Equilibrium Bundle Size of Rodlike Polyelectrolytes with Counterion-Induced Attractive Interactions

TL;DR

This paper models the equilibrium size of polyelectrolyte bundles induced by multivalent counterions, revealing how counterion size and interaction frustration influence whether bundles are finite or infinite in size.

Contribution

It introduces a simple phenomenological model to predict bundle sizes considering counterion size and interaction frustration effects.

Findings

Point-like counterions lead to diverging bundle sizes.

Large counterions result in finite equilibrium bundle sizes.

Interaction frustration can cause finite bundles even with small counterions.

Abstract

Multivalent counterions can induce an effective attraction between like-charged rodlike polyelectrolytes, leading to the formation of polelectrolyte bundles. In this paper, we calculate the equilibrium bundle size using a simple model in which the attraction between polyelectrolytes (assumed to be pairwise additive) is treated phenomenologically. If the counterions are point-like, they almost completely neutralize the charge of the bundle, and the equilibrium bundle size diverges. When the counterions are large, however, steric and short-range electrostatic interactions prevent charge neutralization of the bundle, thus forcing the equilibrium bundle size to be finite. We also consider the possibility that increasing the number of nearest neighbors for each rod in the bundle frustrates the attractive interaction between the rods. Such a frustration leads to the formation of finite size bundles as well, even when the counterions are small.