Molecular origins of higher harmonics in large-amplitude oscillatory shear flow: Shear stress response

Abstract

Recent work has focused on deepening our understanding of the molecular origins of the higher harmonics that arise in the shear stress response of polymeric liquids in large-amplitude oscillatory shear flow. For instance, these higher harmonics have been explained by just considering the orientation distribution of rigid dumbbells suspended in a Newtonian solvent. These dumbbells, when in dilute suspension, form the simplest relevant molecular model of polymer viscoelasticity, and this model specifically neglects interactions between the polymer molecules [R. B. Bird et al., “Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: Shear stress response,” J. Chem. Phys. 140, 074904 (2014)]. In this paper, we explore these interactions by examining the Curtiss-Bird model, a kinetic molecular theory designed specifically to account for the restricted motions that arise when polymer chains are concentrated, thus interacting and specifically, entangled. We begin our comparison using a heretofore ignored explicit analytical solution [X.-J. Fan and R. B. Bird, “A kinetic theory for polymer melts. VI. Calculation of additional material functions,” J. Non-Newtonian Fluid Mech. 15, 341 (1984)]. For concentrated systems, the chain motion transverse to the chain axis is more restricted than along the axis. This anisotropy is described by the link tension coefficient, ϵ, for which several special cases arise: ϵ = 0 corresponds to reptation, ϵ > 1/8 to rod-climbing, 1/5 ≤ ϵ ≤ 3/4 to reasonable predictions for shear-thinning in steady simple shear flow, and ϵ = 1 to the dilute solution without hydrodynamic interaction. In this paper, we examine the shapes of the shear stress versus shear rate loops for the special cases ϵ=0,1/8,3/8,1, and we compare these with those of rigid dumbbell and reptation model predictions.