Diffusion theory for adsorption and desorption of gas atoms at surfaces

Abstract

The time evolution of a nonequilibrium ensemble of gas atoms adsorbed on a solid surface is described. Adsorption and desorption rate constants and adatom (adsorbed atom) energy distributions are obtained in the steady state approximation from the appropriate master equation or an equivalent diffusion equation. Energy transition probabilities are obtained from a classical gas‐surface collision model using an interaction potential composed of an oscillating harmonic repulsion and a stationary attraction. Calculations have been performed over the following range of similarity parameters: inertia ratio ${10}^{\text{−2}}{\mathrm{<\mu =m}}_g{\mathrm{/m}}_s\text{<2}$ , frequency ratio ${\text{1<ν=ω}}_s{\mathrm{/\omega }}_g\text{<10}$ , and well depth $\text{2<δ=D/kT<100}$ . For ``resonance'' values of the frequency ratio, gas‐surface collisions are sufficiently adiabatic that adatom energy distributions are significantly nonequilibrium, and steady state rate constants are depressed below the equilibrium rate constants. Applications include prediction of adsorption and desorption rate constants, sticking and accommodation coefficients, sublimation and condensation rates, and boundary conditions for the Knudsen layer.