Simple Model for Attraction between Like-Charged Polyions

TL;DR

This paper introduces a simple model explaining how like-charged polyions attract each other in polyelectrolyte solutions, emphasizing the role of multivalent counterions and their condensed layer correlations.

Contribution

It proposes a minimal model linking counterion condensation and correlations to the attraction between like-charged polyions, highlighting a threshold condition for attraction.

Findings

Attraction is short-ranged and occurs only with multivalent counterions.

Counterion correlations in condensed layers induce attraction.

A threshold number of condensed counterions is necessary for attraction.

Abstract

We present a simple model for the possible mechanism of appearance of attraction between like charged polyions inside a polyelectrolyte solution. The attraction is found to be short ranged, and exists only in presence of multivalent counterions. The attraction is produced by the correlations in the condensed layers of counterions surrounding each polyion, and appears only if the number of condensed counterions exceeds the threshold, $ n > Z/2 \alpha $, where $\alpha$ is the valence of counterions and $Z$ is the polyion charge.