A full-chain tube-based constitutive model for living linear polymers

TL;DR

This paper introduces a comprehensive full-chain constitutive model for living linear polymers, incorporating population balances and stress relaxation processes, including novel insights into fast chain breaking dynamics.

Contribution

It develops a new full-chain model integrating population balances and stress relaxation, especially addressing fast chain breaking regimes and nonlinear dynamics.

Findings

Reproduces known stress relaxation results with corrections.

Provides new nonlinear stress relaxation predictions.

Validates the model with rheology data.

Abstract

We present a new strategy for introducing population balances into full-chain constitutive models of living polymers with linear chain architectures. We provide equations to describe a range of stress relaxation processes covering both unentangled systems (Rouse-like motion) and well entangled systems (reptation, contour length fluctuations, chain retraction, and constraint release). Special attention is given to the solutions that emerge when the 'breaking time' of the chain becomes fast compared to various stress relaxation processes. In these 'fast breaking' limits, we reproduce previously known results (with some corrections) and also present new results for nonlinear stress relaxation dynamics. Our analysis culminates with a fully developed constitutive model for the fast breaking regime in which stress relaxation is dominated by contour length fluctuations. Linear and nonlinear rheology predictions of the model are presented and discussed.