The use of collective variables and enhanced sampling in the simulations of existing and emerging microporous materials

Microporous materials, including zeolites, metal-organic frameworks, and cage compounds, offer diverse functionalities due to their unique dynamics and guest confinement properties. These materials play a significant role in separation, catalysis, and sensing, but their complexity hinders exploration using traditional atomistic simulations. This review explores collective variables (CVs) paired with enhanced sampling as a powerful approach to enable efficient investigation of key features in microporous materials. We highlight successful applications of CVs in studying adsorption, diffusion, phase transitions, and mechanical properties, demonstrating their crucial role in guiding material design and optimisation. The future of CVs lies in integration with techniques like machine learning, allowing for enhanced efficiency and accuracy. By tailoring CVs to specific materials and developing multi-scale approaches we can further unlock the intricacies of these fascinating materials. Simulations are a cornerstone in unravelling the complexities of microporous materials and are crucial for our future understanding.

Rapid and Accurate Screening of the COF Space for Natural Gas Purification: COFInformatics

In this work, we introduced COFInformatics, a computational approach merging molecular simulations and machine learning (ML) algorithms, to evaluate all synthesized and hypothetical covalent organic frameworks (COFs) for the CO2/CH4 mixture separation under four different adsorption-based processes: pressure swing adsorption (PSA), vacuum swing adsorption (VSA), temperature swing adsorption (TSA), and pressure-temperature swing adsorption (PTSA). We first extracted structural, chemical, energy-based, and graph-based molecular fingerprint features of every single COF structure in the very large COF space, consisting of nearly 70,000 materials, and then performed grand canonical Monte Carlo simulations to calculate the CO2/CH4 mixture adsorption properties of 7540 COFs. These features and simulation results were used to develop ML models that accurately and rapidly predict CO2/CH4 mixture adsorption and separation properties of all 68,614 COFs. The most efficient separation process and the best adsorbent candidates among the entire COF spectrum were identified and analyzed in detail to reveal the most important molecular features that lead to high-performance adsorbents. Our results showed that (i) many hypoCOFs outperform synthesized COFs by achieving higher CO2/CH4 selectivities; (ii) the top COF adsorbents consist of narrow pores and linkers comprising aromatic, triazine, and halogen groups; and (iii) PTSA is the most efficient process to use COF adsorbents for natural gas purification. We believe that COFInformatics promises to expedite the evaluation of COF adsorbents for CO2/CH4 separation, thereby circumventing the extensive, time- and resource-intensive molecular simulations.

A comprehensive transformer-based approach for high-accuracy gas adsorption predictions in metal-organic frameworks

Gas separation is crucial for industrial production and environmental protection, with metal-organic frameworks (MOFs) offering a promising solution due to their tunable structural properties and chemical compositions. Traditional simulation approaches, such as molecular dynamics, are complex and computationally demanding. Although feature engineering-based machine learning methods perform better, they are susceptible to overfitting because of limited labeled data. Furthermore, these methods are typically designed for single tasks, such as predicting gas adsorption capacity under specific conditions, which restricts the utilization of comprehensive datasets including all adsorption capacities. To address these challenges, we propose Uni-MOF, an innovative framework for large-scale, three-dimensional MOF representation learning, designed for multi-purpose gas prediction. Specifically, Uni-MOF serves as a versatile gas adsorption estimator for MOF materials, employing pure three-dimensional representations learned from over 631,000 collected MOF and COF structures. Our experimental results show that Uni-MOF can automatically extract structural representations and predict adsorption capacities under various operating conditions using a single model. For simulated data, Uni-MOF exhibits remarkably high predictive accuracy across all datasets. Additionally, the values predicted by Uni-MOF correspond with the outcomes of adsorption experiments. Furthermore, Uni-MOF demonstrates considerable potential for broad applicability in predicting a wide array of other properties.

Solvent-Directed Construction of a Nanoporous Metal-Organic Framework with Potential in Selective Adsorption and Separation of Gas Mixtures Studied by Grand Canonical Monte Carlo Simulations

