Distribution of counterions near discretely charged planes and rods

TL;DR

This paper explores how discrete surface charges on macromolecules influence counterion distribution, revealing enhanced localization and increased counterion condensation compared to homogeneous charge models.

Contribution

It introduces a mean-field two-state model to analyze charge discretization effects on counterion distribution in planar and cylindrical geometries.

Findings

Discretization causes increased counterion localization near surfaces.

Counterion condensation can surpass classical Oosawa-Manning limits.

Results are validated against numerical solutions of the Poisson-Boltzmann equation.

Abstract

Realistic charged macromolecules are characterized by discrete (rather than homogeneous) charge distributions. We investigate the effects of surface charge discretization on the counterion distribution at the level of mean-field theory using a two-state model. Both planar and cylindrical geometries are considered; for the latter case, we compare our results to numerical solutions of the full Poisson-Boltzmann equation. We find that the discretization of the surface charge can cause enhanced localization of the counterions near the surface; for charged cylinders, counterion condensation can exceed Oosawa-Manning condensation.