Adsorption of binary and ternary hydrocarbon gas mixtures on activated carbon: Experimental determination and theoretical prediction of the ternary equilibrium data

Carbon dioxide separation and capture by adsorption: a review

Rising adverse impact of climate change caused by anthropogenic activities is calling for advanced methods to reduce carbon dioxide emissions. Here, we review adsorption technologies for carbon dioxide capture with focus on materials, techniques, and processes, additive manufacturing, direct air capture, machine learning, life cycle assessment, commercialization and scale-up.

Separation of Azeotropic Hydrofluorocarbon Refrigerant Mixtures: Thermodynamic and Kinetic Modeling for Binary Adsorption of HFC-32 and HFC-125 on Zeolite 5A

Hydrofluorocarbons (HFCs) have been used extensively as refrigerants over the past four decades; however, HFCs are currently being phased out due to large global warming potentials. As the next generation of hydrofluoroolefin refrigerants are phased in, action must be taken to responsibly and sustainably deal with the HFCs currently in circulation. Ideally, unused HFCs can be reclaimed and recycled; however, many HFCs in circulation are azeotropic or near-azeotropic mixtures and must be separated before recycling. Previously, pure gas isotherm data were presented for both HFC-125 (pentafluoroethane) and HFC-32 (difluoromethane) with zeolite 5A, and it was concluded that this zeolite could separate refrigerant R-410A (50/50 wt % HFC-125/HFC-32). To further investigate the separation capabilities of zeolite 5A, binary adsorption was measured for the same system using the Integral Mass Balance method. Zeolite 5A showed a selectivity of 9.6-10.9 for HFC-32 over the composition range of 25-75 mol % HFC-125. Adsorbed phase activity coefficients were calculated from binary adsorption data. The Spreading Pressure Dependent, modified nonrandom two-liquid, and modified Wilson activity coefficient models were fit to experimental data, and the resulting activity coefficient models were used in Real Adsorbed Solution Theory (RAST). RAST binary adsorption model predictions were compared with Ideal Adsorbed Solution Theory (IAST) predictions made using the Dual-Site Langmuir, Tóth, and Jensen and Seaton pure gas isotherm models. Both IAST and RAST yielded qualitatively accurate predictions; however, quantitative accuracy was greatly improved using RAST models. Diffusion behavior of HFC-125 and HFC-32 was also investigated by fitting the isothermal Fickian diffusion model to kinetic data. Molecular-level phenomena were investigated to understand both thermodynamic and kinetic behaviors.

Activity coefficient models for accurate prediction of adsorption azeotropes

In this study seven adsorption azeotropes involving binary systems and zeolite-based adsorbents were systematically investigated. Pure component isotherms and mixed-gas adsorption data were taken from published literature except for the benzene–propene system on silicalite, which is newly presented in this work using molecular simulations. Experimental adsorbed phase composition and total amount adsorbed of the azeotropic systems were compared with the predictions of several models including: the ideal adsorbed solution theory (IAST), the heterogeneous ideal adsorbed solution theory (HIAST) and the real adsorbed solution theory (RAST) coupled with the 1-parameter Margules (1-Margules) and the van Laar equations. In the latter two models an additional loading parameter was incorporated in the expression of the excess Gibbs energy to account for the reduced grand potential dependency of the activity coefficients in the adsorbed phase. It was found that the HIAST and RAST–1-Margules models were able to predict the azeotropic behaviour of some systems with good accuracy. However, only the RAST–van Laar model consistently showed an average relative deviation below 3% compared to experimental data for both the adsorbed phase composition and the total amount adsorbed across the systems. This modified van Laar equation is therefore preferable in those engineering applications when the location of adsorption azeotropes is required with great accuracy and when there is lack of detailed characterization of the adsorbent that is needed to carry out molecular simulations.

