General Theory of Monolayer Physical Adsorption on Solids

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Abstract
By suitable modifications of the general equations given previously [W. A. Steele and M. Ross, J. Chem. Phys. 33, 464 (1960)], a theoretical monolayer adsorption isotherm is given which is written as a power series. The terms in the series involve integrals over the interaction energies of the adsorbed atoms with each other and with the solid. This treatment is based on a virial expansion of the density of the film in powers of the activity of the film, but differs from previous two-dimensional virial expansions in that it explicitly includes the effect of periodic variation of the solid-gas atom potential energy as the atom moves over the surface of the solid. It is shown that this general equation reduces to a sitewise model for large parallel variations in the solid-gas atom energy, and to a perfectly mobile film for small variations. However, when the potential energy for a gas atom over a simple solid is calculated as a function of the relative sizes of the gas and solid atoms, it appears that many adsorption systems may obey neither of the two limiting models. Some possible methods of dealing with adsorption systems which are neither completely localized or completely mobile are outlined and it is shown that some information about the nature of the solid-gas atom potential function may be obtained from an analysis of the experimental data for suitable systems.