Tracer-diffusion coefficients for both localized and nonlocalized adsorption: Theory and molecular-dynamics simulation

Abstract

We present a quantitative analysis of tracer diffusion in a molecular-dynamics simulation of the adsorption of an isolated ethane molecule on Pt(111). In particular, we examine the deviations between the tracer diffusion of ethane in the simulations and the assumptions of the nearest-neighbor adsorbate-hopping model at temperatures for which the kinetic energy of the molecule approaches and exceeds the diffusion-barrier energy. Our method of analysis can be implemented experimentally, with techniques such as scanning-tunneling microscopy. We show that the adsorbate-hopping model cannot accurately describe tracer diffusion at any of the temperatures probed. This is because ethane exhibits very long flights with flight times that are not negligible compared to the time required for the molecule to escape from a binding site. We propose a new formula for the diffusion coefficient that includes the influence of non-nearest-neighbor jumps with non-negligible flight times. In the limit of low temperatures, this expression reduces to a hopping model while, at high temperatures, our model predicts that the diffusivity becomes analogous to that for a two-dimensional gas. We show that our model quantitatively describes the tracer diffusion of ethane on Pt(111) in molecular-dynamics simulations over a wide temperature range, spanning both localized and nonlocalized adsorption. We comment on future research directions that may lead to a quantitative model of tracer diffusion in other similar systems.