Investigating the non-idealities in adsorption of CO2-bearing mixtures in cation-exchanged zeolites

Does Mixed Linker-Induced Surface Heterogeneity Impact the Accuracy of IAST Predictions in UiO-66-NH2?

To move toward more energy-efficient adsorption-based processes, there is a need for accurate multicomponent data under realistic conditions. While the Ideal Adsorbed Solution Theory (IAST) has been established as the preferred prediction method due to its simplicity, limitations and inaccuracies for less ideal adsorption systems have been reported. Here, we use amine-functionalized derivatives of the UiO-66 structure to change the extent of homogeneity of the internal surface toward the adsorption of the two probe molecules carbon dioxide and ethylene. Although it might seem plausible that more functional groups lead to more heterogeneity and, thus, less accurate predictions by IAST, we find a mixed-linker system with increased heterogeneity in terms of added adsorption sites where IAST predictions and experimental loadings agree exceptionally well. We show that incorporating uncertainty analysis into predictions with IAST is important for assessing the accuracy of these predictions. Energetic investigations combined with Grand Canonical Monte Carlo simulations reveal almost homogeneous carbon dioxide but heterogeneous ethylene adsorption in the mixed-linker material, resulting in local, almost pure phases of the individual components.

How Important Is the Internal Hydrophobicity of Metal-Organic Frameworks for the Separation of Water/Alcohol Mixtures?

Short-chain alcohols obtained by fermentation will play a key role in the industrial transformation toward green chemistry because of their use as fuel additives and fuels or for their conversion into olefins. The fermentation broth is often a highly diluted aqueous solution that requires separation, for instance, by liquid phase adsorption in nanoporous materials. However, entropy effects that prefer the adsorption of water might significantly reduce the separation efficiency─even in nanoporous materials with internal hydrophobicity. In this paper, we investigate this assumption by a case study on the separation of aqueous alcohol mixtures by liquid phase adsorption in CAU-10─an ultramicroporous metal-organic framework with internal hydrophobicity─using adsorption experiments and grand canonical Monte Carlo simulations to predict both the unary gas adsorption isotherms of ethanol, n-butanol, or water as well as the multicomponent liquid phase adsorption isotherms of their mixtures. It was observed that separation from the liquid phase is commonly driven by entropy effects and strong interactions between the guest molecules─both favoring the adsorption of water and thus complicating the separation of fermentation product by adsorption─while the internal hydrophobicity of CAU-10 is of comparatively little importance.

Influence of ultra-micropore volume of activated carbons prepared from noble mung bean on the adsorption properties of CO2, CH4, and N2

In this study, mung bean-based nanoporous activated carbons with different pore properties were prepared by varying the mass ratio of activating agent (KOH) and activation temperature.

How Reliable Is the Ideal Adsorbed Solution Theory for the Estimation of Mixture Separation Selectivities in Microporous Crystalline Adsorbents?

Microporous crystalline adsorbents such as zeolites and metal-organic frameworks (MOFs) have potential use in a wide variety of separation applications. The adsorption selectivity S _ads is a key metric that quantifies the efficacy of any microporous adsorbent in mixture separations. The Ideal Adsorbed Solution Theory (IAST) is commonly used for estimating the value of S _ads, with unary isotherms of the constituent guests as data inputs. There are two basic tenets underlying the development of the IAST. The first tenet mandates a homogeneous distribution of adsorbates within the pore landscape. The second tenet requires the surface area occupied by a guest molecule in the mixture to be the same as that for the corresponding pure component. Configurational-bias Monte Carlo (CBMC) simulations are employed in this article to highlight several scenarios in which the IAST fails to provide a quantitatively correct description of mixture adsorption equilibrium due to a failure to conform to either of the two tenets underpinning the IAST. For CO₂ capture with cation-exchanged zeolites and MOFs with open metal sites, there is congregation of CO₂ around the cations and unsaturated metal atoms, resulting in failure of the IAST due to an inhomogeneous distribution of adsorbates in the pore space. Thermodynamic non-idealities also arise due to the preferential location of CO₂ molecules at the window regions of 8-ring zeolites such as DDR and CHA or within pockets of MOR and AFX zeolites. Thermodynamic non-idealities are evidenced for water/alcohol mixtures due to molecular clustering engendered by hydrogen bonding. It is also demonstrated that thermodynamic non-idealities can be strong enough to cause selectivity reversals, which are not anticipated by the IAST.

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.

