Comparison of Continuum and Discrete Lattice Results for Gas–Surface Interactions

Abstract

Closed-form analytical results for trapping and gas–surface energy exchange have been derived for a simple model employing a one-dimensional elastic continuum representation of the solid with (1) a truncated harmonic potential and (2) a Morse potential for the interaction between the gas atom and the surface of the continuum. The results consist of formulas for the thermal accommodation coefficient (a.c.) and critical trapping energy, which are compared with corresponding results of McCarroll and Ehrlich and of Trilling for one-dimensional discrete lattices. With the truncated harmonic potential, the continuum gives practically the same values of a.c. and critical trapping energy as the discrete lattice, in accordance with Landau's 1935 prediction, for cases in which the collision frequency is considerably smaller than the cutoff frequency of the lattice. With a Morse potential, the variation of a.c. with temperature is qualitatively correct for the continuum solid model, but the a.c. values appear to be considerably larger than those predicted by Trilling for a discrete lattice. The analysis for the continuum brings out the fact that both the truncated harmonic and Morse potential formulas for a.c. can be expressed in the form of a similarity relation (Bμ)−1/2α = H(ρ), where α is the a.c., H is a function of ρ, B is the dimensionless potential-well depth, μ is the gas-atom–solid-atom mass ratio, ρ is the average energy per gas atom/potential-well depth. Experimental a.c. data for several gas–solid combinations appear to be correlated fairly well on a plot of α / (Bμ)1/2vsρ.