Manning condensation in two dimensions

Abstract

We consider a macroion confined to a cylindrical cell and neutralized by oppositely charged counterions. Exact results are obtained for the two-dimensional version of this problem, in which ion-ion and ion-macroion interactions are logarithmic. In particular, the threshold for counterion condensation is found to be the same as predicted by mean-field theory. With further increase of the macroion charge, a series of single-ion condensation transitions takes place. Our analytical results are expected to be exact in the vicinity of these transitions and are in very good agreement with recent Monte-Carlo simulation data.

4 pages, 4 figures

References in corpus (2)

• Beyond Poisson-Boltzmann: Fluctuations and Correlations
• Counterions at Charged Cylinders: Criticality and universality beyond mean-field

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• Attraction of like-charged walls with counterions only: Exact results for the 2D cylinder geometry
• Counter-ion density profile around a charged disk: from the weak to the strong association regime
• Ensemble Equivalence for Counterion Condensation on a Two Dimensional Charged Disc
• Electrolyte flows under magnetic fields: Manning-like counterion condensation in one dimension