A Force-Level Theory of the Rheology of Entangled Rod and Chain Polymer Liquids. I. Tube Deformation, Microscopic Yielding and the Nonlinear Elastic Limit

TL;DR

This paper develops a force-level theoretical framework to understand the nonlinear rheology of entangled rod and chain polymers, predicting how deformation affects tube confinement and the conditions for microscopic yielding.

Contribution

It introduces a first principles approach to model anharmonic tube deformation and predicts the effects of shear and extension on polymer entanglement stability in different relaxation regimes.

Findings

Deformation induces tube dilation or compression depending on chain relaxation state.

A finite maximum entanglement force localizes polymers in effective tubes.

Microscopic absolute yielding occurs at stresses around the shear modulus for relaxed chains.

Abstract

We employ a first principles, force-level approach to self-consistently construct the anharmonic tube confinement field for entangled fluids of rigid needles and for primitive-path (PP) level chains in two limiting situations where chain stretching is assumed to either completely relax or remain unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a Gaussian analysis of transverse polymer dynamical fluctuations predicts that deformation-induced orientation leads to tube dilation. In contrast, for deformed polymers in which chain stretch does not relax we find tube compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome (a force imbalance) by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance is found to occur at a stress of order the equilibrium shear modulus and thus a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.