Collective diffusion is investigated within the kinetic lattice gas model for a system of interacting particles in one dimension. Analytic relations between the collective diffusion coefficient, diffusion activation energy, the attempt frequency pre-exponential factor, vs the particle density for both attractive and repulsive particleparticle interactions of an arbitrary strength are derived using the recently proposed ͓Phys. Rev. B 70, 125431 ͑2004͔͒ variational method. The analytic results agree with results of Monte Carlo simulations within a broad range of temperatures. At low coverages for strongly repulsive interactions the activation energy is roughly equal to its value for the noninteracting system but around = 0.5 it decreases rapidly by more than strictly accounted for by adparticle-adparticle interactions. Only at significantly higher coverages it increases reaching the expected limiting value. Peaks in the coverage dependence of the effective attempt frequency ͑for both the repulsive and the attractive interactions͒ are interpreted to reflect peaks in the total number of microscopic configurations accessible to the system at a given coverage and temperature. It is argued that the method used in this work allows for making meaningful estimates of the diffusion coefficient for systems far from thermal equilibrium.

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Collective diffusion in an interacting adsorbate on a nonhomogeneous one-dimensional substrate is investigated within the framework of a variational approximation. The substrate inhomogeneity, appropriate to a periodically stepped adsorbate, is represented by a Schwoebel barrier at the step edge and a modified binding at the step site. An elementary cell of a periodic substrate consists of n identical terrace sites and one step site, i.e. it contains n + 1 sites. The adsorbed particles are allowed to interact with each other, both in equilibrium as well as during the transit of a hopping particle over the potential energy barrier separating the initial and the target adsorption site. The interactions modify the rates of particle jumps between the adsorption sites. Cases n = 1, 3 and 4 are investigated in considerable detail and, where appropriate, a comparison with the available computer simulation results in the literature for an analogous two-dimensional system is made. It is shown that preferential geometrical arrangements at several adsorbate densities (coverages) induced by repulsive intra-adsorbate interactions lead to features on the diffusion coefficient versus the coverage curves which can be consistently interpreted. The origin of these features and their relation to intra-adsorbate correlations are examined and discussed. Where possible, the variational theoretical results are confronted with the results of our own computer simulation studies of diffusion.

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