Microscopic approach to the collective diffusion in the interacting lattice gas

Ritz variational principle for collective diffusion in an adsorbate on a non-homogeneous substrate

“…Crucial for this approach was distributing all possible microstates among equivalence classes of microstates with identical, modulo periodic boundary conditions, relative positions of particles ͑i.e., all microstates within the class have an identical geometrical pattern of occupied sites͒. The same idea is at the basis of the approach described in this paper, as well as in all our earlier work [7][8][9][10][11]17 on diffusion in the interacting lattice gas. 18 Our goal is to develop a systematic approach on collective diffusion of interacting particles on a one-dimensional periodic lattice of adsorption sites with varying binding energies ͑potential well depths͒ and varying barrier heights between the sites, i.e., on a non-homogeneous but periodic substrate.…”

“…We mention here a number of theoretical works devoted to it due to their relevance to this work and to our earlier efforts. [7][8][9][10][11] One of the earliest seems a linear response theory approach by Zwerger, 12 which allowed him to derive analytic expressions for the coverage dependent collective diffusion coefficient D͑͒ for a one-dimensional ͑1D͒ lattice gas with nearestneighbor ͑NN͒ and next-nearest-neighbor ͑NNN͒ interactions. Kreuzer and Zhang, using a version of the kinetic lattice gas model which they developed earlier to study thermal desorption kinetics, 13,14 investigated D͑ , T͒ ͑with T being temperature͒ in a 1D lattice gas with NN interactions and different models of microscopic kinetics.…”

Collective diffusion in the presence of substrate inhomogeneities and particle–particle interactions

“…[23] has been subsequently refined and applied to a variety of problems [24][25][26][27][28]. In essence, the problem of finding the density/coverage dependent collective diffusion coefficient in a system of interacting particles adsorbed on a crystalline substrate is reduced to that of finding the smallest eigenvalue of a rate matrix using the variational approach akin to that used in quantum mechanics to find the ground state energy of a physical system.…”

“…The variational KLGM approach to collective diffusion was initiated in Ref. [23] and then progressively refined in a series of follow-up works [24][25][26][27][28]. Most of these works deal with homogeneous one-dimensional systems with short range interactions but some progress has been also made in two dimensions [24], non-homogeneous substrates [28] and systems with long range particle-particle interactions [27,29].…”

Coupling of orthogonal diffusion modes in two-dimensional nonhomogeneous systems

“…͑1͒. 22,[27][28][29][30] To this end, microscopic states of the systems need to be properly parametrized. Following Ref.…”