Investigating the influence of diffusional coupling on mixture permeation across porous membranes

Using Molecular Simulations to Unravel the Benefits of Characterizing Mixture Permeation in Microporous Membranes in Terms of the Spreading Pressure

The separation performance of microporous crystalline materials in membrane constructs is dictated by a combination of mixture adsorption and intracrystalline diffusion characteristics; the permeation selectivity S _perm is a product of the adsorption selectivity S _ads and the diffusion selectivity, S _diff. The primary objective of this article is to gain fundamental insights into S _ads and S _diff by use of molecular simulations. We performed configurational-bias Monte Carlo (CBMC) simulations of mixture adsorption equilibrium and molecular dynamics (MD) simulations of guest self-diffusivities of a number of binary mixtures of light gaseous molecules (CO₂, CH₄, N₂, H₂, and C₂H₆) in a variety of microporous hosts of different pore dimensions and topologies. Irrespective of the bulk gas compositions and bulk gas fugacities, the adsorption selectivity, S _ads, is found to be uniquely determined by the adsorption potential, Φ, a convenient and practical proxy for the spreading pressure π that is calculable using the ideal adsorbed solution theory for mixture adsorption equilibrium. The adsorption potential Φ is also a proxy for the pore occupancy and is the thermodynamically appropriate yardstick to determine the loading and composition dependences of intracrystalline diffusivities and diffusion selectivities, S _diff. When compared at the same Φ, the component permeabilities, Π _i for CO₂, CH₄, and N₂, determinable from CBMC/MD data, are found to be independent of the partners in the various mixtures investigated and have practically the same values as the values for the corresponding unary permeabilities. In all investigated systems, the H₂ permeability in a mixture is significantly lower than the corresponding unary value. These reported results have important practical consequences in process development and are also useful for screening of materials for use as membrane devices.

Water/Alcohol Mixture Adsorption in Hydrophobic Materials: Enhanced Water Ingress Caused by Hydrogen Bonding

Microporous crystalline porous materials such as zeolites, metal-organic frameworks, and zeolitic imidazolate frameworks (ZIFs) have potential use for separating water/alcohol mixtures in fixed bed adsorbers and membrane permeation devices. For recovery of alcohols present in dilute aqueous solutions, the adsorbent materials need to be hydrophobic in order to prevent the ingress of water. The primary objective of this article is to investigate the accuracy of ideal adsorbed solution theory (IAST) for prediction of water/alcohol mixture adsorption in hydrophobic adsorbents. For this purpose, configurational bias Monte Carlo (CBMC) simulations are used to determine the component loadings for adsorption equilibrium of water/methanol and water/ethanol mixtures in all-silica zeolites (CHA, DDR, and FAU) and ZIF-8. Due to the occurrence of strong hydrogen bonding between water and alcohol molecules and attendant clustering, IAST fails to provide quantitative estimates of the component loadings and the adsorption selectivity. For a range of operating conditions, the water loading in the adsorbed phase may exceed that of pure water by one to two orders of magnitude. Furthermore, the occurrence of water-alcohol clusters moderates size entropy effects that prevail under pore saturation conditions. For quantitative modeling of the CBMC, simulated data requires the application of real adsorbed solution theory by incorporation of activity coefficients, suitably parameterized by the Margules model for the excess Gibbs free energy of adsorption.

Thermodynamically Consistent Methodology for Estimation of Diffusivities of Mixtures of Guest Molecules in Microporous Materials

The Maxwell-Stefan (M-S) formulation, that is grounded in the theory of irreversible thermodynamics, is widely used for describing mixture diffusion in microporous crystalline materials such as zeolites and metal-organic frameworks (MOFs). Binary mixture diffusion is characterized by a set of three M-S diffusivities: Đ ₁, Đ ₂, and Đ ₁₂. The M-S diffusivities Đ ₁ and Đ ₂ characterize interactions of guest molecules with pore walls. The exchange coefficient Đ ₁₂ quantifies correlation effects that result in slowing-down of the more mobile species due to correlated molecular jumps with tardier partners. The primary objective of this article is to develop a methodology for estimating Đ ₁, Đ ₂, and Đ ₁₂ using input data for the constituent unary systems. The dependence of the unary diffusivities Đ ₁ and Đ ₂ on the pore occupancy, θ, is quantified using the quasi-chemical theory that accounts for repulsive, or attractive, forces experienced by a guest molecule with the nearest neighbors. For binary mixtures, the same occupancy dependence of Đ ₁ and Đ ₂ is assumed to hold; in this case, the occupancy, θ, is calculated using the ideal adsorbed solution theory. The exchange coefficient Đ ₁₂ is estimated from the data on unary self-diffusivities. The developed estimation methodology is validated using a large data set of M-S diffusivities determined from molecular dynamics simulations for a wide variety of binary mixtures (H₂/CO₂, Ne/CO₂, CH₄/CO₂, CO₂/N₂, H₂/CH₄, H₂/Ar, CH₄/Ar, Ne/Ar, CH₄/C₂H₆, CH₄/C₃H₈, and C₂H₆/C₃H₈) in zeolites (MFI, BEA, ISV, FAU, NaY, NaX, LTA, CHA, and DDR) and MOFs (IRMOF-1, CuBTC, and MgMOF-74).

