Fluctuating Entanglements in Single-Chain Mean-Field Models

Abstract

We consider four criteria of acceptability for single-chain mean-field entangled polymer models: consistency with a multi-chain level of description, consistency with nonequilibrium thermodynamics, consistency with the stress-optic rule, and self-consistency between Green–Kubo predictions and linear viscoelastic predictions for infinitesimally driven systems. Each of these topics has been considered independently elsewhere. However, we are aware of no molecular entanglement model that satisfies all four criteria simultaneously. Here we show that an idea from Ronca and Allegra, generalized to arbitrary flows, can be implemented in a slip-link model to create a model that does satisfy all four criteria. Aside from the direct benefits of agreement, the result modifies the relation between the initial relaxation modulus G(0) and the entanglement molecular weight Me. If this implementation is correct, current estimates for Me would require modification that brings their values more in line with estimates based on topological analysis of molecular dynamics simulations.