CHEMICAL-POTENTIAL OF ADSORBED MOLECULES FROM A QUANTUM-STATISTICAL FORMULATION

When classical mechanics is used to treat an adsorption system involvi ng a homogeneous surface, it is assumed that all adsorbed molecules ha ve the same adsorption energy. In a quantum mechanical description of a homogeneous surface, the energy at an adsorption site could be any o ne of a discrete set of values and, at any time, a particular value wo uld exist randomly at different adsorption sites. If the adsorbed mole cules are allowed to have internal structure, to interact, and to chan ge the substrate, then their energy spectrum becomes more complex. We report the result of approximating the adsorption of antisymmetric, di atomic molecules on a homogeneous substrate as quantum mechanical, dou ble (two point masses) harmonic oscillators in a potential that change s with the amount of adsorption. The expression for the chemical poten tial is obtained from the canonical partition function and is examined by applying it to obtain the equilibrium adsorption isotherm for CO a dsorbing on Ni(111). The expression for the chemical potential contain s the unknown, coverage dependent, potential energy that results from both adsorbate-adsorbate and adsorbate-substrate interactions. In addi tion, four of the six characteristic frequencies of the harmonic oscil lators are assumed not to be known. A procedure for obtaining this inf ormation from measured equilibrium isotherms allows independent sets o f isotherm measurements to be quantitatively compared; Equilibrium pro perties, including the heat of adsorption and the adsorption-induced c hange in the surface tension, are predicted. As well, an approximate c alculation of the minimum energy of bound molecules is made.