Constructing a new closure theory based on the third-order Ornstein-Zernike equation and a study of the adsorption of simple fluids.

The third-order Ornstein-Zernike equation (OZ3) is used in the construction of a bridge functional that improves over conventional liquid-theory closures (for example, the hypernetted chain or the Percus-Yevick equations). The OZ3 connects the triplet direct correlation C((3)) to the triplet total correlation h((3)). By invoking the convolution approximation of Jackson and Feenberg, we are able to express the third-order bridge function B(3) as a functional of the indirect correlation γ. The resulting expression is generalized to higher-order bridge terms. This new closure is tested on the adsorption of Lennard-Jones fluid on planar hard surfaces by calculating the density profiles and comparing with Monte Carlo simulations. Particular attention is paid to the cases where molecular depletion on the substrate is evident. The results prove to be highly accurate and improve over conventional closures.