Knots in Charged Polymers

TL;DR

This paper explores how topological constraints and Coulomb interactions affect charged polymers, revealing that tight knots form and influence relaxation dynamics, with implications for polymer behavior and manipulation.

Contribution

It demonstrates that Coulomb interactions localize topological constraints into tight knots and analyzes their stability and dynamics in charged polymers.

Findings

Tight knots form due to Coulomb interactions in charged polymers.

Knots are removed mainly by diffusion along the chain, not opening.

Knot diffusion slows with increased charge density, potentially freezing their position.

Abstract

The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction localizes irreducible topological constraints into tight molecular knots, while composite constraints are factored and separated. Even when the forces are screened, tight knots may survive as local (or even global) equilibria, as long as the overall rigidity of the polymer is dominated by the Coulomb interactions. As entanglements involving tight knots are not easy to eliminate, their presence greatly influences the relaxation times of the system. In particular, we find that tight knots in open polymers are removed by diffusion along the chain, rather than by opening up. The knot diffusion coefficient actually decreases with its charge density, and for highly charged polymers the knot's position appears frozen.