A Poisson–Boltzmann treatment of the capacitance of a layer of symmetrical spherical dipoles

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Abstract
The capacitance of a layer of spherical orientable dipoles has been determined. The properties attributed to each dipole are those of two point charges on a diameter of the sphere and equidistant from its centre. A one-dimensional potential distribution is assumed to exist normal to the layer and to be coupled to the charge distribution via Poisson's law. The orientation of the dipoles is random in the absence of polarization, but is taken as governed by Boltzmannian statistics when an applied field is present. The treatment predicts that the capacitance will display a pronounced hump at the point of zero charge. Though this study was motivated by a wish to interpret the inner-layer capacitance at a mercury/aqueous electrolyte solution interface, the treatment is shown to be inapplicable quantitatively to such a system.

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