In this report, a microporous metal-organic framework of [Ca(TDC)(DMA)]n (1) and a two-dimensional coordination polymer of [Ca(TDC)(DMF)2 ]n (2), (TDC2- =Thiophene-2,5-dicarboxylate, DMA=N, N'-dimethylacetamide and DMF=N, N'-dimethylformamide) based on Ca(II) were designed by the effect of solvent, and X-ray analysis was performed for the single crystals of 1 and 2. Then, compound 1 was synthesized in three different methods and identified with a set of analyses. Compared to other adsorbents, MOFs are widely used in the field of adsorption and separation of various gases due to a series of distinctive features such as diverse and adjustable structures pores with different dimensions, high porosity and surface area with regular distribution of active sites. Therefore, the ability of 1 to uptake single gases (CH4 , CO2 , C2 H2 , H2, and N2 ) and separation of several binary mixtures of gases (CO2 /CH4 , CO2 /N2 , CO2 /H2 and CO2 /C2 H2 ), were investigated using Grand Canonical Monte Carlo simulations. Volumetric and gravimetric adsorption isotherms in various operating conditions, the isosteric heat of adsorption (qst ), the chemical potential for each thermodynamic state, and snapshots during the simulation process were reported in all cases. The results obtained from the adsorption simulation indicate that compound 1 has a high capacity for uptake of H2 (16 mmol g-1 ) and N2 (12.5 mmol g-1 ), CO2 (6.6 mmol g-1 ), C2 H2 (5 mmol g-1 ) and CH4 (1.5 mmol g-1 ) gases at 1 bar. It also performs well in separating CO2 in binary mixtures, which can be attributed to the presence of open metal sites in nodes of 1 and their electrostatic tendency to interact with CO2 containing the higher quadrupole dipole moment compared to other components of the mixture.

Molecular adsorption and self-diffusion of NO2, SO2, and their binary mixture in MIL-47(V) material

The loading dependence of self-diffusion coefficients (Ds) of NO2, SO2, and their equimolar binary mixture in MIL-47(V) have been investigated by using classical molecular dynamics (MD) simulations. The Ds of NO2 are found to be two orders of magnitude greater than SO2 at low loadings and temperatures, and its Ds decreases monotonically with loading. The Ds of SO2 exhibit two diffusion patterns, indicating the specific interaction between the gas molecules and the MIL-47(V) lattice. The maximum activation energy (Ea) in the pure component and in the mixture for SO2 are 16.43 and 18.35 kJ mol-1, and for NO2 are 2.69 and 1.89 kJ mol-1, respectively. It is shown that SO2 requires more amount of energy than NO2 to increase the diffusion rate. The radial distribution functions (RDFs) of gas-gas and gas-lattice indicate that the Oh of MIL-47(V) are preferential adsorption site for both NO2 and SO2 molecules. However, the presence of the hydrogen bonding (HB) interaction between the O of SO2 and the H of MIL-47(V) and also their binding angle (θ(OHC)) of 120° with the linkers of lattice indicate a stronger binding interaction between the SO2 and the MIL-47(V), but it does not occur with NO2. The jump-diffusion of SO2 between adsorption sites within the lattice has been confirmed by the 2D density distribution plots. Moreover, the extraordinarily high Sdiff for NO2/SO2 of 623.4 shows that NO2 can diffuse through the MIL-47(V) significantly faster than SO2, especially at low loading and temperature.

Bimetal NiCo-MOF-74 for highly selective NO capture from flue gas under ambient conditions

The mixed bimetal metal-organic framework Ni_0.37Co_0.63-MOF-74 has been constructed by the solvothermal method for NO adsorption. The results showed that bimetal Ni_0.37Co_0.63-MOF-74 takes up NO with a capacity of up to 174.3 cc g^-1 under ambient conditions, which is 16.3% higher than that of the best single metal Co-MOF-74. The IAST adsorption selectivity for a NO/CO₂ binary mixture can reach a maximum of 710 at low adsorption partial pressure, while the regeneration performance can be retained even after five cyclic adsorption-desorption experiments. Its separation performance was further confirmed by breakthrough experiments, indicating this new bimetal Ni_0.37Co_0.63-MOF-74 as one of the best materials for NO adsorption and separation in flue gas.

Metal-organic frameworks as O2-selective adsorbents for air separations

Oxygen is a critical gas in numerous industries and is produced globally on a gigatonne scale, primarily through energy-intensive cryogenic distillation of air. The realization of large-scale adsorption-based air separations could enable a significant reduction in associated worldwide energy consumption and would constitute an important component of broader efforts to combat climate change. Certain small-scale air separations are carried out using N2-selective adsorbents, although the low capacities, poor selectivities, and high regeneration energies associated with these materials limit the extent of their usage. In contrast, the realization of O2-selective adsorbents may facilitate more widespread adoption of adsorptive air separations, which could enable the decentralization of O2 production and utilization and advance new uses for O2. Here, we present a detailed evaluation of the potential of metal-organic frameworks (MOFs) to serve as O2-selective adsorbents for air separations. Drawing insights from biological and molecular systems that selectively bind O2, we survey the field of O2-selective MOFs, highlighting progress and identifying promising areas for future exploration. As a guide for further research, the importance of moving beyond the traditional evaluation of O2 adsorption enthalpy, ΔH, is emphasized, and the free energy of O2 adsorption, ΔG, is discussed as the key metric for understanding and predicting MOF performance under practical conditions. Based on a proof-of-concept assessment of O2 binding carried out for eight different MOFs using experimentally derived capacities and thermodynamic parameters, we identify two existing materials and one proposed framework with nearly optimal ΔG values for operation under user-defined conditions. While enhancements are still needed in other material properties, the insights from the assessments herein serve as a guide for future materials design and evaluation. Computational approaches based on density functional theory with periodic boundary conditions are also discussed as complementary to experimental efforts, and new predictions enable identification of additional promising MOF systems for investigation.

