Monolayer physical adsorption on crystal surfaces

Abstract

In general, statistical thermodynamics provides a method of relating macroscopic thermodynamic variables to the molecular properties of a system of interest. In the case of a nonreactive gas adsorbed on the surface of an inert solid, the relevant molecular quantities are primanly the potential energies of the gas molecules interacting with each other and with the solid. However, in order to write explicit formal expressions for the observables, it is helpful to understand first how the raw measured data are related to thermo-dynamic properties, and then to focus on theoretical approaches that give relatively straightforward expressions for these properties. In particular, the measurements that most frequently appear in the literature are those of the adsorption isotherm and the heat of adsorption. Of course, an isotherm consists of measurements of the moles of gas adsorbed versus pressure at constant temperature; if the data are limited to submonolayer quantities on a solid of known surface area, the density of the gas on the surface is easily calculated from the known amount adsorbed. Furthermore, since the adsorbed phase is in equilibrium with bulk gas, one knows that the chemical potentials o f the two phases are equal; since the chemical potential of the gas is a known function of its pressure, one can view a monolayer isotherm as a determination of the chemical potential μ^(s) of an adsorbed film as a function of its density at fixed temperature. Without going further into the details of the thermodynamic argument,¹ one finds that where μ^†,(g) is the chemical potential of the bulk gas (considered to be ideal) in its standard state (p = 1 atm) at the experimental temperature T.