Applications of the density-functional theory of charged fluids

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Abstract
We apply the density-functional theory of inhomogeneous charged fluids to some simple situations. The Poisson–Boltzmann equation follows as a result of modelling the free energy of a charged fluid as a perfect gas plus electrostatic contributions. A rigorous derivation of a generalised Lippman equation is given, from which the usual form of the Lippman equation follows as a special case. We derive an exact formula for the magnitude of the surface dipole at a molten-salt surface and show how a perturbation theory can be derived for calculating the charge distribution within the surface layer.