Cellular Automata modeling of diffusion under confinement

Both thermodynamic and transport properties of molecular species are strongly influenced by the effect of confinement exerted by microporous materials such as zeolites. The nature of particle-framework interactions, along with geometric effects (size, shape, and connectivity of the pores), provides the energy landscape for the transport process and plays a major role in determining the aptitude of the diffusing species to migrate from pore to pore. Geometrical restrictions can cause a sharp separation on the time scales involved in the diffusion process: intracage motion (short times) and intercage migration (long times). Zeolites provide a three-dimensional framework (connected channels and cages with finite capacity) which, when reduced to its essential constituents, can be represented as a set of structured lattice points (cells) evolving in time according to well defined local rules: these are the basic ingredients of Cellular Automata (CA) models. With their parallel, space-time discrete nature, CA algo-rithms represent a very convenient environment in which physical systems can be modelled in a reductionistic approach, in order to cover large scales of space and time. We constructed a CA satisfying detailed balance to model intercage diffusion and equilibrium properties of particles adsorbed in a ZK4 zeolite.