Strong-Coupling Theory for Counter-Ion Distributions

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 inverse powers of the coupling parameter. For a planar charged wall, our analytical results compare quantitatively with extensive Monte-Carlo simulations.

7 pages, 3 figures; to appear in Europhys. Lett

References in corpus (3)

• Screening of a macroion by multivalent ions: Correlation induced inversion of charge
• The fraction of condensed counterions around a charged rod: Comparison of Poisson-Boltzmann theory and computer simulations
• Novel Electrostatic Attraction from Plasmon Fluctuations

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