Chemical potential of adsorbed molecules from a quantum statistical formulation

When classical mechanics is used to treat an adsorption system involving a homogeneous surface, it is assumed that all adsorbed molecules have the same adsorption energy. In a quantum mechanical description of a homogeneous surface, the energy at an adsorption site could be any one of a discrete set of values and, at any time, a particular value would exist randomly at different adsorption sites. If the adsorbed molecules are allowed to have internal structure, to interact, and to change the substrate, then their energy spectrum becomes more complex. We report the result of approximating the adsorption of antisymmetric, diatomic molecules on a homogeneous substrate as quantum mechanical, double (two point masses) harmonic oscillators in a potential that changes with the amount of adsorption. The expression for the chemical potential is obtained from the canonical partition function and is examined by applying it to obtain the equilibrium adsorption isotherm for CO adsorbing on Ni(111). The expression for the chemical potential contains the unknown, coverage dependent, potential energy that results from both adsorbate-adsorbate and adsorbate-substrate interactions. In addition, four of the six characteristic frequencies of the harmonic oscillators are assumed not to be known. A procedure for obtaining this information from measured equilibrium isotherms allows independent sets of isotherm measurements to be quantitatively compared; Equilibrium properties, including the heat of adsorption and the adsorption-induced change in the surface tension, are predicted. As well, an approximate calculation of the minimum energy of bound molecules is made.