Localization and size distribution of a polymer knot confined in a channel

TL;DR

This study uses Langevin dynamics simulations to analyze how a knotted polymer behaves in narrow channels, revealing strong localization and specific size fluctuation patterns influenced by confinement.

Contribution

It demonstrates the strong localization of a polymer knot in 1D confinement and introduces a simple model explaining size fluctuations based on virtual tube concepts.

Findings

Knot is strongly localized in narrow channels.

Size fluctuations follow a specific scaling behavior.

A simple model explains localization and fluctuation phenomena.

Abstract

We have examined the behaviors of a knotted linear polymer in narrow tubes using Langevin dynamics simulation to investigate the knot localization property in one-dimensional (1D) geometry. We have found that the knot is strongly localized in such a geometry. By observing the distribution function of the size of localized knot, we found the scaling behavior of the fluctuation around the most probable size with radius of confinement. Based on the analysis of the probability distribution of the knot size, we show that the strong localization behavior and the fluctuation around the most probable size can be encompassed by a simple argument based on the virtual tubes composed of parallel strands and overlapping among them.