Quantum statistical theory of localized physisorption

Abstract

A quantum statistical theory of phonon-mediated localized physisorption has been developed by setting up the initial-value problem within nonequilibrium statistical mechanics and calculating the desorption times appropriate for the various experimental procedures, i.e., virgin adsorption, isothermal desorption, and flash desorption. We are able to delimit the temperature range over which the Arrhenius-Frenkel parametrization of the desorption time td = t0d exp(Q/kT) is acceptable. We calculate desorption times for the He/Constantan system which develops one weak bound state at an energy E0/kB = −25 K and show by comparison with experiments that the rather long flash desorption times (t0d ˜ 10−7 sec at temperatures between 4 and 20 K) are the result of the weak coupling (range of surface potential ca. 2.5 A) between the gas and the phonons of the solid. We can correlate isothermal and flash desorption times and suggest the temperature range where differences in these times can be detected. A complete fourth-order calculation enables us to delineate the range of validity of the one-phonon (second-order) theory and of the relaxation time approach to desorption. Extensive numerical results are shown and discussed.