Force field parametrization through fitting on inflection points in isotherms

Adsorption of molecular hydrogen on Be3Al2(SiO3)6-beryl: theoretical insights for catalysis, hydrogen storage, gas separation, sensing, and environmental applications

Employing a combination of Density Functional Theory (DFT) calculations and Molecular Dynamics (MD) simulations, the adsorption of molecular hydrogen (H2) on Be3Al2(SiO3)6-beryl, a prominent silicate mineral, has been studied. The crystal structure of beryl, which consists of interconnected tetrahedral and octahedral sites, provides a fascinating framework for comprehending H2 adsorption behavior. Initial investigation of the interaction between H2 molecules and the beryl surface employed DFT calculations. We identified favorable adsorption sites and gained insight into the binding mechanism through extensive structural optimizations and energy calculations. H2 molecules preferentially adsorb on the exposed oxygen atoms surrounding the octahedral sites, producing weak van der Waals interactions with the beryl surface, according to our findings. To further investigate the dynamic aspects of H2 adsorption, MD simulations employing a suitable force field were conducted. To precisely represent interatomic interactions within the Be3Al2(SiO3)6-beryl-H2 system, the force field parameters were meticulously parameterized. By subjecting the system to a variety of temperatures, we were able to obtain valuable information about the stability, diffusion, and desorption kinetics of H2 molecules within the beryl structure. The comprehensive understanding of the H2 adsorption phenomenon on Be3Al2(SiO3)6-beryl is provided by the combined DFT and MD investigations. The results elucidate the mechanisms underlying H2 binding, highlighting the role of surface oxygen atoms and the effect of temperature on H2 dynamics. This research contributes to a fundamental understanding of hydrogen storage and release in beryllium-based silicates and provides valuable guidance for the design and optimization of materials for hydrogen storage, catalysis, gas separation, sensing and environmental applications.

Computing Mixture Adsorption in Porous Materials through Flat Histogram Monte Carlo Methods

Mixture adsorption properties of porous materials are critical to determine their potential as adsorbents in separation applications. Toward the discovery of optimal adsorbents, in silico screening studies typically employ the grand canonical Monte Carlo (GCMC) technique to compute adsorption properties of gas mixtures in materials of interest at a given condition (i.e., composition, total pressure, and temperature) or to compute their adsorption properties for each component, followed by utilizing methods to predict mixture adsorption isotherms. However, the former approach results in the need for repeated calculations when different conditions such as compositions are considered. For the latter, the predictions may involve uncertainties, sometimes originating from the fitting quality to the pure component isotherms, and repeated simulations may also be needed for different temperatures. To this end, this study demonstrates the potential of flat histogram Monte Carlo methods in addressing the abovementioned shortfalls. Specifically, the so-called NVT + W method, first reported by Smit and co-workers, is extended herein to determine the macrostate probability distribution (MPD) of binary mixtures in porous materials. The obtained MPD can be reweighted to any conditions, yielding accurate adsorption isotherms of any desired compositions and temperatures. This approach, denoted as 2D NVT + W, is also compared with the widely adopted ideal adsorbed solution theory (IAST) method, and the former is found to offer more reliable predictions. Overall, the 2D NVT + W approach represents an efficient and effective alternative to compute mixture adsorption isotherms for porous materials, and the obtained MPD can be conveniently reused by peer researchers. A user-friendly Python code is also provided along with this article to employ this method.

Computational Study of Alkane Adsorption in Brønsted Acid Zeolites for More Efficient Alkane Cracking

Alkane cracking using Brønsted acid zeolites, catalytically converting long-chain molecules into smaller ones, is critical to fuel and chemical production. To enable more energy-efficient cracking processes, developing zeolite catalysts with enhanced performance (i.e., a faster reaction rate with reduced methane formation) plays a substantial role. Given the adsorption thermodynamics of alkanes onto the protons of Brønsted acid zeolites is a key step in the overall cracking reactions; therefore, catalysts possessing a more negative Gibbs free energy of adsorption for alkanes with a larger central-to-terminal bond adsorption selectivity to promote central cracking are of particular interest. This Feature Article discusses recent computational developments and discoveries by Lin and co-workers in studying the adsorption of alkanes in Brønsted acid zeolites. Their developed approach, employing configurational bias Monte Carlo with domain decomposition, with a newly parametrized molecular potential to compute the adsorption properties is first introduced. With these developments, the roles of the Si/Al ratio and Al sitting are explored and discussed. Subsequently, the Feature Article discusses the key findings obtained from a large-scale computational screening of studying more than 100 000 possible zeolite structures. The performance of identified top candidates and associated key structural features leading to desirable adsorption properties are highlighted.