Experimental and Simulation Studies of the Adsorption of Methylbenzene by Fe(III)-Doped NU-1000 (Zr)

Metal-organic framework (MOF) materials, NU-1000(Zr) and Fe(III)-doped NU-1000(Zr), were prepared through the hydrothermal method and used to remove methylbenzene in this work. The pore structure, crystal structure, adsorption capacity, adsorption heat, and adsorption density of Fe(III)-doped NU-1000(Zr) were analyzed based on the experimental and Giant Canonical Monte Carlo (GCMC) simulation methods. The results show that Fe³⁺ has a uniform distribution and a stable structure after NU-1000(Zr) was modified with Fe³⁺. The adsorption-penetration experiments of NU-1000 doped with different concentrations of Fe³⁺ have shown that the adsorption capacity of methylbenzene on the material surface is up to 231 mg g^-1 at Fe/Zr = 0.1, which is due to the less doping of Fe elements and more defective sites in the structure. The GCMC simulation shows that NU-1000(Zr) and Fe(III)-NU-1000(Zr) adsorbed methylbenzene through π-π interaction, and the adsorption effect is good and close to the experimental result. The conclusions of this paper provide important support for the modification of MOF materials and the removal of methylbenzene.

Metal-organic frameworks and covalent organic frameworks as disruptive membrane materials for energy-efficient gas separation

In this Review we survey the molecular sieving behaviour of metal-organic framework (MOF) and covalent organic framework (COF) membranes, which is different from that of classical zeolite membranes. The nature of MOFs as inorganic-organic hybrid materials and COFs as purely organic materials is powerful and disruptive for the field of gas separation membranes. The possibility of growing neat MOFs and COFs on membrane supports, while also allowing successful blending into polymer-filler composites, has a huge advantage over classical zeolite molecular sieves. MOFs and COFs allow synthetic access to more than 100,000 different structures and tailor-made molecular gates. Additionally, soft evacuation below 100 °C is often enough to achieve pore activation. Therefore, a huge number of synthetic methods for supported MOF and COF membrane thin films, such as solvothermal synthesis, seed-mediated growth and counterdiffusion, exist. Among them, methods with high scale-up potential, for example, layer-by-layer dip- and spray-coating, chemical and physical vapour deposition, and electrochemical methods. Additionally, physical methods have been developed that involve external stimuli, such as electric fields and light. A particularly important point is their ability to react to stimuli, which has allowed the 'drawbacks' of the non-ideality of the molecular sieving properties to be exploited in a completely novel research direction. Controllable gas transport through membrane films is a next-level property of MOFs and COFs, leading towards adaptive process deviation. MOF and COF particles are highly compatible with polymers, which allows for mixed-matrix membranes. However, these membranes are not simple MOF-polymer blends, as they require improved polymer-filler interactions, such as cross-linking or surface functionalization.

Recent Development in Coordination Compounds as a Sensor for Cyanide Ions in Biological and Environmental Segments

Rapid detection of toxic ions has taken great attention in the last few decades due to its importance in maintaining a greener environment for human beings. The extreme toxicity of cyanide (CN-) ions is a great environmental concern as its continued industrial use generates interest in facile and sensitive methods for CN- ions detection. Since CN- ions act as a ligand in coordination chemistry which rapidly coordinates with suitable metals and forms complexes, this ability was mainly explored in its detection. It also attacks the central metal in coordination compounds and gives a fluorimetric response. Coordination compounds behave as a sensor for the detection of important ions like CN- ions and have gained great attention due to their facile synthesis, multianalyte detection, clear detection and low detection limit. Recently, considerable efforts have been devoted to the detection and quantification of hazardous multianalyte using a single probe. Cu2+ complexes are the main complexes used for CN- ions detection; however, the complexes of many other metals are also used as sensors. Four basic types of interaction have been discussed in coordination compound sensors for CN- detection. The performances of different sensors are compared with one another and the sensors which have the lowest detection limit are highlighted. This review comprises the progress made by coordination compounds as sensors for the detection of CN- ions in the last six years (2015-2021). To the best of our knowledge, there is no review on coordination compounds as a sensor for CN- ions during this period. [Figure: see text].