Application of pyridine-modified chitosan derivative for simultaneous adsorption of Cu(II) and oxyanions of Cr(VI) from aqueous solution

The bioadsorbent C1, which is a chitosan derivative prepared in a one-step synthesis, was successfully used to adsorb Cr(VI) and Cu(II) simultaneously. Here, for the first time the simultaneous adsorption of a cation and an anion was modeled using the Corsel model for kinetics and the Real Adsorbed Solution Theory model for equilibrium data. Batch studies of the adsorption of Cu(II) and Cr(VI) in single and binary aqueous solutions were performed as a function of initial solute concentration, contact time, and solution pH. The maximum adsorption capacities of C1 in single and binary aqueous solutions were 1.84 and 1.13 mmol g^-1 for Cu(II) and 3.86 and 0.98 mmol g^-1 for Cr(VI), respectively. The reuse of C1 was investigated, with Cu(II) ions being almost completely desorbed and fully re-adsorbed. For Cr(VI), the desorption was incomplete resulting in a lower re-adsorption. Energy-dispersive X-ray spectroscopy was used for mapping the distributions of Cr(VI) and Cu(II) adsorbed on the C1 surface in single and binary adsorption systems. Isothermal titration calorimetry experiments were performed for Cr(VI) and Cu(II) adsorption in single solutions. The thermodynamic parameters of adsorption showed that the adsorption of both metal ions was enthalpically driven, but entropically unfavorable.

Coupling a Feedforward Network (FN) Model to Real Adsorbed Solution Theory (RAST) to Improve Prediction of Bisolute Adsorption on Resins

When predicting bisolute adsorption, the adsorbed solution theory (AST) and real adsorbed solution theory (RAST) either frequently show high prediction deviations or require bisolute adsorption data. Emerging feedforward network (FN) models can provide high prediction accuracy but lack broad applicability. To avoid those limitations, adsorption experiments were performed for a total of 12 single solutes and 55 bisolutes onto two widely used resins (MN200 and XAD-4). Different FN-based models were then built and compared with AST and RAST, based on which a new modeling strategy coupling FN to RAST and requiring only single-solute data was proposed. The root-mean-square error (RMSE) of predictions by the FN-RAST is 0.082 log units for 50 bisolute adsorption on MN200, much lower than that by AST (0.164) and slightly higher than that by RAST (0.069) or the best FN model (0.068). The FN-RAST model further provided satisfactory predictions for 5 bisolute adsorption on XAD-4 (RMSE = 0.10), which is comparable to that by RAST (0.10) and much lower than those by AST (0.26) and FN model (0.38). Therefore, the FN-RAST enjoys both satisfactory prediction accuracy and some broad applicability. The values of Abraham descriptors E and S were also founded to help assess/compare the nonideal behavior in different bisolute mixtures.

Coordinated Water as New Binding Sites for the Separation of Light Hydrocarbons in Metal-Organic Frameworks with Open Metal Sites

Metal-organic frameworks with open metal sites are promising materials for gas separations. Particularly, the M₂(dobdc) (dobdc^4- = 2,5-dioxidobenzenedicarboxylate, M²⁺ = Co²⁺, Mn²⁺, Fe²⁺, ...) framework has been the Drosophila of this research field and has delivered groundbreaking results in terms of sorption selectivity. However, many studies focus on perfect two-component mixtures and use theoretical models, e.g., the ideal adsorbed solution theory, to calculate selectivities. Within this work, we shed light on the comparability of these selectivities with values obtained from propane/propene multicomponent measurements on the prototypical Co₂(dobdc) framework, and we study the impact of impurities like water on the selectivity. Despite the expected capacity loss, the presence of water does not necessarily lead to a decreased selectivity. Density functional theory calculations of the binding energies prove that the water molecules adsorbed to the metal centers introduce new binding sites for the adsorbates.

Predicting adsorption selectivities from pure gas isotherms for gas mixtures in metal-organic frameworks

We perform Grand Canonical Monte Carlo simulations on a lattice of Mg²⁺ sites (GCMC) for adsorption of four binary A/B mixtures, CH₄/N₂, CO/N₂, CO₂/N₂, and CO₂/CH₄, in the metal–organic framework Mg₂(2,5-dioxidobenzedicarboxylate), also known as CPO-27–Mg or Mg–MOF-74. We present a mean field co-adsorption isotherm model and show that its predictions agree with the GCMC results if the same quantum chemical ab initio data are used for Gibbs free energies of adsorption at the individual sites and for lateral interaction energies between the same, A⋯A and B⋯B, and unlike, A⋯B, adsorbed molecules. We use both approaches to test the assumption underlying Ideal Adsorbed Solution Theory (IAST), namely approximating A⋯B interaction energies as the arithmetic mean of A⋯A and B⋯B interaction energies. While IAST works well for mixtures with weak lateral interactions, CH₄/N₂ and CO/N₂, the deviations are large for mixtures with stronger lateral interactions, CO₂/N₂ and CO₂/CH₄. Motivated by the theory of London dispersion forces, we propose use of the geometric mean instead of the arithmetic mean and achieve substantial improvements. For CO₂/CH₄, the lateral interactions become anisotropic. To include this in the geometric mean co-adsorption model, we introduce an anisotropy factor. We propose a protocol, named co-adsorption mean field theory (CAMT), for co-adsorption selectivity prediction from known (experiment or simulation) pure component isotherms which is similar to the IAST protocol but uses the geometric mean to approximate mixed pair interaction energies and yields improved results for non-ideal mixtures.