Thermodynamic Insights into the Characteristics of Unary and Mixture Permeances in Microporous Membranes

The primary objective of this article is to gain fundamental insights into the dependences of component permeances Π _i in microporous membranes on the operating conditions (upstream partial pressures, temperature, and feed composition). It is argued that the permeances Π _i for unary systems and mixtures need to be compared on the basis of the adsorption potential πA/RT, a convenient and practical proxy for the spreading pressure π that is calculable using the ideal adsorbed solution theory for mixture adsorption equilibrium. The use of πA/RT as a yardstick serves to elucidate and rationalize a wide variety of published experimental Π _i data on unary and mixture permeances in microporous membranes. For cage-type host structures such as SAPO-34, DDR, and ZIF-8, the Π _i values are uniquely dictated by the magnitude of πA/RT, irrespective of the partner species in the mixture. For MFI membranes, the tardier species slows down the more mobile partners due to correlated molecular motion within the channels; the degree of correlation is also a function of πA/RT.

Highlighting the Influence of Thermodynamic Coupling on Kinetic Separations with Microporous Crystalline Materials

The main focus of this article is on mixture separations that are driven by differences in intracrystalline diffusivities of guest molecules in microporous crystalline adsorbent materials. Such "kinetic" separations serve to over-ride, and reverse, the selectivities dictated by mixture adsorption equilibrium. The Maxwell-Stefan formulation for the description of intracrystalline fluxes shows that the flux of each species is coupled with that of the partner species. For n-component mixtures, the coupling is quantified by a n × n dimensional matrix of thermodynamic correction factors with elements Γ _ij ; these elements can be determined from the model used to describe the mixture adsorption equilibrium. If the thermodynamic coupling effects are essentially ignored, i.e., the Γ _ij is assumed to be equal to δ _ij , the Kronecker delta, the Maxwell-Stefan formulation degenerates to yield uncoupled flux relations. The significance of thermodynamic coupling is highlighted by detailed analysis of separations of five different mixtures: N₂/CH₄, CO₂/C₂H₆, O₂/N₂, C₃H₆/C₃H₈, and hexane isomers. In all cases, the productivity of the purified raffinate, containing the tardier species, is found to be significantly larger than that anticipated if the simplification Γ _ij = δ _ij is assumed. The reason for the strong influence of Γ _ij on transient breakthroughs is traceable to the phenomenon of uphill intracrystalline diffusion of more mobile species. The major conclusion to emerge from this study is that modeling of kinetic separations needs to properly account for the thermodynamic coupling effects.

Occupancy Dependency of Maxwell-Stefan Diffusivities in Ordered Crystalline Microporous Materials

Molecular dynamics simulation data for a variety of binary guest mixtures (H₂/CO₂, Ne/CO₂, CH₄/CO₂, CO₂/N₂, H₂/CH₄, H₂/Ar, CH₄/Ar, Ar/Kr, Ne/Ar, CH₄/C₂H₆, CH₄/C₃H₈, C₂H₆C₃H₈, CH₄/nC₄H₁₀, and CH₄/nC₅H₁₁) in zeolites (MFI, BEA, ISV, FAU (all-silica), NaY, NaX, LTA, CHA, DDR) and metal-organic frameworks (MOFs) (IRMOF-1, CuBTC, MgMOF-74) show that the Maxwell-Stefan (M-S) diffusivities, Đ ₁, Đ ₂, Đ ₁₂, are strongly dependent on the molar loadings. The main aim of this article is to develop a fundamental basis for describing the loading dependence of M-S diffusivities. Using the ideal adsorbed solution theory, a thermodynamically rigorous definition of the occupancy, θ, is derived; this serves as a convenient proxy for the spreading pressure, π, and provides the correct metric to describe the loading dependence of diffusivities. Configurational-bias Monte Carlo simulations of the unary adsorption isotherms are used for the calculation of the spreading pressure, π, and occupancy, θ. The M-S diffusivity, Đ _i , of either constituent in binary mixtures has the same value as that for unary diffusion, provided the comparison is made at the same θ. Furthermore, compared at the same value of θ, the M-S diffusivity Đ _i of any component in a mixture does not depend on it partner species. The Đ _i versus θ dependence is amenable to simple interpretation using lattice-models. The degree of correlations, defined by the ratio Đ ₁/Đ ₁₂, that characterizes mixture diffusion shows a linear increase with occupancy θ, implying that correlations become increasingly important as pore saturation conditions are approached.