Highlighting the Anti-Synergy between Adsorption and Diffusion in Cation-Exchanged Faujasite Zeolites

Using configurational-bias Monte Carlo simulations of adsorption equilibrium and molecular dynamics simulations of guest diffusivities of CO₂, CH₄, N₂, and O₂ in FAU zeolites with varying amounts of extra-framework cations (Na⁺ or Li⁺), we demonstrate that adsorption and diffusion do not, in general, proceed hand-in-hand. Stronger adsorption often implies reduced mobility. The anti-synergy between adsorption and diffusion has consequences for the design and development of pressure-swing adsorption and membrane separation technologies for CO₂ capture and N₂/O₂ separations.

Concluding remarks: current and next generation MOFs

This paper describes the content of my "Concluding remarks" talk at the Faraday Discussion meeting on "MOFs for energy and the environment" (online, 23-25 June 2021). The panel consisted of sessions on the design of MOFs and MOF hybrids (synthetic chemistry), their applications (e.g., capture, storage, separation, electrical devices, photocatalysis), advanced characterization (e.g., transmission electron microscopy, solid-state nuclear magnetic resonance), theory and modeling, and commercialization. MOF chemistry is undergoing a significant evolution from simply network chemistry to the chemistry of synergistic integration with heterogeneous materials involving other disciplines (we call this the fourth generation type). As reflected in the papers of the invited speakers and discussions with the participants, the present and future of this field will be described in detail.

CO2 Capture at Medium to High Temperature Using Solid Oxide-Based Sorbents: Fundamental Aspects, Mechanistic Insights, and Recent Advances

Carbon dioxide capture and mitigation form a key part of the technological response to combat climate change and reduce CO₂ emissions. Solid materials capable of reversibly absorbing CO₂ have been the focus of intense research for the past two decades, with promising stability and low energy costs to implement and operate compared to the more widely used liquid amines. In this review, we explore the fundamental aspects underpinning solid CO₂ sorbents based on alkali and alkaline earth metal oxides operating at medium to high temperature: how their structure, chemical composition, and morphology impact their performance and long-term use. Various optimization strategies are outlined to improve upon the most promising materials, and we combine recent advances across disparate scientific disciplines, including materials discovery, synthesis, and in situ characterization, to present a coherent understanding of the mechanisms of CO₂ absorption both at surfaces and within solid materials.

Zr-MOFs for CF4/CH4, CH4/H2, and CH4/N2 separation: towards the goal of discovering stable and effective adsorbents

Zirconium metal-organic frameworks (MOFs) can be promising adsorbents for various applications as they are highly stable in different chemical environments. In this work, a collection of Zr-MOFs comprised of more than 100 materials is screened for CF₄/CH₄, CH₄/H₂, and CH₄/N₂ separations using atomistic-level simulations. The top three MOFs for the CF₄/CH₄ separation are identified as PCN-700-BPDC-TPDC, LIFM-90, and BUT-67 exhibiting CF₄/CH₄ adsorption selectivities of 4.8, 4.6, and 4.7, CF₄ working capacities of 2.0, 2.0, and 2.1 mol kg^-1, and regenerabilities of 85.1, 84.2, and 75.7%, respectively. For the CH₄/H₂ separation, MOF-812, BUT-67, and BUT-66 are determined to be the top performing MOFs demonstrating CH₄/H₂ selectivities of 61.6, 36.7, and 46.2, CH₄ working capacities of 3.0, 4.1, and 3.4 mol kg^-1, and CH₄ regenerabilities of 70.7, 82.7, and 74.7%, respectively. Regarding the CH₄/N₂ separation, BUT-67, Zr-AbBA, and PCN-702 achieving CH₄/N₂ selectivities of 4.5, 3.4, and 3.8, CH₄ working capacities of 3.6, 3.9, and 3.5 mol kg^-1, and CH₄ regenerabilities of 81.1, 84.0, and 84.5%, in successive order, show the best overall separation performances. To further elucidate the adsorption in top performing adsorbents, the adsorption sites in these materials are analyzed using radial distribution functions and adsorbate density profiles. Finally, the water affinities of Zr-MOFs are explored to comment on their practical use in real gas separation applications. Our findings may inspire future studies probing the adsorption/separation mechanisms and performances of Zr-MOFs for different gases.

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.

