Topological Forces in a Model System for Reptation Dynamics

TL;DR

This study models topological constraints in polymer dynamics, revealing how topological forces influence relaxation and nonlinear behavior through nonlocal entropic effects and coupling between different dynamic modes.

Contribution

It introduces a micromechanical model that explicitly demonstrates the role of topological forces beyond simple confinement, highlighting their impact on relaxation and nonlinear response.

Findings

Topological forces slow down linear relaxation along the tube.

Entropic forces during nonlinear motion are strong and nonlocal.

Coupling between orientational and longitudinal dynamics is observed.

Abstract

We construct a micromechanical version of an early model for topologically constrained polymers -- a 2D chain amongst point-like uncrossable obstacles -- which allows us to explicitly elucidate the role of topological forces beyond confining the chain to a curvilinear tube-like path. Our simulations reveal that linear relaxation of the contour length \textit{along the tube} is slowed down by the presence of topological forces that can be considered as additional effective topological ``friction'' in quiescence. However, this perspective fails in predicting the strong forces that resist the imposed curvilinear motion of the chain during nonlinear startup microrheology. These entropic forces are nonlocal in nature and result from an unexpected coupling between orientational and longitudinal dynamics.