Separation of Geometrical and Topological Entanglement in Confined Polymers Driven Out-Of-Equilibrium

TL;DR

This study uses simulations to distinguish and analyze geometrical and topological entanglement in confined polymers under out-of-equilibrium conditions, revealing their uncoupled dynamics and dependence on different parameters.

Contribution

It introduces a method to separately quantify geometrical and topological entanglement in polymers and demonstrates their distinct evolution under dynamic confinement.

Findings

Geometrical and topological entanglements evolve independently.

Geometrical entanglement correlates with force and cyclic deformation.

Topological entanglement depends on force and duration, and can be optimized.

Abstract

We use Brownian dynamics simulations and advanced topological profiling methods to characterize the out-of-equilibrium evolution of self-entanglement in linear polymers confined into nano-channels and under periodic compression. We distinguish two main forms of entanglement, geometrical and topological. The latter is measured by the number of (essential) crossings of the physical knot detected after a suitable bridging of the chain termini. The former is instead measured as the average number of times a linear chain appears to cross itself when viewed under all projections, and is irrespective of the physical knotted state. The key discovery of our work is that these two forms of entanglement are uncoupled and evolve with distinct dynamics. While geometrical entanglement is typically in phase with the compression-elongation cycles and it is primarily sensitive to its force f, the topological measure is mildly sensitive to cyclic modulation but strongly depends on both compression force f and duration k. The findings could assist the interpretation of experiments using fluorescence molecular tracers to track physical knots in polymers. Furthermore, we identify optimal regions in the experimentally-controllable parameter space in which to obtain more/less topological and geometrical entanglement; this may help designing polymers with targeted topology.