Analytic Solution for the Linear Rheology of Living Polymers

TL;DR

This paper presents an analytic solution for the linear rheology of living polymers, specifically addressing the complexities beyond single relaxation time models, and offers a converging series solution that performs well in fast-breaking limits.

Contribution

The work introduces a novel analytic solution for the shuffling model of living polymers, improving understanding of their relaxation behavior beyond traditional numerical methods.

Findings

Analytic solution expressed as a converging infinite series.

Solution performs optimally in the fast-breaking limit.

Provides better interpretation of experimental data.

Abstract

It is often said that well-entangled and fast-breaking living polymers (such as wormlike micelles) exhibit a single relaxation time in their reptation dynamics, but the full story is somewhat more complicated. Understanding departures from single-Maxwell behavior is crucial for fitting and interpreting experimental data, but in some limiting cases numerical methods of solving living polymer models can struggle to produce reliable predictions/interpretations. In this work, we develop an analytic solution for the shuffling model of living polymers. The analytic solution is a converging infinite series, and it converges fastest in the fast-breaking limit where other methods can struggle.