Relaxation of a Single Knotted Ring Polymer

TL;DR

This study investigates how a single knotted ring polymer relaxes over time using Brownian dynamics simulations, revealing how the relaxation rates depend on wave number and polymer size, and identifying a structural transition related to knot localization.

Contribution

The paper introduces a detailed analysis of relaxation rates in knotted ring polymers, highlighting a size-dependent crossover in relaxation behavior linked to knot localization.

Findings

Relaxation rate scales as lambda_q=A(1/N)^x for q=1

Relaxation rate scales as lambda_q=A'(q/N)^x' for q=2,3

Crossover in slowest relaxation wave number from q=2 to q=1 with increasing N

Abstract

The relaxation of a single knotted ring polymer is studied by Brownian dynamics simulations. The relaxation rate lambda_q for the wave number q is estimated by the least square fit of the equilibrium time-displaced correlation function to a double exponential decay at long times. The relaxation rate distribution of a single ring polymer with the trefoil knot appears to behave as lambda_q=A(1/N^)x for q=1 and lambda_q=A'(q/N)^x' for q=2 and 3, where x=2.61, x'=2.02 and A>A'. The wave number q of the slowest relaxation rate for each N is given by q=2 for small values of N, while it is given by q=1 for large values of N. This crossover corresponds to the change of the structure of the ring polymer caused by the localization of the knotted part to a part of the ring polymer.