Probing Polyelectrolyte Elasticity Using Radial Distribution Function

TL;DR

This study investigates how electrostatic interactions influence the end-to-end distance distribution of polyelectrolytes, proposing a universal scaling law and a new method for defining electrostatic persistence length to better match wormlike chain models.

Contribution

It introduces a universal scaling formula linking persistence length to charge density and screening, and proposes an improved electrostatic persistence length definition based on distribution maxima.

Findings

Universal scaling law for persistence length

New electrostatic persistence length definition

Enhanced accuracy in distribution matching

Abstract

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rodlike limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with its linear charge density and the Debye screening of its self-interaction. An alternative definition of the electrostatic persistence length is proposed based on matching of the maximum of the distribution with that of an effective wormlike chain, as opposed to the traditional matching of the first or the second moments of the distributions. It is shown that this definition provides a more accurate probe of the affinity of the distribution to that of the wormlike chains, as compared to the traditional definition. It is also found that the length of a polyelectrolyte segment can act as a crucial parameter in determining its elastic properties.