Connecting theory and simulation with experiment for the study of diffusion in nanoporous solids

Nanoporous solids are ubiquitous in chemical, energy, and environmental processes, where controlled transport of molecules through the pores plays a crucial role. They are used as sorbents, chromatographic or membrane materials for separations, and as catalysts and catalyst supports. Defined as materials where confinement effects lead to substantial deviations from bulk diffusion, nanoporous materials include crystalline microporous zeotypes and metal–organic frameworks (MOFs), and a number of semi-crystalline and amorphous mesoporous solids, as well as hierarchically structured materials, containing both nanopores and wider meso- or macropores to facilitate transport over macroscopic distances. The ranges of pore sizes, shapes, and topologies spanned by these materials represent a considerable challenge for predicting molecular diffusivities, but fundamental understanding also provides an opportunity to guide the design of new nanoporous materials to increase the performance of transport limited processes. Remarkable progress in synthesis increasingly allows these designs to be put into practice. Molecular simulation techniques have been used in conjunction with experimental measurements to examine in detail the fundamental diffusion processes within nanoporous solids, to provide insight into the free energy landscape navigated by adsorbates, and to better understand nano-confinement effects. Pore network models, discrete particle models and synthesis-mimicking atomistic models allow to tackle diffusion in mesoporous and hierarchically structured porous materials, where multiscale approaches benefit from ever cheaper parallel computing and higher resolution imaging. Here, we discuss synergistic combinations of simulation and experiment to showcase theoretical progress and computational techniques that have been successful in predicting guest diffusion and providing insights. We also outline where new fundamental developments and experimental techniques are needed to enable more accurate predictions for complex systems.

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.

Simultaneous interlayer and intralayer space control in two-dimensional metal-organic frameworks for acetylene/ethylene separation

Three-dimensional metal−organic frameworks (MOFs) are cutting-edge materials in the adsorptive removal of trace gases due to the availability of abundant pores with specific chemistry. However, the development of ideal adsorbents combining high adsorption capacity with high selectivity and stability remains challenging. Here we demonstrate a strategy to design adsorbents that utilizes the tunability of interlayer and intralayer space of two-dimensional fluorinated MOFs for capturing acetylene from ethylene. Validated by X-ray diffraction and modeling, a systematic variation of linker atom oxidation state enables fine regulation of layer stacking pattern and linker conformation, which affords a strong interlayer trapping of molecules along with cooperative intralayer binding. The resultant robust materials (ZUL-100 and ZUL-200) exhibit benchmark capacity in the pressure range of 0.001–0.05 bar with high selectivity. Their efficiency in acetylene/ethylene separation is confirmed by breakthrough experiments, giving excellent ethylene productivities (121 mmol/g from 1/99 mixture, 99.9999%), even when cycled under moist conditions.

Designing efficient adsorbents for trace gas removal remains a serious challenge. Here, the authors show promise in layered 2D metal−organic frameworks, often overlooked in favor of 3D frameworks, for separating trace acetylene from ethylene with enhanced performance and high stability.

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.

Computational Selection of High-Performing Covalent Organic Frameworks for Adsorption and Membrane-Based CO2/H2 Separation

Covalent organic frameworks (COFs) have high potential in gas separation technologies because of their porous structures, large surface areas, and good stabilities. The number of synthesized COFs already reached several hundreds, but only a handful of materials were tested as adsorbents and/or membranes. We used a high-throughput computational screening approach to uncover adsorption-based and membrane-based CO₂/H₂ separation potentials of 288 COFs, representing the highest number of experimentally synthesized COFs studied to date for precombustion CO₂ capture. Grand canonical Monte Carlo (GCMC) simulations were performed to assess CO₂/H₂ mixture separation performances of COFs for five different cyclic adsorption processes: pressure swing adsorption, vacuum swing adsorption, temperature swing adsorption (TSA), pressure-temperature swing adsorption (PTSA), and vacuum-temperature swing adsorption (VTSA). The results showed that many COFs outperform traditional zeolites in terms of CO₂ selectivities and working capacities and PTSA is the best process leading to the highest adsorbent performance scores. Combining GCMC and molecular dynamics (MD) simulations, CO₂ and H₂ permeabilities and selectivities of COF membranes were calculated. The majority of COF membranes surpass Robeson's upper bound because of their higher H₂ permeabilities compared to polymers, indicating that the usage of COFs has enormous potential to replace current materials in membrane-based H₂/CO₂ separation processes. Performance analysis based on the structural properties showed that COFs with narrow pores [the largest cavity diameter (LCD) < 15 Å] and low porosities (ϕ < 0.75) are the top adsorbents for selective separation of CO₂ from H₂, whereas materials with large pores (LCD > 20 Å) and high porosities (ϕ > 0.85) are generally the best COF membranes for selective separation of H₂ from CO₂. These results will help to speed up the engineering of new COFs with desired structural properties to achieve high-performance CO₂/H₂ separations.

