Strong-coupling theory for counter-ion distributions
Max-Planck-Institut für Kolloid-
Am Mühlenberg, 14424 Potsdam, Germany
Accepted: 16 October 2000
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.
PACS: 82.70.-y – Disperse systems / 61.20.Qg – Structure of associated liquids: electrolytes, molten salts, etc / 82.45.+z – Electrochemistry and electrophoresis
© EDP Sciences, 2000