Extending effective medium theory to finite size systems: Theory and simulation for permeation in mixed-matrix membranes

How 2D Nanoflakes Improve Transport in Mixed Matrix Membranes: Insights from a Simple Lattice Model and Dynamic Mean Field Theory

Mixed matrix membranes (MMMs), incorporating graphene and graphene oxide structural fragments, have emerged as promising materials for challenging gas separation processes. What remains unclear is the actual molecular mechanism responsible for the enhanced permeability and perm-selectivity of these materials. With the fully atomistic models still unable to handle the required time and length scales, here, we employ a simple qualitative model based on the lattice representation of the physical system and dynamic mean field theory. We demonstrate that the performance enhancement results from the flux-regularization impact of the 2D nanoflakes and that this effect sensitively depends on the orientation of the nanoflakes and the properties of the interface between the nanoflakes and the polymer.

Monte Carlo Simulations for the Estimation of the Effective Permeability of Mixed-Matrix Membranes

Recent years have seen the explosive development of mixed-matrix membranes (MMMs) for a myriad of applications. In gas separation, it is desired to concurrently enhance the permeability, selectivity and physicochemical properties of the membrane. To help achieving these objectives, experimental characterization and predictive models can be used synergistically. In this investigation, a Monte Carlo (MC) algorithm is proposed to rapidly and accurately estimate the relative permeability of ideal MMMs over a wide range of conditions. The difference in diffusivity coefficients between the polymer matrix and the filler particle is used to adjust the random progression of the migrating species inside each phase. The solubility coefficients of both phases at the polymer−filler interface are used to control the migration of molecules from one phase to the other in a way to achieve progressively phase equilibrium at the interface. Results for various MMMs were compared with the results obtained with the finite difference method under identical conditions, where the results from the finite difference method are used in this investigation as the benchmark method to test the accuracy of the Monte Carlo algorithm. Results were found to be very accurate (in general, <1% error) over a wide range of polymer and filler characteristics. The MC algorithm is simple and swift to implement and provides an accurate estimation of the relative permeability of ideal MMMs. The MC method can easily be extended to investigate more readily non-ideal MMMs with particle agglomeration, interfacial void, polymer-chain rigidification and/or pore blockage, and MMMs with any filler geometry.

Recent Development in Composite Membranes for Flow Batteries

Flow batteries (FBs) are one of the most attractive candidates for stationary energy storage and vital in realizing the wide application of renewable energies. Membranes play an important role in isolating redox couples while transporting ions to close the internal electrical circuit. Therefore, membranes with high selectivity and conductivity are highly important. Among different membranes, a composite membrane with independent design of support layer and thin selective top layer becomes one of the most promising candidates to break the trade-off between selectivity and conductivity. In this Review, recent studies on composite membranes for FBs and the principles of membrane design in different systems are discussed and summarized. Finally, the future direction on membrane design for different FBs is presented, which will provide an extensive, comprehensive reference to design and construct high-performance composite membranes for FBs.

Modeling Permeation through Mixed-Matrix Membranes: A Review

Over the past three decades, mixed-matrix membranes (MMMs), comprising an inorganic filler phase embedded in a polymer matrix, have emerged as a promising alternative to overcome limitations of conventional polymer and inorganic membranes. However, while much effort has been devoted to MMMs in practice, their modeling is largely based on early theories for transport in composites. These theories consider uniform transport properties and driving force, and thus models for the permeability in MMMs often perform unsatisfactorily when compared to experimental permeation data. In this work, we review existing theories for permeation in MMMs and discuss their fundamental assumptions and limitations with the aim of providing future directions permitting new models to consider realistic MMM operating conditions. Furthermore, we compare predictions of popular permeation models against available experimental and simulation-based permeation data, and discuss the suitability of these models for predicting MMM permeability under typical operating conditions.

Structure and Gas Transport at the Polymer-Zeolite Interface: Insights from Molecular Dynamics Simulations

We investigate the structure of polyimide (PI) at the surface of a silicalite zeolite (MFI), as part of a model hybrid organic-inorganic mixed matrix membrane system, through equilibrium molecular dynamics simulations. Furthermore, we report a comparison of the adsorption and transport characteristics of pure components CO₂ and CH₄ in PI, MFI, and PI-MFI composite membranes. It is seen that incorporation of MFI zeolite into PI results in the formation of densified polymer layers (rigidified region) near the surface, having thickness around 1.2 nm, before bulklike behavior of the polymer is attained, contrary to empirical fits suggesting the existence of an approximately 1 μm thick interface between the polymer and filler. This region offers an extra resistance to gas diffusion especially for the gas with a larger kinetic diameter, CH₄, thus improving the CO₂/CH₄ kinetic selectivity in the PI-MFI composite membrane. Furthermore, we find that the kinetic selectivity of CO₂ over CH₄ in the rigidified region increases with temperature and that additivity of transport resistances in MFI, interfacial layer, and bulklike region of the polymer satisfactorily explains transport behavior in the composite sandwich investigated. The gas adsorption isotherms are extracted considering the dynamics and structural transitions in the PI and PI-MFI composite upon gas adsorption, and it is seen that the rigidified layer affects the gas adsorption in the polymer in the PI-MFI hybrid system. A significant increase in CO₂/CH₄ selectivity as well as gas permeability is observed in the PI-MFI composite membrane compared to that in the pure PI polymer membrane, which is correlated with the high selectivity of the rigidified interfacial layer in the polymer. Thus, while enhancing transport resistance, the rigidified layer is beneficial to membrane selectivity, leading to improved performance based on the Robeson upper bound plot for polymers.