The contact theorem for charged fluids: from planar to curved geometries

Abstract

When a Coulombic fluid is confined between two parallel charged plates, an exact relation links the difference of ionic densities at contact with the plates, to the surface charges of these boundaries. It no longer applies when the boundaries are curved, and we work out how it generalizes when the fluid is confined between two concentric spheres (or cylinders), in two and in three space dimensions. The analysis is thus performed within the cell model picture. The generalized contact relation opens the possibility to derive new exact expressions, of particular interest in the regime of strong coulombic couplings. Some emphasis is put on cylindrical geometry, for which we discuss in depth the phenomenon of counter-ion evaporation/condensation, and obtain novel results. Good agreement is found with Monte Carlo simulation data.

24 pages, 15 figures

References in corpus (3)

• Scaling and Universality in the Counterion-Condensation Transition at Charged Cylinders
• On the bulk modulus of the cell model of charged macromolecules suspensions
• Equation of state for hard sphere fluids with and without Kac tails

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• Counter-Ions Near a Charged Wall: Exact Results for Disc and Planar Geometries
• Counter-ion density profile around a charged disk: from the weak to the strong association regime
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• Quasi-universality in mixed counterions systems
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• A simple approximation for the distribution of ions between charged plates in the weak coupling regime
• Contact value theorem for electric double layers with modulated surface charge density