A Constitutive Model for Entangled Polydisperse Linear Flexible Polymers with Entanglement Dynamics and a Configuration Dependent Friction Coefficient. Part II. Modeling Shear Modification Following Cessation of Fast Shear Flows

The polydisperse Mead-Park (MP) toy molecular constitutive model developed in Paper I [Mead et al., J. Rheol. 62, 121-134 (2017)] as well as our previously published work [e.g., J. Rheol. 59, 335-363 (2015)] is used in the forward direction to study model polydisperse melts of entangled linear flexible polymers in severe, fast shear flows. The properties of our new model are elucidated by way of numerical simulation of a representative model polydisperse polymer melt in step shear rate and interrupted shear flow. In particular, we demonstrate how the MP model simulates the individual molecular weight distribution (MWD) component dynamics as well as the bulk material properties. Additionally, we demonstrate that the polydisperse MP model predicts the phenomenon of shear modification for model MWD\u27s with a long, high molecular weight tail. Specifically, the terminal dynamic moduli following cessation of severe, disentangling deformation, are shown to slowly heal/recover on the orientational relaxation time scale of the longest chains in the MWD. This is the first molecular constitutive equation to predict the phenomenon of shear modification. We provide detailed insight into the molecular mechanism responsible for this previously enigmatic and important phenomenon. Additionally, the presence of shear modification is not necessarily associated with the presence of shear stress peak overshoot transients in interrupted shear flow. Specifically, we examine and analyze the interrupted shear experiments reported by Tsang and Dealy [J. Non-Newtonian Fluid Mech. 9, 203-222 (1981)] and demonstrate quantitatively their lack of a relationship to shear modification. We also demonstrate that the new MP model accurately predicts the Cox-Merz rule, Laun\u27s rule and Gleissele\u27s mirror relations in steady shear