Effects of Degrees of Freedom on Calculating Diffusion Properties in Nanoporous Materials

If one carries out a molecular simulation of N particles using periodic boundary conditions, linear momentum is conserved, and hence, the number of degrees of freedom is set to 3N - 3. In most programs, this number of degrees of freedom is the default setting. However, if one carries out a molecular simulation in an external field, one needs to ensure that degrees of freedom are changed from this default setting to 3N, as in an external field the velocity of the center of mass can change. Using the correct degrees of freedom is important in calculating the temperature and in some algorithms to simulate at constant temperature. For sufficiently large systems, the difference between 3N and 3N - 3 is negligible. However, there are systems in which the comparison with experimental data requires molecular dynamics simulations of a small number of particles. In this work, we illustrate the effect of an incorrect setting of degrees of freedom in molecular dynamic simulations studying the diffusion properties of guest molecules in nanoporous materials. We show that previously published results have reported a surprising diffusion dependence on the loading, which could be traced back to an incorrect setting of the degrees of freedom. As the correct settings are convoluted and counterintuitive in some of the most commonly used molecular dynamics programs, we carried out a systematic study on the consequences of the various commonly used (incorrect) settings. Our conclusion is that for systems smaller than 50 particles the results are most likely unreliable as these are either performed at an incorrect temperature or the temperature is incorrectly used in some of the results. Furthermore, a novel and efficient method to calculate diffusion coefficients of guest molecules into nanoporous materials at zero-loading conditions is introduced.

The development of a comprehensive toolbox based on multi-level, high-throughput screening of MOFs for CO/N2 separations

The separation of CO/N2 mixtures is a challenging problem in the petrochemical sector due to the very similar physical properties of these two molecules, such as size, molecular weight and boiling point. To solve this and other challenging gas separations, one requires a holistic approach. The complexity of a screening exercise for adsorption-based separations arises from the multitude of existing porous materials, including metal-organic frameworks. Besides, the multivariate nature of the performance criteria that needs to be considered when designing an optimal adsorbent and a separation process - i.e. an optimal material requires fulfillment of several criteria simultaneously - makes the screening challenging. To address this, we have developed a multi-scale approach combining high-throughput molecular simulation screening, data mining and advanced visualization, as well as process system modelling, backed up by experimental validation. We have applied our recent advances in the engineering of porous materials' morphology to develop advanced monolithic structures. These conformed, shaped monoliths can be used readily in industrial applications, bringing a valuable strategy for the development of advanced materials. This toolbox is flexible enough to be applied to multiple adsorption-based gas separation applications.

Stepped Propane Adsorption in Pure-Silica ITW Zeolite

Gas adsorption over zeolites is at the basis of important applications of this class of microporous crystalline solids, notably as separation media and catalysts, but it may also be complex and not straightforward to understand. Here we report that for temperature below 323 K propane adsorption on the small-pore pure-silica zeolite ITW exhibits a clear step (pseudosaturation). This is absent in the case of propene and the other small linear alkanes. An intermediate plateau, clearly observed in the 293 K isotherm, always occurs when one molecule of propane is loaded in every other cage, i.e., at half-saturation. The simulation results show a swelling of the ITW structure upon propane adsorption. The strong dependence of available pore volume on the adsorbate loading level implies that adsorption cannot occur on the void structure while saturation can only be reached on highly loaded structures. To account for this unprecedented adsorption phenomenon, we propose the term "guest-modulated effect".

