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

Ladislav Šamaj,Martin Trulsson,Emmanuel Trizac

doi:10.1103/physreve.102.042604

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 pointlike 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 subpopulations, one for each plate, and integrates out one subpopulation 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.

Highlights

The dominant part of colloids release microions of low valence from the surfaces at deionized conditions [1,2,3]
By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions
While most previous analysis have focused on pointlike counterions, we treat them as charged hard spheres

Summary

Introduction

The dominant part of colloids release microions of low valence from the surfaces at deionized conditions [1,2,3]. The geometry of two parallel and uniformly charged walls at distance d with counterions in between provides the simplest setting for studying effective interactions between like-charged macromolecules It was shown in early experiments [7,8,9,10,11], and more recently in membranes, vesicle, or bilayer systems [12,13,14,15], as well as in numerical simulations [16,17,18,19], that like-charged colloid surfaces can attract each other under the action of Coulombic forces alone. These include, for example, systems with bulky counterions like ionic liquids [21,22], highly charged surfaces like calcium silicate hydrates where the size of the (hydrated) ions are comparable to the average distance between neighboring surface

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