Topological disentanglement of linear polymers under tension

TL;DR

This paper presents a theoretical model for the topological disentanglement of linear polymers under tension, focusing on how knots decay and unknot, validated by molecular dynamics simulations.

Contribution

It introduces a novel particle diffusion model for knot behavior in polymers, linking topological invariants to disentanglement processes.

Findings

Model accurately predicts knot decay and unknotting events.

Theoretical results show excellent agreement with molecular dynamics simulations.

Topological invariants effectively determine knot dynamics.

Abstract

We develop a theoretical description of the topological disentanglement occurring when torus knots reach the ends of a semi-flexible polymer under tension. These include decays into simpler knots and total unknotting. The minimal number of crossings and the minimal knot contour length are the topological invariants playing a key role in the model. The crossings behave as particles diffusing along the chain and the application of appropriate boundary conditions at the ends of the chain accounts for the knot disentanglement. Starting from the number of particles and their positions, suitable rules allow reconstructing the type and location of the knot moving on the chain. Our theory is extensively benchmarked with corresponding Molecular Dynamics simulations and the results show a remarkable agreement between the simulations and the theoretical predictions of the model.