Self-reptation and slow topological time scale of knotted polymers

TL;DR

This paper studies the dynamics of knotted ring polymers, revealing a slow topological time scale linked to self-reptation, with implications for understanding their diffusion and fluctuation behaviors.

Contribution

It introduces a novel characterization of the topological time scale in knotted polymers and relates it to self-reptation dynamics, advancing understanding of polymer topology effects.

Findings

Identifies a topological time scale related to self-reptation.

Determines the dynamical exponent $z_T=2.32\,\pm\,0.1$ for knotted polymers.

Shows the topological time scale influences various dynamical quantities.

Abstract

We investigate the Rouse dynamics of a flexible ring polymer with a prime knot. Within a Monte Carlo approach, we locate the knot, follow its diffusion, and observe the fluctuations of its length. We characterise a topological time scale, and show that it is related to a self-reptation of the knotted region. The associated dynamical exponent, $z_T=2.32\pm.1$, can be related to that of the equilibrium knot length distribution and determines the behaviour of several dynamical quantities.