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

Effect of Ligand Aromaticity on Cyclohexane and Benzene Sorption in IRMOFs: A Computational Study

A series of four isoreticular MOFs (IRMOF-1, -10, -14, and -16) were selected for a computational investigation of the effect of ligand aromaticity on the adsorption capacity of an aromatic VOC (benzene) compared to its nonaromatic analog (cyclohexane). The affinity of the adsorbates was evaluated by calculating Henry's constants and adsorption enthalpies. It has been evidenced that while KH values decrease with ligand elongation (IRMOF-10 and -16), inserting a pyrene core into the MOF structure (IRMOF-14) increases both the cyclohexane and benzene adsorption efficiency by ∼290 and 54%, respectively. To elucidate host-guest interactions, we sought to locate preferential adsorption sites in MOF structures for the two VOCs studied by using the GCMC method. It appears that benzene interacts with the metal center (Zn4O clusters) and most of the ligand while cyclohexane tends to localize preferentially only near the Zn4O clusters. Coadsorption isotherms (equimolar mixture of benzene and cyclohexane) demonstrated the preferential adsorption of cyclohexane due to the stronger affinity for the MOF structure. On the other hand, for other isoreticular structures, the ligand elongation leads to a shift of the adsorption curve of cyclohexane caused by pore size increase and therefore less interactions with the walls. This phenomenon is counterbalanced in the case of IRMOF-14 due to stronger interactions between the cyclohexane and pyrene groups. The present results thus open perspectives in the design of promising MOF candidates for high-performing separation and sorption/detection of hydrocarbon VOCs.

A Robust Framework for Generating Adsorption Isotherms to Screen Materials for Carbon Capture

To rank the performance of materials for a given carbon capture process, we rely on pure component isotherms from which we predict the mixture isotherms. For screening a large number of materials, we also increasingly rely on isotherms predicted from molecular simulations. In particular, for such screening studies, it is important that the procedures to generate the data are accurate, reliable, and robust. In this work, we develop an efficient and automated workflow for a meticulous sampling of pure component isotherms. The workflow was tested on a set of metal-organic frameworks (MOFs) and proved to be reliable given different guest molecules. We show that the coupling of our workflow with the Clausius-Clapeyron relation saves CPU time, yet enables us to accurately predict pure component isotherms at the temperatures of interest, starting from a reference isotherm at a given temperature. We also show that one can accurately predict the CO₂ and N₂ mixture isotherms using ideal adsorbed solution theory (IAST). In particular, we show that IAST is a more reliable numerical tool to predict binary adsorption uptakes for a range of pressures, temperatures, and compositions, as it does not rely on the fitting of experimental data, which typically needs to be done with analytical models such as dual-site Langmuir (DSL). This makes IAST a more suitable and general technique to bridge the gap between adsorption (raw) data and process modeling. To demonstrate this point, we show that the ranking of materials, for a standard three-step temperature swing adsorption (TSA) process, can be significantly different depending on the thermodynamic method used to predict binary adsorption data. We show that, for the design of processes that capture CO₂ from low concentration (0.4%) streams, the commonly used methodology to predict mixture isotherms incorrectly assigns up to 33% of the materials as top-performing.

Separation and Purification of Hydrocarbons with Porous Materials

This Minireview focuses on the developments of the adsorptive separation of methane/nitrogen, ethene/ethane, propene/propane mixtures as well as on the separation of C8 aromatics (i.e. xylene isomers) with a wide variety of materials, including carbonaceous materials, zeolites, metal-organic frameworks, and porous organic frameworks. Some recent important developments for these adsorptive separations are also highlighted. The advantages and disadvantages of each material category are discussed and guidelines for the design of improved materials are proposed. Furthermore, challenges and future developments of each material type and separation processes are discussed.

Adsorption-Based Separation of Near-Azeotropic Mixtures-A Challenging Example for High-Throughput Development of Adsorbents

Adsorption of gas mixtures is central to adsorption-based gas separations, and the number of adsorbate mixture/adsorbent systems that exist is staggering. Because examples of machine learning (ML) models predicting single-component adsorption of arbitrary molecules in large libraries of crystalline adsorbents have been developed, it is interesting to determine whether these models can accurately predict mixture adsorption. Here, we use molecular simulations to generate mixture adsorption data with a set of 12 near-azeotropic molecules in a diverse set of MOFs. These data provide a challenging example for any method to rapidly predict mixture adsorption in MOFs. We combine a previous ML single-component isotherm model with ideal adsorbed solution theory (IAST) to make predictions that can be compared directly with molecular simulation data for these adsorbed mixtures. This combination of ML and IAST illustrates the scope that is available with these methods, but the accuracy of the resulting predictions is disappointing. By examining the same examples with IAST based on minimal molecular simulation data for single-component isotherms, we show that having an accurate description of adsorption in the dilute loading limit is critical to being able to accurately predict mixture adsorption. This observation points to a useful direction for future work developing robust ML models of adsorption isotherms for diverse collections of molecules and adsorbents.

