Shear Banding in Entangled Polymers: Stress Plateau, Banding Location, and Lever Rule

Using molecular dynamics simulation, we study shear banding of entangled polymer melts under a steady shear. The steady shear stress vs shear rate curve exhibits a plateau spanning nearly two decades of shear rates in which shear banding is observed, and the steady shear stress remains unchanged after switching the shear rates halfway in the range of shear rates within the plateau region. In addition, we find strong correlation in the location of the shear bands between different shear rates starting from the same microstate configurations at equilibrium, which suggests the importance of the inherent structural heterogeneity in the entangled polymer network for shear banding. Furthermore, for the steady shear bands persisting to the longest simulated time of 9.0τ d0 (disengagement time), the shear rate in the slow band and the relative proportion of the bands do not change very much with the increase of imposed shear rate, but the shear rate in the fast band increases approximately in proportion to the imposed shear rates, in contradiction to the lever rule.