A dynamical mean field theory for the study of surface diffusion constants

Abstract

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion. We apply our formalism to three very different strongly interacting systems and compare the results of the new approach with those of usual Monte Carlo simulations. We find that the combined approach works very well for collective diffusion, whereas for tracer diffusion the influence of interactions on the memory effects is more prominent.

Memory effects and coverage dependence of surface diffusion in a model adsorption system

“…This implies that the overall behavior of D T arises mainly from the kinetic factor ⌫. Similar results have been found in previous studies of some adsorption systems 13,15,16,20 as well as for more complex models of chainlike molecules. 15,16 …”

“…,N, and is defined in terms of their positions r ជ i (t) at time t. Note that D T is actually a tensor quantity; for the purposes of the present work we use a simple scalar notation. Then, within the lattice-gas description, a formally exact way of describing the temperature and coverage dependent tracer diffusion coefficient D T ( ,T) is to write it as 13,15 …”

“…The approximation where f T ϵ1 is called the dynamical mean field ͑DMF͒ theory for D T . 15,16 The decomposition in Eq. ͑2͒ allows a convenient estimation of the actual memory effects.…”

“…14 Within this approach, the tracer diffusion coefficient D T can be expressed formally as a product of the average single-particle transition rate ⌫ and the correlation factor f T , which accounts for all the memory effects arising from correlations between consecutive displacements of a tagged particle. 13,15,16 The collective diffusion coefficient D C can be similarly expressed as a product of ⌫ and the correlation factor f C accounting for the memory effects in the center-ofmass motion of the diffusing particles, and an additional contribution due to thermodynamic particle number fluctuations. 13,15,16 Previous theoretical works for interacting adsorption systems have mainly focused on how the diffusion coefficients D T and D C depend on thermodynamic conditions such as the presence of ordered phases and phase transition boundaries.…”

“…13,15,16 The collective diffusion coefficient D C can be similarly expressed as a product of ⌫ and the correlation factor f C accounting for the memory effects in the center-ofmass motion of the diffusing particles, and an additional contribution due to thermodynamic particle number fluctuations. 13,15,16 Previous theoretical works for interacting adsorption systems have mainly focused on how the diffusion coefficients D T and D C depend on thermodynamic conditions such as the presence of ordered phases and phase transition boundaries. 4,[17][18][19][20][21][22][23][24][25][26] Of special interest has been the behavior of the prefactor and the diffusion barrier extracted from an Arrhenius analysis of the temperature dependence of the diffusion coefficients.…”