Strong-coupling theory of counterions with hard cores between symmetrically charged walls

TL;DR

This paper combines simulations and analytical methods to study how finite-sized counterions influence the effective interactions between charged walls, revealing that steric effects minimally impact pressure except at very close distances.

Contribution

It introduces a novel analytical framework for counterions as charged hard spheres, extending previous point-charge models to include steric effects in strong coupling regimes.

Findings

Steric effects are negligible at large distances between plates.

Hard sphere overlaps occur only at very small separations.

Effective pressure remains largely unaffected by sterics at high coupling.

Abstract

By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on point-like counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two sub-populations, one for each plate, and integrates out one sub-population to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard sphere overlap are unavoidable, and thus rule out configurations.