A new mixing rule (geometric mean) is proposed with substantial improvements compared to the widely used ideal adsorbed solution theory for adsorbates with strong lateral interactions.

Langmuir's Theory of Adsorption: A Centennial Review

The 100th anniversary of Langmuir's theory of adsorption is a significant landmark for the physical chemistry and chemical engineering communities. Despite its simplicity, the Langmuir adsorption model captures the key physics of molecular interactions at interfaces and laid the foundation for further progress in understanding interfacial phenomena, developing new adsorbent materials, and designing engineering processes. The Langmuir model has had an exceptional impact on diverse fields within the chemical sciences (ranging from chemical biology to materials science), an impact that became clearer with the development of modified adsorption theories and continues to be relevant today.

Rigorous prognostication and modeling of gas adsorption on activated carbon and Zeolite-5A

Gas adsorption on various adsorbents is of highly important issue for the separation of gas mixtures in many industrial processes. In this work, estimation of pure gases (CH₄, N₂, CO₂, H₂, C₂H₄) adsorption on activated carbon (AC) and CO₂, CH₄, N₂ on Zeolite-5A adsorbent were studied by developing four different computing techniques, namely MLP-ANN, ANFIS, LSSVM, and PSO-ANFIS for a broad range of experimental data found in the literature. Temperature, pressure, pore size (only for AC) and kinetic diameter of adsorbed gases are considered as the inputs and the gas adsorption as the output parameters of the developed models. We also used several statistical and graphical tools to assess the accuracy and applicability of the proposed models. The results of the study suggest the reliability and validity of all the models developed for estimating the equilibrium adsorption of gases on the adsorbents. Also, it is found that of all the models developed, the ANN model estimates experimental data of the gas adsorption on AC more accurately due to its values of R² and AARD%, 0.9865 and 0.8948, respectively. Besides, PSO-ANFIS is the best model to prognosticate gas adsorption on zeolite 5A with R² and AARD%, 0.9897 and 0.9551, respectively.

Modeling Bisolute Adsorption of Aromatic Compounds Based on Adsorbed Solution Theories

A large number of organic contaminants are commonly found in industrial and municipal wastewaters. For proper unit design to remove contaminant mixtures by adsorption, multicomponent adsorption equilibrium models are necessary. The present work examined the applicability of Ideal Adsorbed Solution Theory (IAST), a prevailing thermodynamic model, and its derivatives, i.e., Segregated IAST (SIAST) and Real Adsorbed Solution Theory (RAST), to bisolute adsorption of organic compounds onto a hyper-cross-linked polystyrene resin, MN200. Both IAST and SIAST were found to be less accurate in fitting the experimental bisolute adsorption isotherms than RAST. RAST incorporated with an empirical four-parameter equation developed in this work can fit the adsorbed phase activity coefficients, γ_i, better than RAST combined with the Wilson equation or the Nonrandom two-liquid (NRTL) model. Moreover, two polyparameter linear free energy relationships were developed for the adsorption of a number of solutes at low concentrations in the presence of a major contaminant (4-methylphenol or nitrobenzene). Results show that these relationships have a great potential in predicting γ_i of solutes when the adsorbed amounts are dominated by a major contaminant. To the best of our knowledge, this is the first study predicting γ_i for bisolute adsorption based on molecular descriptors. Overall, our findings have proved a major step forward to accurately modeling multisolute adsorption equilibrium.