Prediction of Adsorption Isotherms and Selectivities: Comparison between Classical Density Functional Theory Based on the Perturbed-Chain Statistical Associating Fluid Theory Equation of State and Ideal Adsorbed Solution Theory

This study gives an assessment of the predictive capability of classical density functional theory (DFT) for adsorption processes of pure substances and mixtures of spherical and nonspherical molecular species. A Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) is applied to calculate isotherms and selectivities of multicomponent adsorption. In order to unambiguously assess the accuracy of the DFT model, we conduct molecular simulations. Monte Carlo (MC) simulations are performed in the grand canonical ensemble using the transition matrix. Two types of systems are studied: a model system, where fluid-fluid and solid-fluid interactions are defined as (single-site) Lennard-Jones interactions, and a more realistic methane-n-butane mixture in a graphite-like pore. Differences between a slit-shaped and a cylindrical pore geometry are examined for the model system. Adsorption isotherms and selectivities obtained from DFT calculations and MC simulations are found in very good agreement, particularly at high pressures. Capillary condensation observed along adsorption isotherms containing n-butane was accurately predicted, both, in equilibrium pressure and in density-increase. Comparisons with results from the ideal adsorbed solution theory are presented, confirming powerful predictions of the DFT approach.

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.

A microporous MOF with open metal sites and Lewis basic sites for selective CO2 capture

A new robust indium–organic framework (InOF-15, In-BQDC) exhibits high IAST selective CO₂ sorption performance for CO₂/CH₄ and CO₂/N₂ mixtures at 273 K, which has been attributed to the coexistence of OMSs and LBSs for strong synergistic effect.

New insights into the ideal adsorbed solution theory

The GCMC technique is used for simulation of adsorption of CO2-CH4, CO2-N2 and CH4-N2 mixtures (at 298 K) on six porous carbon models. Next we formulate a new condition of the IAS concept application, showing that our simulated data obey this condition. Calculated deviations between IAS predictions and simulation results increase with the rise in pressure as in the real experiment. For the weakly adsorbed mixture component the deviation from IAS predictions is higher, especially when its content in the gas mixture is low, and this is in agreement with the experimental data. Calculated activity coefficients have similar plots to deviations between IAS and simulations, moreover obtained from simulated data activity coefficients are similar qualitatively as well as quantitatively to experimental data. Since the physical interpretation of activity coefficients is completely lacking we show for the first time that they can be described by the formulas derived from the expression for G(ex) for the ternary mixture. Finally we also for the first time show the linear relationship between the chemical potentials of nonideal and ideal solutions and the reduced temperature of interacting mixture components, and it is proved that the deviation from ideality is larger if adsorption occurs in a more microporous system.

Accelerating applications of metal-organic frameworks for gas adsorption and separation by computational screening of materials

The selection of metal-organic frameworks (MOFs) for gas adsorption and separation has become a significant challenge over the past decade because of the large number of new structures reported every year. We applied a multiscale computational approach to screen existing MOFs for CO(2)/N(2) separation. Pore characteristics of 1163 MOFs were analyzed by the method developed by Haldoupis, Nair, and Sholl (Haldoupis, E.; Nair, S.; Sholl, D. S. J. Am. Chem. Soc.2010, 132, 7528) using a simple steric model. On the basis of the pore size analysis, 359 MOFs were examined by classical molecular simulations. Adsorption and diffusion properties were computed using grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations, respectively. These molecular simulations were used to assess which materials hold the greatest promise as membrane materials for CO(2)/N(2) separations. Finally, density functional theory (DFT) calculations were performed to provide preliminary information on the dynamic framework motion of selected MOFs.

