Writhe-induced knotting in a lattice polymer

TL;DR

This paper investigates a lattice polymer model where a topological phase transition is driven by writhe-induced knotting, revealing a first-order transition linked to increased knotting rather than other structural effects.

Contribution

It introduces a lattice model of open polymers with a focus on writhe and demonstrates a topological phase transition caused by knotting, distinct from other structural phenomena.

Findings

First-order phase transition observed regardless of applied force

Transition attributed to increased knotting in the polymer

Knotting, not plectonemes, drives the phase change

Abstract

We consider a simple lattice model of a topological phase transition in open polymers. To be precise, we study a model of self-avoiding walks on the simple cubic lattice tethered to a surface and weighted by an appropriately defined writhe. We also consider the effect of pulling the untethered end of the polymer from the surface. Regardless of the force we find a first-order phase transition which we argue is a consequence of increased knotting in the lattice polymer, rather than due to other effects such as the formation of plectonemes.