Nanomaterials in Dentistry: State of the Art and Future Challenges

Nanomaterials are commonly considered as those materials in which the shape and molecular composition at a nanometer scale can be controlled. Subsequently, they present extraordinary properties that are being useful for the development of new and improved applications in many fields, including medicine. In dentistry, several research efforts are being conducted, especially during the last decade, for the improvement of the properties of materials used in dentistry. The objective of the present article is to offer the audience a complete and comprehensive review of the main applications that have been developed in dentistry, by the use of these materials, during the last two decades. It was shown how these materials are improving the treatments in mainly all the important areas of dentistry, such as endodontics, periodontics, implants, tissue engineering and restorative dentistry. The scope of the present review is, subsequently, to revise the main applications regarding nano-shaped materials in dentistry, including nanorods, nanofibers, nanotubes, nanospheres/nanoparticles, and zeolites and other orders porous materials. The results of the bibliographic analysis show that the most explored nanomaterials in dentistry are graphene and carbon nanotubes, and their derivatives. A detailed analysis and a comparative study of their applications show that, although they are quite similar, graphene-based materials seem to be more promising for most of the applications of interest in dentistry. The bibliographic study also demonstrated the potential of zeolite-based materials, although the low number of studies on their applications shows that they have not been totally explored, as well as other porous nanomaterials that have found important applications in medicine, such as metal organic frameworks, have not been explored. Subsequently, it is expected that the research effort will concentrate on graphene and zeolite-based materials in the coming years. Thus, the present review paper presents a detailed bibliographic study, with more than 200 references, in order to briefly describe the main achievements that have been described in dentistry using nanomaterials, compare and analyze them in a critical way, with the aim of predicting the future challenges.

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.

Trends in Solid Adsorbent Materials Development for CO2 Capture

A recent report from the United Nations has warned about the excessive CO₂ emissions and the necessity of making efforts to keep the increase in global temperature below 2 °C. Current CO₂ capture technologies are inadequate for reaching that goal, and effective mitigation strategies must be pursued. In this work, we summarize trends in materials development for CO₂ adsorption with focus on recent studies. We put adsorbent materials into four main groups: (I) carbon-based materials, (II) silica/alumina/zeolites, (III) porous crystalline solids, and (IV) metal oxides. Trends in computational investigations along with experimental findings are covered to find promising candidates in light of practical challenges imposed by process economics.

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).

From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5

The development of first-principles-quality reactive atomistic potentials for organic-inorganic hybrid materials is still a substantial challenge because of the very different physics of the atomic interactions-from covalent via ionic bonding to dispersion-that have to be described in an accurate and balanced way. In this work we used a prototypical metal-organic framework, MOF-5, as a benchmark case to investigate the applicability of high-dimensional neural network potentials (HDNNPs) to this class of materials. In HDNNPs, which belong to the class of machine learning potentials, the energy is constructed as a sum of environment-dependent atomic energy contributions. We demonstrate that by the use of this approach it is possible to obtain a high-quality potential for the periodic MOF-5 crystal using density functional theory (DFT) reference calculations of small molecular fragments only. The resulting HDNNP, which has a root-mean-square error (RMSE) of 1.6 meV/atom for the energies of molecular fragments not included in the training set, is able to provide the equilibrium lattice constant of the bulk MOF-5 structure with an error of about 0.1% relative to DFT, and also, the negative thermal expansion behavior is accurately predicted. The total energy RMSE of periodic structures that are completely absent in the training set is about 6.5 meV/atom, with errors on the order of 2 meV/atom for energy differences. We show that in contrast to energy differences, achieving a high accuracy for total energies requires careful variation of the stoichiometries of the training structures to avoid energy offsets, as atomic energies are not physical observables. The forces, which have RMSEs of about 94 meV/ a₀ for the molecular fragments and 130 meV/ a₀ for bulk structures not included in the training set, are insensitive to such offsets. Therefore, forces, which are the relevant properties for molecular dynamics simulations, provide a realistic estimate of the accuracy of atomistic potentials.