Using Molecular Simulations for Elucidation of Thermodynamic Nonidealities in Adsorption of CO2-Containing Mixtures in NaX Zeolite

Cation-exchanged zeolites are of potential use in pressure swing adsorption (PSA) technologies for CO₂ capture applications. Published experimental data for CO₂/CH₄, CO₂/N₂, and CO₂/C₃H₈ mixture adsorption in NaX zeolite, also commonly referred to by its trade name 13X, have demonstrated that the ideal adsorbed solution theory (IAST) fails to provide adequately accurate estimates of mixture adsorption equilibrium. In particular, the IAST estimates of CO₂/CH₄ and CO₂/N₂ selectivities are significantly higher than those realized in experiments. For CO₂/C₃H₈ mixtures, the IAST fails to anticipate the selectivity reversal phenomena observed in experiments. In this article, configurational-bias Monte Carlo (CBMC) simulations are employed to provide confirmation of the observed thermodynamic nonidealities in adsorption of CO₂/CH₄, CO₂/N₂, and CO₂/C₃H₈ mixtures in NaX zeolite. The CBMC simulations provide valuable insights into the root cause of the failure of the IAST, whose applicability mandates a homogeneous distribution of adsorbates within the pore landscape. By sampling 10⁵ equilibrated spatial locations of individual guest molecules within the cages of NaX zeolite, the radial distribution functions (RDFs) of each of the pairs of guest molecules are determined. Examination of the RDFs clearly reveals congregation effects, wherein the CO₂ guests occupy positions in close proximity to the Na⁺ cations. The positioning of the partner molecules (CH₄, N₂, or C₃H₈) is further removed from the CO₂ guest molecules; consequently, the competition in mixture adsorption faced by the partner molecules is less severe than that anticipated by the IAST. The important message to emerge from this article is the need for quantification of thermodynamic nonideality effects in mixture adsorption.

Metrics for Evaluation and Screening of Metal-Organic Frameworks for Applications in Mixture Separations

For mixture separations, metal-organic frameworks (MOFs) are of practical interest. Such separations are carried out in fixed bed adsorption devices that are commonly operated in a transient mode, utilizing the pressure swing adsorption (PSA) technology, consisting of adsorption and desorption cycles. The primary objective of this article is to provide an assessment of the variety of metrics that are appropriate for screening and ranking MOFs for use in fixed bed adsorbers. By detailed analysis of several mixture separations of industrial significance, it is demonstrated that besides the adsorption selectivity, the performance of a specific MOF in PSA separation technologies is also dictated by a number of factors that include uptake capacities, intracrystalline diffusion influences, and regenerability. Low uptake capacities often reduce the efficacy of separations of MOFs with high selectivities. A combined selectivity-capacity metric, Δq, termed as the separation potential and calculable from ideal adsorbed solution theory, quantifies the maximum productivity of a component that can be recovered in either the adsorption or desorption cycle of transient fixed bed operations. As a result of intracrystalline diffusion limitations, the transient breakthroughs have distended characteristics, leading to diminished productivities in a number of cases. This article also highlights the possibility of harnessing intracrystalline diffusion limitations to reverse the adsorption selectivity; this strategy is useful for selective capture of nitrogen from natural gas.

Elucidation of Selectivity Reversals for Binary Mixture Adsorption in Microporous Adsorbents

The adsorption selectivity, S _ads, is a key metric that quantifies the efficacy of any adsorbent in mixture separations. It is common practice to use ideal adsorbed solution theory (IAST) for estimating the value of S _ads, using unary isotherm data inputs. In a number of experimental investigations, the phenomena of selectivity reversals and adsorption azeotropy (S _ads = 1) have been reported in the published literature; such reversals may result from changes in mixture compositions, pressures, or pore loadings. In many cases, IAST is unable to anticipate such selectivity reversals. In this article, configurational-bias Monte Carlo simulations are used to gain insights into the phenomena of selectivity reversals. Two fundamentally different scenarios of selectivity reversals have been identified. In the first scenario, selectivity reversals are caused by inhomogeneous distribution of adsorbates due to preferential location and siting of a guest species in the pore space. For example, CO₂ locates preferentially in the side pockets of mordenite and in window regions of DDR, CHA, and LTA zeolites. CO₂ also congregates around the extra-framework cations of NaX zeolite. IAST fails to anticipate such selectivity reversals because its development relies on the assumption that the competition between guest species is uniform within the pore space. In the second scenario, selectivity reversals are caused by entropy effects that manifest near pore saturation conditions; the component that is preferentially adsorbed is the one that has the higher packing efficiency. For a homologous series of compounds, the component with the smaller chain length is favored at high pore occupancies. For adsorption of mixtures of alkane isomers within the intersecting channel network of MFI zeolite, the linear isomer is favored on the basis of entropic considerations.

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.