Wigner crystal model of counterion induced bundle formation of rod-like polyelectrolytes

TL;DR

This paper presents a theoretical model based on Wigner crystal formation to explain how polyvalent ions induce bundling of rod-like polyelectrolytes, providing insights into DNA condensation and potential applications to other systems.

Contribution

It introduces a simple electrostatic theory linking Manning condensation to Wigner crystal formation, explaining polyelectrolyte bundling mechanisms.

Findings

Wigner crystal formation depends on a key dimensionless parameter.

Different crystal structures (3D, 2D, 1D) are possible based on system conditions.

The model applies to DNA and other polyelectrolyte self-assembly processes.

Abstract

A simple electrostatic theory of condensation of rod-like polyelectrolytes under influence of polyvalent ions is proposed. It is based on the idea that Manning condensation of ions results in formation of the Wigner crystal on a background of a bundle of rods. It is shown that, depending on a single dimensionless parameter, this can be the densely packed three-dimensional Wigner crystal or the two-dimensional crystal on the rod surfaces. For DNA the location of charge on the spiral results in a model of the one-dimensional Wigner crystal. It is also argued that the Wigner crystal idea can be applied to self-assembly of other polyelectrolytes, for example, colloids and DNA-lipid complexes.