For fluids adsorbed at walls the MWDA density functional theory is equivalent to an HNC approach

Abstract

The modified weighted density approximation (MWDA) introduced by Denton and Ashcroft in 1989 in a density functional theory of inhomogeneous fluids is applied to the case of fluid adsorption at planar walls. It is shown that the MWDA is completely equivalent to the hypernetted-chain closure of the wall-particle Ornstein-Zernike equation (HNCWP) for such problems. Because of the nature of the uniform fluid higher-order direct correlation functions within the MWDA, this theory of adsorption constitutes a truncation of the functional expansion of the free energy. The MWDA can also be used as the basis of a theory for the radial distribution function of a homogeneous fluid, where it is equivalent to the bulk HNC. For fluids confined in pores, however, the MWDA is not identical to the HNCWP.