Diffusion of binary mixtures in zeolites: molecular dynamics simulations versus Maxwell–Stefan theory

Trajectory-Extending Kinetic Monte Carlo Simulations to Evaluate Pure and Gas Mixture Diffusivities through a Dense Polymeric Membrane

With renewed interest in CO2 separations, carbon molecular sieving (CMS) membrane performance evaluation requires diffusion coefficients as inputs to have a reliable estimate of the permeability. An optimal material is desired to have both high selectivity and permeability. Gases diffusing through dense CMS and polymeric membranes experience extended subdiffusive regimes, which hinders reliable extraction of diffusion coefficients from mean squared displacement data. We improve the sampling of the diffusive landscape by implementing the trajectory-extending kinetic Monte Carlo (TEKMC) technique to efficiently extend molecular dynamics (MD) trajectories from ns to μs time scales. The obtained self-diffusion coefficient of pure CO2 in CMS membranes derived from a 6FDA/BPDA-DAM precursor polymer melt is found to linearly increase from 0.8-1.3 × 10-6 cm2 s-1 in the pressure range of 1-20 bar, which supports previous experimental findings. We also extended the TEKMC algorithm to evaluate the mixture diffusivities in binary mixtures to determine the permselectivity of CO2 in CH4 and N2 mixtures. The mixture diffusion coefficient of CO2 ranges from 1.3-7 × 10-6 cm2 s-1 in the binary mixture CO2/CH4, which is significantly higher than the pure gas diffusion coefficient. Robeson plot comparisons show that the permselectivity obtained from pure gas diffusion data is significantly lower than that predicted using mixture diffusivity data. Specifically, in the case of the CO2/N2 mixture, we find that using mixture diffusivities led to permselectivities lying above the Robeson limit highlighting the importance of using mixture diffusivity data for an accurate evaluation of the membrane performance. Combined with gas solubilities obtained from grand canonical Monte Carlo (GCMC) simulations, our work shows that simulations with the TEKMC method can be used to reliably evaluate the performance of materials for gas separations.

Perfluoropolymer/Molecular Sieve Mixed-Matrix Membranes

Despite the outstanding chemical, thermal and transport properties of amorphous and glassy perfluorinated polymers, only few works exist on the preparation and transport properties of perfluoropolymer/molecular sieves mixed-matrix membranes (MMMs), probably because of their poor compatibility. In this review, the compatibilization of ceramic molecular sieves with perfluorinated matrices is considered first, examining the effect of the surface treatment on the gas transport properties of the filler. Then the preparation of the defect-free hybrid membranes and their gas separation capabilities are described. Finally, recent modelling of the gas transport properties of the perfluoropolymer MMMs is reviewed. The systematic use of molecular sieves of different size and shape, either permeable or impermeable, and the calculation of the bulk transport properties of the molecular sieves-i.e., the unrestricted diffusion and permeability-allow to understand the nature of the physical phenomena at work in the MMMs, that is the larger the perfluoropolymer fractional free volume at the interface, and restricted diffusion at the molecular sieves. This knowledge led to the formulation of a new four-phase approach for the modelling of gas transport. The four-phase approach was implemented in the frame of the Maxwell model and also for the finite element simulation. The four-phase approach is a convenient representation of the transport in MMMs when more than one single interfacial effect is present.

Zeolite membranes – a review and comparison with MOFs

The latest developments in zeolite and MOF membranes are reviewed, with an emphasis on synthesis techniques. Industrial applications, hydrothermal stability, polymer-supported and mixed matrix membranes are some of the aspects discussed.

Potential Applications of Zeolite Membranes in Reaction Coupling Separation Processes

Future production of chemicals (e.g., fine and specialty chemicals) in industry is faced with the challenge of limited material and energy resources. However, process intensification might play a significant role in alleviating this problem. A vision of process intensification through multifunctional reactors has stimulated research on membrane-based reactive separation processes, in which membrane separation and catalytic reaction occur simultaneously in one unit. These processes are rather attractive applications because they are potentially compact, less capital intensive, and have lower processing costs than traditional processes. Therefore this review discusses the progress and potential applications that have occurred in the field of zeolite membrane reactors during the last few years. The aim of this article is to update researchers in the field of process intensification and also provoke their thoughts on further research efforts to explore and exploit the potential applications of zeolite membrane reactors in industry. Further evaluation of this technology for industrial acceptability is essential in this regard. Therefore, studies such as techno-economical feasibility, optimization and scale-up are of the utmost importance.

Testing the accuracy of correlations for multicomponent mass transport of adsorbed gases in metal-organic frameworks: diffusion of H2/CH4 mixtures in CuBTC

Mass transport of chemical mixtures in nanoporous materials is important in applications such as membrane separations, but measuring diffusion of mixtures experimentally is challenging. Methods that can predict multicomponent diffusion coefficients from single-component data can be extremely useful if these methods are known to be accurate. We present the first test of a method of this kind for molecules adsorbed in a metal-organic framework (MOF). Specifically, we examine the method proposed by Skoulidas, Sholl, and Krishna (SSK) ( Langmuir, 2003, 19, 7977) by comparing predictions made with this method to molecular simulations of mixture transport of H 2/CH 4 mixtures in CuBTC. These calculations provide the first direct information on mixture transport of any species in a MOF. The predictions of the SSK approach are in good agreement with our direct simulations of binary diffusion, suggesting that this approach may be a powerful one for examining multicomponent diffusion in MOFs. We also use our molecular simulation data to test the ideal adsorbed solution theory method for predicting binary adsorption isotherms and a method for predicting mixture self-diffusion coefficients.

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

The role of molecular interactions and interfaces in diffusion: Transport diffusivity and evaluation of the Darken approximation

Kinetic Monte Carlo (KMC) simulations are carried out to directly study diffusion of benzene through thin (37-100 nm) NaX zeolite membranes under a gradient in chemical potential. Nonlinearities in adsorbate loading near the membrane boundaries are shown to arise from the difference in adsorbate density between the zeolite and adjacent fluid phase. Direct extraction of the transport diffusivity from gradient KMC simulations enables testing of the Darken approximation. This rigorous approach reveals limitations of the Darken approximation and, for the first time, the potentially complex nonunique functionality and multiplicity of the transport diffusivity for strongly interacting adsorbates. In the companion paper we explore these nonlinear interfacial effects in the context of permeation through both single-crystal and polycrystalline membranes.

Analytical results for the reactivity of a single-file system

We derive analytical expressions for the reactivity of a single-file system with fast diffusion and particles entering and leaving the system at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size, and the conversion is about 100%. If the reaction is slow, then the reactivity becomes proportional to the system size, the loading, and the reaction rate constant. If the system size increases the reactivity goes to the geometric mean of the reaction rate constant and the rate of particles entering and leaving the system. For large systems, the number of unconverted particles decreases exponentially with distance from the open end.

Application of the general rate model and the generalized Maxwell-Stefan equation to the study of the mass transfer kinetics of a pair of enantiomers

The general rate model of chromatography can be coupled with the generalized Maxwell-Stefan equation that describes the surface diffusion flux. The resulting model is useful to describe the behavior of two enantiomers during their separation on chiral phases, cases in which the mass transfer kinetics is known to be sluggish. A case in point is the modeling of the elution profiles of the racemic mixture of the two enantiomers of 1-phenyl-1-propanol on cellulose tribenzoate coated on silica, a popular chiral stationary phase. The competitive equilibrium isotherm behavior of the two enantiomers on the chiral stationary phase was described using the competitive Tóth isotherm model. An excellent agreement between the experimental and the calculated profiles was observed in the whole range of experimental conditions investigated, at low and high column loadings.