Understanding the effect of host flexibility on the adsorption of CH4, CO2 and SF6 in porous organic cages

Molecular simulations for gas adsorption in microporous materials with flexible host structures is challenging and, hence, relatively rare. To date, most gas adsorption simulations have been carried out using the grand-canonical Monte Carlo (GCMC) method, which fundamentally does not allow the structural flexibility of the host to be accounted for. As a result, GCMC simulations preclude investigation into the effect of host flexibility on gas adsorption. On the other hand, approaches such as molecular dynamics (MD) that simulate the dynamic evolution of a system almost always require a fixed number of particles in the simulation box. Here we use a hybrid GCMC/MD scheme to include host flexibility in gas adsorption simulations. We study the adsorption of three gases – CH4, CO2 and SF6 – in the crystal of a porous organic cage (POC) molecule, CC3-R, whose structural flexibility is known by experiment to play an important role in adsorption of large guest molecules [L. Chen, P. S. Reiss, S. Y. Chong, D. Holden, K. E. Jelfs, T. Hasell, M. A. Little, A. Kewley, M. E. Briggs, A. Stephenson, K. Mark Thomas, J. A. Armstrong, J. Bell, J. Busto, R. Noel, J. Liu, D. M. Strachan, P. K. Thallapally, A. I. Cooper, Separation of rare gases and chiral molecules by selective binding in porous organic cages. Nat. Mater. 2014, 13, 954, D. Holden, S. Y. Chong, L. Chen, K. E. Jelfs, T. Hasell, A. I. Cooper, Understanding static, dynamic and cooperative porosity in molecular materials. Chem. Sci. 2016, 7, 4875]. The results suggest that hybrid GCMC/MD simulations can reproduce experimental adsorption results, without the need to adjust the host–guest interactions in an ad hoc way. Negligible errors in adsorption capacity and isosteric heat are observed with the rigid-host assumption for small gas molecules such as CH4 and CO2 in CC3-R, but the adsorption capacity of the larger SF6 molecule in CC3-R is hugely underestimated if flexibility is ignored. By contrast, hybrid GCMC/MD adsorption simulations of SF6 in CC3-R can accurately reproduce experiment. This work also provides a molecular level understanding of the cooperative adsorption mechanism of SF6 in the CC3-R molecular crystal.

Design of organic structure directing agents to control the synthesis of zeolites for carbon capture and storage

We have de novo designed organic structure directing agents (OSDAs) for zeolites that have been predicted to be effective materials for carbon capture and storage. The zeolites were selected for their reduced parasitic energy when used as CO₂ adsorbants in a pressure–temperature swing process in coal- or natural gas-fired power plants. Synthetically accessible OSDAs were designed for five known and two theoretical frameworks.

Zeolites more efficient at carbon capture than scrubbing with aqueous monoethanolamine, and the best OSDAs designed for the synthesis of each.

A robust and water-stable two-fold interpenetrated metal–organic framework containing both rigid tetrapodal carboxylate and rigid bifunctional nitrogen linkers exhibiting selective CO2 capture

A robust and water-stable two-fold interpenetrated metal–organic framework containing both rigid tetrapodal carboxylate and rigid bifunctional nitrogen linkers exhibiting selective CO₂ capture is reported.

High-Throughput Screening of MOF Adsorbents and Membranes for H2 Purification and CO2 Capture

Metal organic frameworks (MOFs) have emerged as great adsorbent and membrane candidates for separation of CO2/H2 mixtures. The main challenge is the existence of thousands of MOFs, which requires computational screening methods to identify the best materials prior to experimental efforts. In this study, we performed high-throughput computational screening of MOFs to examine their adsorbent and membrane performances for CO2/H2 separation. Grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations were used to compute various adsorbent and membrane performance metrics of 3857 MOFs. CO2/H2 adsorption selectivities of MOFs at pressure swing adsorption (PSA) and vacuum swing adsorption (VSA) conditions were calculated to be in the range of 2.5-25 000 and 2.5-85 000, respectively, outperforming many zeolite adsorbents. Correlations between the ranking of MOF adsorbents at the PSA and VSA conditions were examined. H2/CO2 selectivities and H2 permeabilities of MOF membranes were computed as 2.1 × 10-5-6.3 and 230-1.7 × 106 Barrer, respectively. A high number of MOF membranes was identified to surpass the upper bound defined for polymers due to high gas permeabilities of MOFs. Structure-performance relations revealed that MOFs with narrow pore sizes and low porosities are the best adsorbent materials for separation of CO2 from H2, whereas MOFs with large pore sizes and high porosities are the best membrane materials for selective separation of H2. Our results will guide the selection of MOF adsorbents and membranes for efficient H2 purification and CO2 capture processes.

