Diffusion in tight confinement: A lattice-gas cellular automaton approach. I. Structural equilibrium properties

Abstract

The thermodynamic and transport properties of diffusing species in microporous materials are strongly influenced by their interactions with the confining framework, which provide the energy landscape for the transport process. The simple topology and the cellular nature of the alpha cages of a ZK4 zeolite suggest that it is appropriate to apply to the study of the problem of diffusion in tight confinement a time-space discrete model such as a lattice-gas cellular automaton (LGCA). In this paper we investigate the properties of an equilibrium LGCA constituted by a constant number of noninteracting identical particles, distributed among a fixed number of identical cells arranged in a three-dimensional cubic network and performing a synchronous random walk at constant temperature. Each cell of this network is characterized by a finite number of two types of adsorption sites: the exit sites available to particle transfer and the inner sites not available to such transfers. We represent the particle-framework interactions by assuming a differentiation in binding energy of the two types of sites. This leads to a strong dependence of equilibrium and transport properties on loading and temperature. The evolution rule of our LGCA model is constituted by two operations (randomization, in which the number of particles which will be able to try a jump to neighboring cells is determined, and propagation, in which the allowed jumps are performed), each one applied synchronously to all of the cells. The authors study the equilibrium distribution of states and the adsorption isotherm of the model under various conditions of loading and temperature. In connection with the differentiation in energy between exit and inner sites, the adsorption isotherm is described by a conventional Langmuir isotherm at high temperature and by a dual-site Langmuir isotherm at low temperature, while a first order diffuse phase transition takes place at very low temperature.