Collective diffusion in two-dimensional systems: exact analysis based on the kinetic lattice gas model

Abstract

Using a gradient expansion of the local microscopic particle current, in the long-time and large-scale limit, we derive an exact analytical expression for the density and temperature dependence of the diffusivity in terms of the density dependence of correlation functions on a rectangular lattice. The latter are calculated by transfer matrix methods, generalized to an adsorbate with lateral interactions and subjected to an external field. This allows an examination of the effects of generalized hopping kinetics. Where both initial and final state interactions are involved, the Reed-Ehrlich factorization, commonly assumed, cannot apply.

Effect of particle-hole symmetry on the behavior of tracer and jump diffusion coefficients

“…(22)- (27). As we mentioned in the Introduction, the particle-hole symmetry is fulfilled when the transition rate for a given configuration is the same as the transition rate for the same configuration, when particles are changed by holes (vacancies).…”

“…V is the interaction between nearest-neighbor particles. Longer-range interactions, like next-nearest-neighbor and trio interactions, can be included [25][26][27]. Let us introduce a function P (n,t), which gives the probability that a given microstate n = {n 1,1 , .…”

“…We restrict our description of diffusion to that resulting from the hopping of single particles from an occupied site to a neighboring unoccupied site. Then we can write this transition probability as [25][26][27]33]…”

“…(22) can be obtained. In the Appendix, the configurations leading to the rest of the equations (23)- (27) corresponding to PHS conditions are shown. Note that the rate transitions between those configurations in which the number of empty (occupied) sites surrounding the hopping particle is the same as the number of occupied (empty) sites surrounding the hopping vacancy cancel each other out.…”

“…A rather general approach has been proposed by Payne and Kreuzer (PK) [25] for one-dimensional (1D) and 2D diffusion * sergiojmanzi@gmail.com [26,27]. They have exactly corroborated the RE factorization [1] for any range of interactions and for any form of the hopping rates that satisfies the principle of detailed balance.…”