Statistical mechanics of the disjoining pressure of a planar film

The physics of wetting transitions (stability of fluid films adsorbed at planar substrates) is reassessed in the context of the original theory of wetting known as Frumkin-Derjaguin theory [A. Frumkin, Zh. Fiz. Khim. 12, 337 (1938)]. In particular, the Russian School classify wetting phenomena in terms of the mean-field disjoining pressure. The integral of the mean-field disjoining pressure, with respect to film thickness, defines the interface potential accessible from density-functional theory (DFT). For wall-fluid models (substrate defined as an external field), the exact disjoining pressure of an adsorbed film can be expressed as a one-body sum rule. One of the aims of this work is to verify the internal consistency of the statistical thermodynamics of Frumkin-Derjaguin theory, by direct evaluation of the disjoining pressure sum rule, using DFT. For short-range models, the form of the interface potential (and hence disjoining pressure) is directly obtainable from liquid-state asymptotics. The second aim of this work is to verify from DFT that for standard short-range models there are three qualitatively different regimes, arising from competition between the correlation lengths predicted by asymptotic theory. A variety of related issues are also considered, including (i) crossover between the various regimes, (ii) incorporation of capillary-wave fluctuations (beyond mean-field), and (iii) qualitative changes induced by power-law dispersion interactions and the related prediction of two-stage wetting.