Bulk mediated surface diffusion: finite bulk case

J.A. REVELLI, C.E. BUDDE, D. PRATO AND H.S. WIO

EUROPEAN PHYSICAL JOURNAL B - CONDENSED MATTER

EDP Sciences, Societá Italiana di Fisica, Springer-Verlag.

Año: 2004 vol. 37 p. 205 - 212

1434-6028

Within the framework of a Master Equation scheme, we address the dynamics of adsorbed molecules (a fundamental issue in surface physics) and study the diffusion of particles in a finite cubic lattice whose boundaries are at the z=1 and the z=L planes where L=2,3,4,... while the x and y directions are unbounded. As we are interested in the effective diffusion process at the interfase z=1, we calculate analytically the conditional probability for finding the particle on the z=1 plane as well as the surface dispersion as a function of time and compare these results with the Monte Carlo simulations finding an excellent agreement. These results show that there exists an optimal number of layers that maximize <r^2> ib the interface; for a small number the layers the long time effective diffusivity  on the interface is normal, over abruptly towards a subdiffusive behavior as the number of layers increases.