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 Ree​ and entanglement density Z is observed at
homogeneous flow before the onset of shear banding and at shear banding state,
where Ree​∼[ln(Wi0.87​)−ξ0​]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 Vd​ and
Weissenberg number Wi​ as Vd​∼Wi0.87​ 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