Computational Screening of Metal-Organic Frameworks for Membrane-Based CO2/N2/H2O Separations: Best Materials for Flue Gas Separation

It has become a significant challenge to select the best metal-organic frameworks (MOFs) for membrane-based gas separations because the number of synthesized MOFs is growing exceptionally fast. In this work, we used high-throughput computational screening to identify the top MOF membranes for flue gas separation. Grand canonical Monte Carlo and molecular dynamics simulations were performed to assess adsorption and diffusion properties of CO₂ and N₂ in 3806 different MOFs. Using these data, selectivities and permeabilities of MOF membranes were predicted and compared with those of conventional membranes, polymers, and zeolites. The best performing MOF membranes offering CO₂/N₂ selectivity > 350 and CO₂ permeability > 10⁶ Barrer were identified. Ternary CO₂/N₂/H₂O mixture simulations were then performed for the top MOFs to unlock their potential under industrial operating conditions, and results showed that the presence of water decreases CO₂/N₂ selectivity and CO₂ permeability of some MOF membranes. As a result of this stepwise screening procedure, the number of promising MOF membranes to be investigated for flue gas separation in future experimental studies was narrowed down from thousands to tens. We finally examined the structure-performance relations of MOFs to understand which properties lead to the greatest promise for flue gas separation and concluded that lanthanide-based MOFs with narrow pore openings (<4.5 Å), low porosities (<0.75), and low surface areas (<1000 m²/g) are the best materials for membrane-based CO₂/N₂ separations.

Database for CO2 Separation Performances of MOFs Based on Computational Materials Screening

Metal-organic frameworks (MOFs) are potential adsorbents for CO2 capture. Because thousands of MOFs exist, computational studies become very useful in identifying the top performing materials for target applications in a time-effective manner. In this study, molecular simulations were performed to screen the MOF database to identify the best materials for CO2 separation from flue gas (CO2/N2) and landfill gas (CO2/CH4) under realistic operating conditions. We validated the accuracy of our computational approach by comparing the simulation results for the CO2 uptakes, CO2/N2 and CO2/CH4 selectivities of various types of MOFs with the available experimental data. Binary CO2/N2 and CO2/CH4 mixture adsorption data were then calculated for the entire MOF database. These data were then used to predict selectivity, working capacity, regenerability, and separation potential of MOFs. The top performing MOF adsorbents that can separate CO2/N2 and CO2/CH4 with high performance were identified. Molecular simulations for the adsorption of a ternary CO2/N2/CH4 mixture were performed for these top materials to provide a more realistic performance assessment of MOF adsorbents. The structure-performance analysis showed that MOFs with Δ Qst0 > 30 kJ/mol, 3.8 Å < pore-limiting diameter < 5 Å, 5 Å < largest cavity diameter < 7.5 Å, 0.5 < ϕ < 0.75, surface area < 1000 m2/g, and ρ > 1 g/cm3 are the best candidates for selective separation of CO2 from flue gas and landfill gas. This information will be very useful to design novel MOFs exhibiting high CO2 separation potentials. Finally, an online, freely accessible database https://cosmoserc.ku.edu.tr was established, for the first time in the literature, which reports all of the computed adsorbent metrics of 3816 MOFs for CO2/N2, CO2/CH4, and CO2/N2/CH4 separations in addition to various structural properties of MOFs.

Computer simulations of 4240 MOF membranes for H2/CH4 separations: insights into structure-performance relations

Design of new membranes having high H₂/CH₄ selectivity and high H₂ permeability is strongly desired to reduce the energy demand for H₂ production. Metal organic frameworks (MOFs) offer a great promise for membrane-based gas separations due to their tunable physical and chemical properties. We performed a high-throughput computational screening study to examine membrane-based H₂/CH₄ separation potentials of 4240 MOFs. Grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations were used to compute adsorption and diffusion of H₂ and CH₄ in MOFs. Simulation results were then used to predict adsorption selectivity, diffusion selectivity, gas permeability and membrane selectivity of MOFs. A large number of MOF membranes was found to outperform traditional polymer and zeolite membranes by exceeding the Robeson's upper bound for selective separation of H₂ from CH₄. Structure-performance analysis was carried out to understand the relations between MOF membranes' selectivities and their pore sizes, surface areas, porosities, densities, lattice systems, and metal types. Results showed that MOFs with pore limiting diameters between 3.8 and 6 Å, the largest cavity diameters between 6 and 12 Å, surface areas less than 1000 m² g^-1, porosities between 0.5 and 0.75, and densities between 1 and 1.5 g cm^-3 are the most promising membranes leading to H₂ selectivities >10 and H₂ permeabilities >10⁴ Barrer. Our results suggest that monoclinic MOFs having copper metals are the best membrane candidates for H₂/CH₄ separations. This study represents the first high-throughput computational screening of the most recent MOF database for membrane-based H₂/CH₄ separation and microscopic insight provided from molecular simulations will be highly useful for the future design of new MOFs having extraordinarily high H₂ selectivities.