Facile synthesis of oxidized activated carbons for high-selectivity and low-enthalpy CO2 capture from flue gas

The oxidized activated carbon obtained using a facile synthetic approach shows high-capacity and low-enthalpy CO₂ capture with a selectivity of 48.5 toward flue gas, which is double that of the pristine activated carbon.

Highlighting diffusional coupling effects in zeolite catalyzed reactions by combining the Maxwell–Stefan and Langmuir–Hinshelwood formulations

The combined phenomena of intra-crystalline adsorption, diffusion and reversible chemical reactions inside microporous crystalline zeolite catalyst particles are described by combining the Langmuir–Hinshelwood kinetics with the Maxwell–Stefan (M–S) diffusion formulation.

Tracing the origins of transient overshoots for binary mixture diffusion in microporous crystalline materials

Due to thermodynamic coupling overshoots in the loading of the more mobile species are observed during transient uptake.

Hydroquinone and Quinone-Grafted Porous Carbons for Highly Selective CO2 Capture from Flue Gases and Natural Gas Upgrading

Hydroquinone and quinone functional groups were grafted onto a hierarchical porous carbon framework via the Friedel-Crafts reaction to develop more efficient adsorbents for the selective capture and removal of carbon dioxide from flue gases and natural gas. The oxygen-doped porous carbons were characterized with scanning electron microscopy, transmission electron microscopy, X-ray powder diffraction, Fourier transform infrared spectroscopy, and Raman spectroscopy. CO2, CH4, and N2 adsorption isotherms were measured and correlated with the Langmuir model. An ideal adsorbed solution theory (IAST) selectivity for the CO2/N2 separation of 26.5 (298 K, 1 atm) was obtained on the hydroquinone-grafted carbon, which is 58.7% higher than that of the pristine porous carbon, and a CO2/CH4 selectivity value of 4.6 (298 K, 1 atm) was obtained on the quinone-grafted carbon (OAC-2), which represents a 28.4% improvement over the pristine porous carbon. The highest CO2 adsorption capacity on the oxygen-doped carbon adsorbents is 3.46 mmol g(-1) at 298 K and 1 atm. In addition, transient breakthrough simulations for CO2/CH4/N2 mixture separation were conducted to demonstrate the good separation performance of the oxygen-doped carbons in fixed bed adsorbers. Combining excellent adsorption separation properties and low heats of adsorption, the oxygen-doped carbons developed in this work appear to be very promising for flue gas treatment and natural gas upgrading.

Uphill diffusion in multicomponent mixtures

Diffusional coupling effects may cause uphill transport of a species against its concentration gradient. Transient overshoots and serpentine equilibration trajectories in composition space are fingerprints of uphill diffusion. Serpentine diffusion trajectories may enter meta-stable zones, leading to spontaneous emulsification and the Ouzo effect.

Methodologies for evaluation of metal–organic frameworks in separation applications

The separation performance of fixed-bed adsorbers is governed by a number of factors that include (a) adsorption selectivity, (b) uptake capacity, and (c) intra-crystalline diffusion limitations.

Influence of adsorption thermodynamics on guest diffusivities in nanoporous crystalline materials

Published experimental data, underpinned by molecular simulations, are used to highlight the strong influence of adsorption thermodynamics on diffusivities of guest molecules inside ordered nanoporous crystalline materials such as zeolites, metal-organic frameworks (MOFs), and zeolitic imidazolate frameworks (ZIFs). For cage-type structures (e.g. LTA, CHA, DDR, and ZIF-8), the variation of the free energy barrier for inter-cage hopping across the narrow windows, -δFi, provides a rationalization of the observed strong influence of pore concentrations, ci, on diffusivities. In open structures with large pore volumes (e.g. FAU, IRMOF-1, CuBTC) and within channels (MFI, BEA, MgMOF-74, MIL-47, MIL-53), the pore concentration (ci) dependence of the self- (Di,self), Maxwell-Stefan (Đi), and Fick (Di) diffusivities are often strongly dictated by the inverse thermodynamic correction factor, 1/Γi≡∂ln ci/∂ln pi; the magnitudes of the diffusivities are dictated by the binding energies for adsorption. For many guest-host combinations Đi-ci dependence is directly related to the 1/Γivs. ci variation. When molecular clustering occurs, we get 1/Γi > 1, causing unusual Đivs. ci dependencies. The match, or mis-match, between the periodicity of the pore landscape and the conformations of adsorbed chain molecules often leads to non-monotonic variation of diffusivities with chain lengths.