Unwinding relaxation dynamics of polymers

TL;DR

This paper studies the relaxation dynamics of polymers wound around obstacles, combining simulations and Langevin analysis to reveal how winding angle relaxation scales with polymer length and time.

Contribution

It introduces a Langevin equation model with winding-dependent friction that accurately predicts relaxation behavior, supported by numerical simulations.

Findings

Relaxation time scales as a power of polymer length with a logarithmic correction.

Winding angle decreases as a power-law at short times.

Reduced Langevin model captures key relaxation features.

Abstract

The relaxation dynamics of a polymer wound around a fixed obstacle constitutes a fundamental instance of polymer with twist and torque and it is of relevance also for DNA denaturation dynamics. We investigate it by simulations and Langevin equation analysis. The latter predicts a relaxation time scaling as a power of the polymer length times a logarithmic correction related to the equilibrium fluctuations of the winding angle. The numerical data support this result and show that at short times the winding angle decreases as a power-law. This is also in agreement with the Langevin equation provided a winding-dependent friction is used, suggesting that such reduced description of the system captures the basic features of the problem.