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

Abstract

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.

A non-equilibrium thermodynamics model for combined adsorption and diffusion processes in micro- and nanopores

“…For α > 10, interactions monotonically reduce the effective diffusion coefficient as c increases. As in the previous case, the non-monotonic behavior manifested by the correction factor agrees well with the non-monotonic behavior of the effective diffusion coefficient observed in simulations and experiments 12,[28][29][30] .…”

“…Our purpose in this article is to propose a simple model able to analyze the mutual influence of diffusion and adsorption processes in micro and nanopores, a situation observed in zeolites, bentonites or in new engineered highly porous materials 19,21,[24][25][26][27] . We are interested in provide a simple theoretical model able to explain, at least in qualitative form, how this mutual influence is responsible for interesting effects observed in experiments 12 and recently studied via molecular dynamics and cellular automaton techniques on the diffusion properties of the particles in the pore [28][29][30] . Examples of these effects are the non-monotonic behavior of the diffusivity as a function of particle concentration or particle loading of the pore, or even the strong suppression of self-diffusivity as the number of particles in the pore increases [28][29][30] .…”

“…We are interested in provide a simple theoretical model able to explain, at least in qualitative form, how this mutual influence is responsible for interesting effects observed in experiments 12 and recently studied via molecular dynamics and cellular automaton techniques on the diffusion properties of the particles in the pore [28][29][30] . Examples of these effects are the non-monotonic behavior of the diffusivity as a function of particle concentration or particle loading of the pore, or even the strong suppression of self-diffusivity as the number of particles in the pore increases [28][29][30] . The model describes diffusion of one component in another at rest by means of the Fick law and adsorption through a generalized Langmuir equation obtained from non-equilibrium thermodynamics 4 .…”

“…The generalization to the case when non-isothermal effects, such as pervaporation associated to the mass transport through a zeolite membrane could also be performed by following a non-equilibrium thermodynamics analysis similar to that of Ref. [30].…”

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

“…Methane molecules, represented by the united atom approximation as Lennard-Jones (LJ) spheres, confined in the all-silica zeolite ITQ-29 (formerly called ZK4) have been widely used in the literature as a host-guest system to test statistical-mechanical theories, adsorptiondiffusion models, methods for the calculation of free energy profiles, and coarse-graining approaches under various computational environments (like kinetic Monte Carlo and Cellular Automata). [27][28][29][30][31][45][46][47][48][49][50][51] The ITQ-29 framework is particularly interesting because of its peculiar structure of relatively wide pores (when compared to methane size), called α-cages (∼ 11.4 Å in diameter), arranged in a simple cubic network (ν = 6), and interconnected through narrower eight-ringed windows (∼ 4.5 Å in diameter), allowing the passage of one methane molecule at a time. We modeled guest-guest and hostguest interactions according to the force fields used by Dubbeldam et al 47 with a cutoff of 12 Å, and, since the zeolite flexibility does not affect significantly the sorption properties of methane (although it would be not negligible for larger molecules 52 ), a pre-tabulation of the host-guest potential energy on a grid of ∼ 0.2 Å of spacing allowed for a significant reduction of the CPU time of the simulations.…”