Desorption times from rate equations, the master equation, and the Fokker-Planck equation

A set of rate equations for the bound-state occupation functions with transition probabilities calculated microscopically serves as a basis for a detailed study of various approximations available for the calculation of desorption times in gas-solid systems exhibiting physisorption. The exact time evolution of the adsorbate during the desorption process shows that quasiequilibrium is only maintained at low temperatures, where perturbation theory of the master equation yields a simple analytic expression for the desorption time in weakly coupled gas-solid systems. At intermediate temperatures we derive another simple expression from the Fokker-Planck equation. Classical and phenomenological equilibrium theories of desorption are critically assessed. Lower limits for the preexponential factor in the desorption time of the order of ${10}^{-16\mathrm{}}$ sec proportional to the inverse of the heat of adsorption are derived.