Adsorptive process design for the separation of hexane isomers using zeolites

The product of catalytic isomerization is a mixture of linear and branched hydrocarbons that are in thermodynamic equilibrium, and their separation becomes necessary in the petrochemical industry. Zeolite 5A is usually industrially used to sieve alkane isomers, but its pore size allows only the separation of linear alkanes from the monobranched and dibranched alkanes by a kinetic mechanism. A more efficient approach to improve the average research octane number would be to adsorptively separate the di-methyl alkanes as products and recycle both the linear and mono-methyl alkanes to the isomerization reactor. Since the microscopic processes of adsorbates in zeolites are generally difficult or impossible to determine by experiments, especially in the case of mixtures, molecular simulation represents an attractive alternative. In this computational study, we propose a conceptual separation process for hexane isomers consisting of several adsorptive steps. Different zeolite topologies were examined for their ability to conduct this separation based on adsorption equilibrium and kinetics.

Unravelling the influence of carbon dioxide on the adsorptive recovery of butanol from fermentation broth using ITQ-29 and ZIF-8

The presence of CO₂during the vapor phase adsorption of butanol from ABE fermentation at the head space of the fermenter has an important roll on the efficient recovery of biobutanol.

Polarizable Force Fields for CO2 and CH4 Adsorption in M-MOF-74

The family of M-MOF-74, with M = Co, Cr, Cu, Fe, Mg, Mn, Ni, Ti, V, and Zn, provides opportunities for numerous energy related gas separation applications. The pore structure of M-MOF-74 exhibits a high internal surface area and an exceptionally large adsorption capacity. The chemical environment of the adsorbate molecule in M-MOF-74 can be tuned by exchanging the metal ion incorporated in the structure. To optimize materials for a given separation process, insights into how the choice of the metal ion affects the interaction strength with adsorbate molecules and how to model these interactions are essential. Here, we quantitatively highlight the importance of polarization by comparing the proposed polarizable force field to orbital interaction energies from DFT calculations. Adsorption isotherms and heats of adsorption are computed for CO2, CH4, and their mixtures in M-MOF-74 with all 10 metal ions. The results are compared to experimental data, and to previous simulation results using nonpolarizable force fields derived from quantum mechanics. To the best of our knowledge, the developed polarizable force field is the only one so far trying to cover such a large set of possible metal ions. For the majority of metal ions, our simulations are in good agreement with experiments, demonstrating the effectiveness of our polarizable potential and the transferability of the adopted approach.

A Simulation Study of Alkanes in Linde Type A Zeolites

Monte Carlo simulations were performed to study the adsorption and diffusion of small hydrocarbons in Linde Type A zeolites as a function of their calcium/sodium ratio. The diffusion studies were focused on methane whereas the adsorption simulations were performed from methane up to pentane. The results obtained showed that an increase in the number of cations in the structure (exchange of univalent sodium ions by divalent calcium ions) led to an increase in the adsorption of linear alkanes at low and medium pressure, but caused a decrease in adsorption at the highest pressures. An increase in the amount of cations favours molecular attraction and hence results in lower mobility. At higher cation loading the ions block the windows interconnecting the LTA cages, leading to a further decrease in diffusion. Methane self-diffusion coefficients obtained from our simulations were twice as high for the Linde Type 5A zeolite as for the Linde Type 4A zeolite. These results are consistent with previous experimental studies and provide a molecular picture of the influence of the zeolite type, the amount of cations contained and their location in the structure.

Defects in metal–organic frameworks: a compromise between adsorption and stability?

Defect engineering has arisen as a promising approach to tune and optimise the adsorptive performance of metal–organic frameworks.

Comparing gas separation performance between all known zeolites and their zeolitic imidazolate framework counterparts

Candidate structures for environmental and industrial gas separations. No correlation between zeolites and their respective Zeolitic Imidazolate framework counterparts.

Computing the Heat of Adsorption using Molecular Simulations: The Effect of Strong Coulombic Interactions

Molecular simulations are an important tool for the study of adsorption of hydrocarbons in nanoporous materials such as zeolites. The heat of adsorption is an important thermodynamic quantity that can be measured both in experiments and molecular simulations, and therefore it is often used to investigate the quality of a force field for a certain guest-host (g - h) system. In molecular simulations, the heat of adsorption in zeolites is often computed using either of the following methods: (1) using the Clausius-Clapeyron equation, which requires the partial derivative of the pressure with respect to temperature at constant loading, (2) using the energy difference between the host with and without a single guest molecule present, and (3) from energy/particle fluctuations in the grand-canonical ensemble. To calculate the heat of adsorption from experiments (besides direct calorimetry), only the first method is usually applicable. Although the computation of the heat of adsorption is straightforward for all-silica zeolites, severe difficulties arise when applying the conventional methods to systems with nonframework cations present. The reason for this is that these nonframework cations have very strong Coulombic interactions with the zeolite. We will present an alternative method based on biased interactions of guest molecules that suffers less from these difficulties. This method requires only a single simulation of the host structure. In addition, we will review some of the other important issues concerning the handling of these strong Coulombic interactions in simulating the adsorption of guest molecules. It turns out that the recently proposed Wolf method ( J. Chem. Phys. 1999, 110 , 8254 ) performs poorly for zeolites as a large cutoff radius is needed for convergence.

