Flow-deformed conformations of entangled polymers as persistent random walks

TL;DR

This paper develops a two-scale model to analyze the conformations of entangled polymers under flow, linking chain-level statistics with Kuhn-scale behavior using persistent random walks and a self-consistent potential.

Contribution

It introduces a novel two-scale/two-mode model that combines persistent random walks with a self-consistent potential to study entangled polymer conformations under flow.

Findings

The model accurately predicts chain conformation statistics under various flow conditions.

Self-consistent potentials modify strand conformations, affecting polymer rheology.

The approach enables detailed analysis of Kuhn-scale structure in entangled polymers.

Abstract

Evolving structure and rheology across Kuhn scale interfaces in entangled polymer fluids under flow play a prominent role in processing of manufactured plastics, and have numerous other applications. Quantitative tracking of chain conformation statistics on the Kuhn scale is essential for developing computational models of such phenomena. For this purpose, we formulate here a two-scale/two-mode model of entangled polymer chains under flow. Each chain is partitioned by successive entanglements into strands that are in one of two modes: entangled or dangling. On the strand scale, conformation statistics of ideal (non-interacting) strands follows a differential evolution equation for the second moment of its end-to-end distance. The latter regulates persistent random walks sampling conformation statistics of ideal entangled strands on the Kuhn scale, as follows from a generalized Green-Kubo relation and the Maximum Entropy Principle. We test it numerically for a range of deformation rates at the start-up of simple elongational and shear flows. A self-consistent potential, representing segmental interactions, modifies strand conformation statistics on the Kuhn scale, as it renormalizes the parameters controlling the persistent random walk. The generalized Green-Kubo relation is then inverted to determine how the second moment of the strand end-to-end distance is changed by the self-consistent potential. This allows us to devise a two-scale propagation scheme for the statistical weights of subchains of the entangled chain. The latter is used to calculate local volume fractions for each chemical type of Kuhn segments in entangled chains, thus determining the self-consistent potential.