On the failure of certain integral equations theories to account for complete wetting at solid-fluid interfaces

We examine the usefulness of the integral equations derived from the HNC and PY closures of the wall-particle Ornstein-Zernike equation for describing the density profile and pairwise distribution function of models of the solid-fluid interface. It is shown that these, and closely related closure approximations, cannot account for complete wetting of a solid-gas interface by liquid or complete wetting by gas of a purely repulsive substrate at a solid-liquid interface. The closure approximation to the first YBG equation which sets the total pairwise correlation function equal to that of the bulk fluid exhibits the same failings. Since none of these approaches can describe liquid-gas coexistence, they cannot be used as a basis for a self consistent theory of contact angle and wetting phenomena. Moreover, they cannot account for the growth of thick, liquid-like, adsorbed films which develop at solid-gas interfaces at temperatures T above the wetting transition temperature Tw. Such approaches also give an inadequate description of pairwise correla- tions in the interface. This is illustrated by the introduction of a ' surface ' compressibility sum rule which relates an integral over the interracial part of the pairwise distribution function to (SI'/~/~)T, the derivative with respect to chemical potential/~ of the coverage r. For T> T,¢ r and, hence, (er/~,)T diverge as p~approaches its value at saturation with exponents that reflect the asymptotic behaviour of the attractive part of the solid-gas potential. The sum rule shows that the range of transverse (parallel to the surface) pairwise correlations must diverge in an equivalent fashion. Divergences of this kind are not predicted by the integral equation approaches. The growth of long-ranged transverse correlations has important repercussions for com- puter simulations of thick adsorbed films.