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Complex Geometry and Electric Double Layers

Published online by Cambridge University Press:  25 February 2011

Bertrand Duplantier
Bertrand Duplantier*
Affiliation:
Service de Physique Thétidle;orique† de Saclay, CE-Saclay, 91191 Gif-sur-Yvette Cedex, France and The James Franck Institute, The University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637
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Abstract

The properties of electric double layers near curved surfaces of arbitrary shape and genus are obtained exactly within the Debye-Hückel theory by means of multiple-scattering expansion. For smooth membranes, geometric and topological feature of the electrostatic free energy then emerge through convergent expansions in inverse powers of the principal radii of curvature. Some consequences for the electrostatic stability of various membrane shapes are considered. We also study the effects of surface singularities, e.g., wedges, on the thermodynamics of electric double layers near a rough colloid. Each wedge yields an additive contribution to the free energy that is a functionof the angle. A probabilistic Brownian representation of is given, which is entirely similar to that of vibration eigenmodes given by M. Kac long ago in “Canone hear the shape of a drum?” [Amer. Math. Monthly 73S, 1 (1966)]. The analysis yields a universal scaling law for the free energy of a rough colloid with its fractal Minkowski dimension.

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References

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