than in any bead-spring simulations, which may account for the lack of banding in experimental melts.