Cellular automata for the mesoscopic simulation of adsorption and diffusion in zeolites

The thermodynamic and transport properties of molecules hosted in the confining framework of a microporous material like a zeolite are strongly affected by the geometrical restrictions imposed by the pore walls. In the ongoing effort to understand the phenomena induced by the effect of confinement, the use of numerical simulation methods at the atomistic scale like Molecular Dynamics turns out to be computationally very costly due to the large number of degrees of freedom involved. This motivated the search for a further simplified description of a host/guest system. In the present thesis a Cellular Automata approach has been used to embed the local, fully-reliable structure of cell thermodynamic models together with a kinetic scheme mimicking the competition mechanism in which guest molecules move between different locations in a zeolitic host. The resulting model is a Thermodynamic Partitioning Cellular Automaton (ThPCA), designed ad hoc to simulate both adsorption and transport properties of simple guest species in a LTA-type zeolitic host at the mesoscopic scale. Effects of correlation in the guests’ motion affecting their diffusivity under confinement are also modeled, thus making the ThPCA model an efficient and easy environment to perform coarse-grained simulations of adsorption and diffusion of simple molecules in microporous materials

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

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 α 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

Diffusion in tight confinement: a lattice-gas cellular automaton approach. II. Transport properties

In this second paper the authors study the transport properties of the lattice-gas cellular automaton presented in Paper I [J. Chem. Phys. 126, 194709 (2007)] to model adsorption and dynamics of particles in a lattice of confining cells. Their work shows how a surprisingly simple parallel rule applied to a static network of cells joined by links set in space and time can generate a wide range of dynamical behaviors. In their model the cells are the elementary constituent objects of the network. They are a portion of space structured in sites which are energetically different. Each cell can accommodate a given maximum number of particles, and each pair of neighboring cells can exchange at most one particle at a time. The predictions of the model are in qualitative agreement with both experimental observations and molecular dynamics simulation results

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

A Coarse-grained model for diffusion in zeolites based on clustering of short MD trajectories

Zeolites form a class of microporous aluminosilicates of great interest due to their multifarious applications in industry and everyday life. Their porous structure allows small molecules to be adsorbed and to diffuse inside crystals, and depending on the zeolite type and on the diffusant species a variety of behaviours is possible. Molecular Dynamics is now widely used in order to understand the microscopic mechanisms of adsorption and diffusion occurring within these materials as well as in MOFs and ZIFs. A major drawback of MD for this kind of systems is its high computational cost, so that coarse-grained methods, speeding up simulations without losing the essential features of dynamics, are valuable tools for exploring the behaviour of guest molecules on time and space scales hardly, if at all, reachable with ordinary MD. The first step in our proposed method is the clustering of MD trajectories to obtain a discretized version of the motion of adsorbed molecules within the zeolite. Each pore in the aluminosilicate is partitioned in a number of regions and each point in the original trajectory is mapped to the proper region based on a distance criterion. The regions correspond roughly to the main basins in the potential energy surface (PES)

Modelling diffusion in zeolites with cellular automata

Exploiting the analogy between the partitioned spatial structure of zeolites and the space-discrete nature of Cellular Automata (CA), we developed a probabilistic Cellular Automaton (CA) able to capture both static and transport properties of diffusing species in zeolites at a coarse-grained level. Our model uses cells to represent pores. It focuses on the sensitivity of each cell upon its instantaneous occupancy to mimic the particle-framework and particle-particle interactions of adsorbates into real zeolite pores. It makes use of local partition functions and kinetic barriers to build up a simple and fast evolution rule allowing our model to reproduce data such as adsorption isotherms, global and local distributions of occupancies inside of the zeolite pores, diffusivities, correlations in space and time, etc. from experimental and/or atomistic simulation. The local and parallel nature of our CA, together with its drastically reduced number of degrees of freedom makes it a powerful tool to enlarge the space-time scales of numerical simulations of diffusion in zeolites