Theory of direct scattering, trapping, and desorption in atom-surface collisions

As a part of his studies explaining how an enclosed gas comes to equilibrium, Maxwell [Philos. Trans. R. Soc. Lond. 170, 231 (1879)] proposed what is now known as the "Maxwell assumption," namely, that when gas particles collide with the walls of their container, a fraction is directly scattered with little change in state, while the remaining fraction becomes trapped at the surface and subsequently desorbs in a distribution at equilibrium with the surface temperature. In this paper a scattering theory is developed, using an iterative algorithm and classical mechanics for the collision process, which describes both direct scattering and trapping-desorption of the incident beam. That portion of an incident beam that is initially trapped in the physisorption potential well can be followed as the trapped atoms continue to make further interactions with the surface until they are all eventually ejected back into the continuum and leave the surface region. Several calculations show that this theory predicts when a system will obey the Maxwell assumption. Additional calculations show that the theory quantitatively explains recent experimental measurements [K. D. Gibson, N. Isa, and S. J. Sibener, J. Chem. Phys. 119, 13083 (2003)] of Ar scattering from a self-assembled monolayer on Ag(111) in which clear signals of both direct scattering and a trapping-desorption fraction are exhibited in the energy-resolved spectra.