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 intimately accompanied by the entanglement heterogeneity. Interestingly, the same linear relationship between the end-to-end distance Ree and entanglement density Z is observed at homogeneous flow before the onset of shear banding and at the shear banding state, where Ree ∼ ln(Wi0.87)-ξ0Z is proposed as the criterion to describe the dynamic force balance of the molecular chain in flow with a high rate. Deviating from this relation leads to a force imbalance and results in the emergence of shear banding. We establish a scaling relation between the disentanglement rate Vd and the Weissenberg number Wi as Vd∼Wi0.87 for stable flow in homogeneous shear and shear banding states. The formation of shear banding prevents chains 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.