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Strong-Coupling Theory for Counter-Ion Distributions

Andre G. Moreira·Roland R. Netz
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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.

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Andre G. Moreira, Roland R. Netz. 2000-09-25. Strong-Coupling Theory for Counter-Ion Distributions. https://doi.org/10.1209/epl%2Fi2000-00495-1

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