Tight and loose shapes in flat entangled dense polymers

TL;DR

This study explores how topological constraints affect the shape and localization of entangled dense polymer loops in two dimensions, revealing differences from dilute polymers and implications for polymer physics.

Contribution

It provides new insights into the effects of topological constraints on dense polymers, showing weaker entropic forces and different knot localizations compared to dilute conditions.

Findings

Entropic force favoring tightness is weaker in dense polymers.

Prime knots are loosely spread out over the chain in dense and Theta conditions.

Uncontracted knot configurations are most likely in dense and Theta conditions.

Abstract

We investigate the effects of topological constraints (entanglements) on two dimensional polymer loops in the dense phase, and at the collapse transition (Theta point). Previous studies have shown that in the dilute phase the entangled region becomes tight, and is thus localised on a small portion of the polymer. We find that the entropic force favouring tightness is considerably weaker in dense polymers. While the simple figure-eight structure, created by a single crossing in the polymer loop, localises weakly, the trefoil knot and all other prime knots are loosely spread out over the entire chain. In both the dense and Theta conditions, the uncontracted knot configuration is the most likely shape within a scaling analysis. By contrast, a strongly localised figure-eight is the most likely shape for dilute prime knots. Our findings are compared to recent simulations.