Surface Coverage Dynamics for Reversible Dissociative Adsorption on Finite Linear Lattices

TL;DR

This paper derives analytical expressions for the equilibrium surface coverage in reversible dissociative adsorption on finite linear lattices, revealing significant odd-even size effects and the influence of surface diffusion on configuration accessibility.

Contribution

It provides the first analytical characterization of finite size effects and odd-even dependence in surface coverage dynamics with reversible dissociative adsorption.

Findings

Finite size effects are larger for even N than odd N.

Surface diffusion eliminates odd-even dependence in configurations.

Analytical results are confirmed by kinetic Monte Carlo simulations.

Abstract

Dissociative adsorption onto a surface introduces dynamic correlations between neighboring sites not found in non-dissociative absorption. We study surface coverage dynamics where reversible dissociative adsorption of dimers occurs on a finite linear lattice. We derive analytic expressions for the equilibrium surface coverage as a function of the number of reactive sites, $N$, and the ratio of the adsorption and desorption rates. Using these results, we characterize the finite size effect on the equilibrium surface coverage. For comparable $N$'s, the finite size effect is significantly larger when $N$ is even than when $N$ is odd. Moreover, as $N$ increases, the size effect decays more slowly in the even case than in the odd case. The finite-size effect becomes significant when adsorption and desorption rates are considerably different. These finite-size effects are related to the number of accessible configurations in a finite system where the odd-even dependence arises from the limited number of accessible configurations in the even case. We confirm our analytical results with kinetic Monte Carlo simulations. We also analyze the surface-diffusion case where adsorbed atoms can hop into neighboring sites. As expected, the odd-even dependence disappears because more configurations are accessible in the even case due to surface diffusion.