Wigner Crystal Model of Counterion Induced Bundle Formation of Rodlike Polyelectrolytes

Abstract

A simple electrostatic theory of condensation of rodlike polyelectrolytes under influence of polyvalent counterions is proposed. It is based on the idea that counterions form a Wigner crystal on a background of a bundle of rods. It is shown that, depending on a single dimensionless parameter, this can be a densely packed three-dimensional Wigner crystal or a 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.