Film formation on a weakly attractive substrate within the lattice-gas model

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Abstract
Adsorption of a dense film on a weakly attractive substrate is studied using a lattice-gas model in the mean-field approximation. The model and method of solution are much the same as those employed by de Oliveira and Griffiths. In the present theory, the particles of the gas interact via either a Lennard-Jones (6-12) potential or a nearest-neighbor potential, and a gas particle interacts with the substrate through a (9-3) potential. For sufficiently weak substrate potentials no film is found. For sufficiently strong ones a film forms and grows with increasing vapor pressure or chemical potential either continuously or in one-atomic-layer steps as found by de Oliveira and Griffiths. For potentials of intermediate strength, there is a discontinuity in the film thickness from a partial layer to an arbitrarily large number of layers, depending on the temperature, as the vapor pressure is increased. The phase diagram in these cases is strikingly similar to that found by Ebner and Saam from a density-functional theory of nonuniform fluids; there is, however, a sizable difference in the substrate potential strengths at which the large discontinuity in film thickness appears.