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

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.