A model for the interaction of two electric double layers in two dimensions: The metal electrolyte interface and the Donnan membrane

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Abstract
A model for the interface of two media with different background densities, separated by a charged bilayer, is solved exactly in a two dimensional, one component plasma at reduced temperature 2. When the two media are in direct contact (no gap), then we can think of it as a model of a classical metal and an electrolytic solution or just two metals. The contact potential, or potential of zero charge appears to be a very simple function of the ratio of the background densities. We also find that the potential does not depend on the surface charge, a fact that we explain using a corollary of the perfect screening theorem. A second case of interest is the case of the two media separated by a gap that in our case could be charged: this is a model of a two dimensional membrane, or the polarization layer of the inner Helmholtz region. Very surprisingly, we find that also the surface dipole is completely screened by the charges surrounding the interface, so that the potential drop across the interface only depends on the logarithm of the charge densities, as found by Ballone, Senatore, and Tosi for the most simple case of a discharged contact.

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