Polyelectrolyte Knot Delocalization Induced by Counterion Condensation

TL;DR

This study uses molecular dynamics simulations to explore how counterion condensation affects knot localization in polyelectrolytes, revealing that it generally causes knot delocalization under strong electrostatic conditions.

Contribution

It provides a systematic analysis of counterion condensation effects on knot behavior in polyelectrolytes across different electrostatic and solvent conditions, which was previously unclear.

Findings

Counterion condensation delocalizes knots at high electrostatic strength.

Knot and chain sizes can be positively or negatively correlated at intermediate electrostatic strength.

Electrostatic correlation and solvent quality influence knot size and chain behavior.

Abstract

Knots on ring polymers tend to be tight. For knots on charged polymers (polyelectrolytes), electrostatic repulsion among the monomers is considered to enhance the persistence length and further localize the knots. However, the effects of counterion condensation on knots behavior are not clear. Here we use molecular dynamics simulations to systematically study the effect of counterion condensation on the knot behavior under different electrostatic strength and solvent quality conditions, with the focus on the knot sizes. We show that generally counterion condensation \emph{delocalizes} the knots in systems with strong electrostatic strength. At small to intermediate electrostatic strength, the knot size and overall chain size and can be positive correlated or negative correlated, as a result of the interplay between electrostatic correlation and solvent quality.