Retardation and many-body effects in multilayer-film adsorption

A discussion is presented of the relation between the film thickness d and the coexisting vapor pressure P for a physisorbed film. The theory of Dzyaloshinskii, Lifshitz, and Pitaevskii (DLP) is used to calculate the chemical potential {Δ}{μ}{≡}-{γ}(d)d^-3 relative to the value for bulk liquid. The relation is established between the DLP theory and a many-body expansion, of which the Frenkel-Halsey-Hill (FHH) theory is a first approximation to the nonretarded limit. Numerical calculations are performed for the cases of ⁴He, Ne, H₂, N₂, Ar, O₂, CH₄, Kr, and Xe films on glass, gold, graphite, Si, quartz, and Al. Typically, the effect of retardation is to reduce the thickness by 20% for d{~}200 A{}. The function {γ}(d) is shown to have a universal retardation behavior with a thickness scale (d1/2) depending on both adsorbate and substrate characteristic frequencies.