Introducing a Cellular Automaton as an Empirical Model to Study Static and Dynamic Properties of Molecules Adsorbed in Zeolites

Local free energies for the coarse-graining of adsorption phenomena: The interacting pair approximation

We investigate the coarse-graining of host-guest systems under the perspective of the local distribution of pore occupancies, along with the physical meaning and actual computability of the coarse-interaction terms. We show that the widely accepted approach, in which the contributions to the free energy given by the molecules located in two neighboring pores are estimated through Monte Carlo simulations where the two pores are kept separated from the rest of the system, leads to inaccurate results at high sorbate densities. In the coarse-graining strategy that we propose, which is based on the Bethe-Peierls approximation, density-independent interaction terms are instead computed according to local effective potentials that take into account the correlations between the pore pair and its surroundings by means of mean-field correction terms without the need for simulating the pore pair separately. Use of the interaction parameters obtained this way allows the coarse-grained system to reproduce more closely the equilibrium properties of the original one. Results are shown for lattice-gases where the local free energy can be computed exactly and for a system of Lennard-Jones particles under the effect of a static confining field.

Diffusion of interacting particles in discrete geometries: Equilibrium and dynamical properties

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.110601]. 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 interparticle 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 1/L 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.

A parallelizable block cellular automaton for the study of diffusion of binary mixtures containing CO2 in microporous materials

We applied a method based on a block cellular automaton (BCA) algorithm to the study of diffusion of various binary mixtures adsorbed in a model microporous material, such as zeolite ZK4. Our aim was to test the capability of our model to cope with systems in which more than one species is present, using a set of parameters based on heuristic considerations from the molecular dynamics (MD) results present in the literature. A rigorous methodology for the assignment of suitable adsorption energies and diffusion activation barriers for our BCA has not been developed yet, nonetheless the results were quite interesting at this stage and we obtained a good qualitative agreement with MD data in the literature. The mixtures we investigated contain CO(2), which causes the so-called segregation-effect, a strong suppression of self-diffusivity of co-adsorbed species. This effect gives rise to relevant problems in the application of some well established and robust methods, while our model proved to be able to reproduce both the common features and the segregation anomaly in the trends of diffusion.

The central cell model: a mesoscopic hopping model for the study of the displacement autocorrelation function

On the mesoscale, the molecular motion in a microporous material can be represented as a sequence of hops between different pore locations and from one pore to the other. On the same scale, the memory effects in the motion of a tagged particle are embedded in the displacement autocorrelation function (DACF), the discrete counterpart of the velocity autocorrelation function (VACF). In this paper, a mesoscopic hopping model, based on a lattice-gas automata dynamics, is presented for the coarse-grained modeling of the DACF in a microporous material under conditions of thermodynamic equilibrium. In our model, that we will refer to as central cell model, the motion of one tagged particle is mimicked through probabilistic hops from one location to the other in a small lattice of cells where all the other particles are indistinguishable; the cells closest to the one containing the tagged particle are simulated explicitly in the canonical ensemble, whereas the border cells are treated as mean-field cells in the grand-canonical ensemble. In the present paper, numerical simulation of the central cell model are shown to provide the same results as a traditional lattice-gas simulation. Along with this a mean-field theory of self-diffusion which incorporates time correlations is discussed.