Driven Anomalous Diffusion: An example from Polymer Stretching

TL;DR

This paper investigates the anomalous dynamics of tension propagation in stretched polymers, revealing nonlinear memory effects and stress hardening through theoretical analysis and molecular dynamics simulations.

Contribution

It introduces a detailed analysis of tension propagation in polymers under strong forces, highlighting nonlinear memory effects and stress hardening in the dynamics.

Findings

Response exhibits anomalous drift characterized by nonlinear memory kernel

Fluctuation-response relation is nontrivial in the strong force regime

Molecular dynamics simulations support the theoretical framework

Abstract

The way tension propagates along a chain is a key to govern many of anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the dynamical fluctuations of a segment in a long polymer during its stretching process is investigated. We show that the response, i.e., average drift, is anomalous, which is characterized by the nonlinear memory kernel, and its relation to the fluctuation is nontrivial. These features are discussed on the basis of the generalized Langevin equation, in which the role of the temporal change in spring constant due to the stress hardening is pinpointed. We carried out the molecular dynamics simulation, which supports our theory.