Binary Adsorption of Vapours in Active Carbons Described by the Combined Theories of Myers—Prausnitz and Dubinin (II)

The new MPD method, described recently, has been applied to the adsorption of benzene +1,2-dichloroethane vapours by a typical active carbon at 293 K. A total of 102 experiments have been carried out for adsorbed mole fractions between 0.06 and 0.94. Good agreement was found between the experimental and calculated values of the selectivity of the carbon for benzene, which decreased as the mole fraction of benzene increased. This variation reflects the heterogeneity of the carbon, which is taken into account by the DR equation. Although the liquid mixture is ideal, deviations from Raoult's law are observed in the adsorbed state, indicating a clear preference for benzene. The values of the activity coefficients obtained from the liquid/solid equilibrium improve the fit of the MPD method.

Application of the Dubinin–Astakhov Equation to the Study of the Geometric Structure, Energetic Surface Heterogeneity and Surface Topography of Carbonaceous Adsorbents

The new theoretical approach to multisite-occupancy adsorption on heterogeneous surfaces, developed recently by Rudziński and Everett, is generalized for the case of adsorption systems characterized by non-Gaussian adsorption energy distributions. Attention is focused on the adsorption energy distribution which, in the case of one-site-occupancy adsorption, leads to the Dubinin–Astakhov isotherm equation. In effect, a generalized form of that isotherm equation is developed for the common case of multisite-occupancy adorption in actual adsorption systems. The generalized equation is sensitive to surface topography; hence, fitting it to experimental adsorption isotherms creates a chance to study the surface topography of carbonaceous surfaces. An example of such computer exercises is reported here before a more systematic study is published.

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.

A semiempirical model for adsorption of binary mixtures

The statistical thermodynamics of polyatomic species mixtures adsorbed on two-dimensional lattices was developed based on generalization of the semiempirical approximation for the adsorption of single components [Romá, F. et al., Langmuir, 2006, 22, 3192-3197]. In this scheme, the partial adsorption isotherms are obtained using a correction function C[combining tilde], which relates to the conditional probability of finding the ith empty site to a lattice with i- 1 already vacant sites. This approximation allows us to write a new theoretical model using a combination of the correction functions corresponding to exact 1-D calculations and the Guggenheim-DiMarzio approach. Finally, comparisons with MC simulations and experimental data of methane-ethane and ethane-propylene mixtures on activated carbon are used to test the accuracy and reliability of the proposed model. The obtained results indicate that the new thermodynamic description is significantly better than the existing theoretical models developed to treat adsorption of interacting binary mixtures of polyatomics.

Adsorption equilibria of binary gas mixtures on graphitized carbon black

Adsorption equilibria for binary gas mixtures (methane-carbon dioxide, methane-ethane, and carbon dioxide-ethane) on the graphitized carbon black STH-2 were measured by the open flow method at 293.2 K. The experimental pressure range was (0 to 1.6) MPa. The extended Langmuir (EL) model and the ideal adsorption solution theory (IAST) have been adopted to predict the equilibria of binary gas mixtures. The results indicate that gas mixtures adsorbed on the homogeneous surface of STH-2 exhibit the nonideal behavior, which is mainly induced by adsorbate-adsorbate interactions. The real adsorption solution theory (RAST) has been used to analyze the property of the adsorbed mixtures. The activity coefficients have been correlated with the Wilson equation. The investigation demonstrates that the nonideality of adsorbed phase is completely dissimilar with the bulk liquid phase. The adsorption of the heavier component would benefit the adsorption of the lighter component.

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.

Examining the accuracy of ideal adsorbed solution theory without curve-fitting using transition matrix Monte Carlo simulations

Ideal adsorbed solution theory (IAST) is a well-known approach to predicting multicomponent adsorption isotherms in microporous materials from experimental or simulation data for single-component adsorption. A limitation in practical applications of IAST is that useful calculations often require extrapolation of fitted single-component isotherms beyond the range for which data are available. We introduce a molecular simulation approach in which the intrinsic accuracy of IAST can be examined in a context that avoids any need to perform curve fitting with single-component data. Our approach is based on using transition matrix Monte Carlo to define single-component adsorption isotherms for arbitrary bulk-phase pressures from a single simulation. We apply our approach to several light gas mixtures in silica zeolites and a carbon nanotube to examine the intrinsic accuracy of IAST for these model systems.