Shear banding in monodisperse polymer melt

We performed a series of molecular dynamics simulations on monodisperse polymer melts to investigate the formation of shear banding. Under high shear rates, shear banding occurs, which is accompanied with the entanglement heterogeneity intimately. Interestingly, the same linear relationship between the end-to-end distance $R_{ee}$ and entanglement density $Z$ is observed at homogeneous flow before the onset of shear banding and at shear banding state, where $R_{ee} \sim [ln(W_i^{0.87})- \xi_0]Z$ is proposed as the criterion to describe the dynamic force balance of molecular chain in flow with a high rate. We establish a scaling relation between the disentanglement rate $V_d$ and Weissenberg number $W_i$ as $V_d \sim W_i^{0.87}$ for stable flow in homogeneous shear and shear banding states. Deviating from this relation leads to force imbalance and results in the emergence of shear banding. The formation of shear banding prevents chain from further stretching and disentanglement. The transition from homogeneous shear to shear banding partially dissipates the increased free energy from shear and reduces the free energy of the system.