Improving the functionality of non-stretching approximations

TL;DR

This paper enhances non-stretching approximations for entangled polymers by deriving systematic asymptotic models that incorporate effects like finite chain stretching, flow-induced disentanglement, and scission, improving rheological predictions.

Contribution

It introduces generalized non-stretching models using asymptotic methods, extending the Rolie Poly model to include finite stretch effects and other physical phenomena.

Findings

Non-stretching models accurately approximate entangled polymer rheology.

Asymptotic derivations improve model accuracy and flexibility.

Models show excellent agreement with detailed constitutive equations.

Abstract

Entangled polymers are an important class of materials for their toughness, processability, and functionalizability. However, physically detailed modeling of highly entangled polymers can prove challenging, especially as one considers additional layers of physical or chemical complexity. To address these challenges, we present a series of generalizations for the useful "non-stretching" approximation, using asymptotic methods to formalize and expand the analysis. First, we rederive the popular non-stretching Rolie Poly model and extend it second order, reintroducing effects from finite chain stretching. Then, we extended the non-stretching framework to other special cases, accounting for flow-induced disentanglement, polydispersity, and reversible scission reactions. Benchmark calculations confirm that non-stretching models derived via systematic asymptotic methods provide excellent and improvable approximations for the rheology of well-entangled polymer constitutive equations with finite-time stretch relaxation dynamics.