A density functional theory for inhomogeneous charged fluids

Abstract

We formulate a density functional theory for the one particle densities and the thermodynamic properties of multicomponent, classical, inhomogeneous, charged fluids. We show that for slowly varying densities, the Helmholtz free energy can be expanded as a series of density gradients plus an explicit electrostatic contribution. The coefficients in this expansion are directly proportional to moments of the non-coulombic part of the Ornstein-Zernike direct correlation functions of a uniform mixture. An explicit formula for the stress tensor is derived. The theory is applied to the liquid-vapour interface of a molten alkali halide and some formally exact results for the ionic density profiles and surface tension are derived. Using the truncated gradient expansion, we develop a tractable approximation scheme for the surface properties. The surface tension is of the van der Waals form plus a contribution which involves the integral of the off-diagonal part of the Maxwell stress tensor through the interface. The electrical double layer is treated in a properly self consistent fashion. We describe the bulk quantities which are required to implement the theory. Other possible applications of the general formalism to problems in electrochemistry are briefly mentioned.