Computational study of adsorption and separation of CO2, CH4, and N2 by an rht-type metal-organic framework

In this work, a computational study is performed to evaluate the adsorption-based separation of CO(2) from flue gas (mixtures of CO(2) and N(2)) and natural gas (mixtures of CO(2) and CH(4)) using microporous metal organic framework Cu-TDPAT as a sorbent material. The results show that electrostatic interactions can greatly enhance the separation efficiency of this MOF for gas mixtures of different components. Furthermore, the study also suggests that Cu-TDPAT is a promising material for the separation of CO(2) from N(2) and CH(4), and its macroscopic separation behavior can be elucidated on a molecular level to give insight into the underlying mechanisms. On the basis of the single-component CO(2), N(2), and CH(4) isotherms, binary mixture adsorption (CO(2)/N(2) and CO(2)/CH(4)) and ternary mixture adsorption (CO(2)/N(2)/CH(4)) were predicted using the ideal adsorbed solution theory (IAST). The effect of H(2)O vapor on the CO(2) adsorption selectivity and capacity was also examined. The applicability of IAST to this system was validated by performing GCMC simulations for both single-component and mixture adsorption processes.

Finding MOFs for highly selective CO2/N2 adsorption using materials screening based on efficient assignment of atomic point charges

Electrostatic interactions are a critical factor in the adsorption of quadrupolar species such as CO(2) and N(2) in metal-organic frameworks (MOFs) and other nanoporous materials. We show how a version of the semiempirical charge equilibration method suitable for periodic materials can be used to efficiently assign charges and allow molecular simulations for a large number of MOFs. This approach is illustrated by simulating CO(2) and N(2) adsorption in ~500 MOFs; this is the largest set of structures for which this information has been reported to date. For materials predicted by our calculations to have promising adsorption selectivities, we performed more detailed calculations in which accurate quantum chemistry methods were used to assign atomic point charges, and molecular simulations were used to assess molecular diffusivities and binary adsorption isotherms. Our results identify two MOFs, experimentally known to be stable upon solvent removal, that are predicted to show no diffusion limitations for adsorbed molecules and extremely high CO(2)/N(2) adsorption selectivities for CO(2) adsorption from dry air and from gas mixtures typical of dry flue gas.

Can metal-organic framework materials play a useful role in large-scale carbon dioxide separations?

Metal-organic frameworks (MOFs) are a fascinating class of crystalline nanoporous materials that can be synthesized with a diverse range of pore dimensions, topologies, and chemical functionality. As with other well-known nanoporous materials, such as activated carbon and zeolites, MOFs have potential uses in a range of chemical separation applications because of the possibility of selective adsorption and diffusion of molecules in their pores. We review the current state of knowledge surrounding the possibility of using MOFs in large-scale carbon dioxide separations. There are reasons to be optimistic that MOFs may make useful contributions to this important problem, but there are several critical issues for which only very limited information is available. By identifying these issues, we provide what we hope is a path forward to definitively answering the question posed in our title.

Insights Into Crowding Effects on Protein Stability From a Coarse-Grained Model

Proteins aggregate and precipitate from high concentration solutions in a wide variety of problems of natural and technological interest. Consequently, there is a broad interest in developing new ways to model the thermodynamic and kinetic aspects of protein stability in these crowded cellular or solution environments. We use a coarse-grained modeling approach to study the effects of different crowding agents on the conformational equilibria of proteins and the thermodynamic phase behavior of their solutions. At low to moderate protein concentrations, we find that crowding species can either stabilize or destabilize the native state, depending on the strength of their attractive interaction with the proteins. At high protein concentrations, crowders tend to stabilize the native state due to excluded volume effects, irrespective of the strength of the crowder-protein attraction. Crowding agents reduce the tendency of protein solutions to undergo a liquid-liquid phase separation driven by strong protein-protein attractions. The aforementioned equilibrium trends represent, to our knowledge, the first simulation predictions for how the properties of crowding species impact the global thermodynamic stability of proteins and their solutions.

Testing isotherm models and recovering empirical relationships for adsorption in microporous carbons using virtual carbon models and grand canonical Monte Carlo simulations

Using the plausible model of activated carbon proposed by Harris and co-workers and grand canonical Monte Carlo simulations, we study the applicability of standard methods for describing adsorption data on microporous carbons widely used in adsorption science. Two carbon structures are studied, one with a small distribution of micropores in the range up to 1 nm, and the other with micropores covering a wide range of porosity. For both structures, adsorption isotherms of noble gases (from Ne to Xe), carbon tetrachloride and benzene are simulated. The data obtained are considered in terms of Dubinin-Radushkevich plots. Moreover, for benzene and carbon tetrachloride the temperature invariance of the characteristic curve is also studied. We show that using simulated data some empirical relationships obtained from experiment can be successfully recovered. Next we test the applicability of Dubinin's related models including the Dubinin-Izotova, Dubinin-Radushkevich-Stoeckli, and Jaroniec-Choma equations. The results obtained demonstrate the limits and applications of the models studied in the field of carbon porosity characterization.

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.