  We expand on a recent study of a lattice model of interacting particles
[Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium
fluctuations in particle number are discussed as a function of the interaction.
Their behavior is similar to that of interacting particles in porous materials.
Different expressions for the particle jump rates are derived from transition
state theory. Which expression should be used depends on the strength of the
inter-particle interactions. Analytical expressions for the self- and transport
diffusion are derived when correlations, caused by memory effects in the
environment, are neglected. The diffusive behavior is studied numerically with
kinetic Monte Carlo (kMC) simulations, which reproduces the diffusion including
correlations. The effect of correlations is studied by comparing the analytical
expressions with the kMC simulations. It is found that the Maxwell-Stefan
diffusion can exceed the self-diffusion. To our knowledge, this is the first
time this is observed. The diffusive behavior in one-dimensional and higher
dimensional systems is qualitatively the same, with the effect of correlations
decreasing for increasing dimension. The length dependence of both the self-
and transport diffusion is studied for one-dimensional systems. For long
lengths the self-diffusion shows a one over length dependence. Finally, we
discuss when agreement with experiments and simulations can be expected. The
assumption that particles in different cavities do not interact is expected to
hold quantitatively at low and medium particle concentrations, if the particles
are not strongly interacting.
