Strong-coupling theory for counter-ion distributions

Max-Planck-Institut für Kolloid- und Grenzflächenforschung Am Mühlenberg, 14424 Potsdam, Germany

Received: 16 June 2000
Accepted: 16 October 2000

Abstract

The Poisson-Boltzmann approach gives asymptotically exact counter-ion density profiles around charged objects in the weak-coupling limit of low valency and high temperature. In this paper we derive, using field-theoretic methods, a theory which becomes exact in the opposite limit of strong coupling. Formally, it corresponds to a standard virial expansion. Long-range divergences, which render the virial expansion intractable for homogeneous bulk systems, are shown to be renormalizable for the case of inhomogeneous distribution functions by a systematic expansion in powers of the fugacity. For a planar charged wall, our analytical results compare quantitatively with extensive Monte Carlo simulations.