Toward a Coarse Graining/All Atoms Force Field (CG/AA) from a Multiscale Optimization Method: An Application to the MCM-41 Mesoporous Silicates

Many interesting physical phenomena occur on length and time scales that are not accessible by atomistic molecular simulations. By introducing a coarse graining of the degrees of freedom, coarse-grained (CG) models allow ther study of larger scale systems for longer times. Coarse-grained force fields have been mostly derived for large molecules, including polymeric materials and proteins. By contrast, there exist no satisfactory CG potentials for mesostructured porous solid materials in the literature. This issue has become critical among a growing number of studies on confinement effects on fluid properties, which require both long time and large scale simulations and the conservation of a sufficient level of atomistic description to account for interfacial phenomena. In this paper, we present a general multiscale procedure to derive a hybrid coarse grained/all atoms force field CG/AA model for mesoporous systems. The method is applied to mesostructured MCM-41 molecular sieves, while the parameters of the mesoscopic interaction potentials are obtained and validated from the computation of the adsorption isotherm of methanol by grand canonical molecular dynamic simulation.

Transferable force fields for adsorption of small gases in zeolites

We provide transferable force fields for oxygen, nitrogen, and carbon monoxide that are able to reproduce experimental adsorption in both pure silica and alumino-substituted zeolites at cryogenic and high temperatures.

A study of interaction potentials for H2 adsorption in Single Walled Nano Tubes: a possible way to more realistic predictions

A comparative analysis of interaction potentials, classified according to the parametrization method, namely Lorentz-Berthelot rules, semi-empirical or ab initio calculations, found their energy depths to scale, respectively, to ca 30K, ca 40K, and ca 60K. We draw the Potential Energy Surfaces (PESs) for a hydrogen probe molecule inside a Carbon Nano-Tube (CNT): it is shown that the adsorption energy increases with the hard radius of the interaction potential and decreases as the CNT pore enlarges. This is valid just for low-medium pressures, when hydrogen repulsions are negligible. If not, adsorption is driven by H2-H2 hard radius despite all other parameters. Monte Carlo (MC) simulations, following the Gibbs Ensemble (GE) in high density conditions, confirm that the thermodynamic equilibrium of an order-disorder phase transition show no changes throughout any of the studied potentials. We also analyse, in the Grand Canonical (GC) ensemble, the geometric and structural characteristics of square lattice bundles of Single Walled Nano Tubes (SWNTs) with regard to their influence on adsorption storage. To do so, we develop a method for independently simulate inner or outer adsorption in infinitely long nanotube lattice systems. Our results suggest a pressure range for convenient H2 storage and enlighten the influence of CNT size on adsorption performance. In addition, larger CNTs are capable to host further hydrogen layers, but only at very high pressures.

Optimizing nanoporous materials for gas storage

In this work, we address the question of which thermodynamic factors determine the deliverable capacity of methane in nanoporous materials. The deliverable capacity is one of the key factors that determines the performance of a material for methane storage in automotive fuel tanks. To obtain insights into how the molecular characteristics of a material are related to the deliverable capacity, we developed several statistical thermodynamic models. The predictions of these models are compared with the classical thermodynamics approach of Bhatia and Myers [Bhatia and Myers, Langmuir, 2005, 22, 1688] and with the results of molecular simulations in which we screen the International Zeolite Association (IZA) structure database and a hypothetical zeolite database of over 100,000 structures. Both the simulations and our models do not support the rule of thumb that, for methane storage, one should aim for an optimal heat of adsorption of 18.8 kJ mol(-1). Instead, our models show that one can identify an optimal heat of adsorption, but that this optimal heat of adsorption depends on the structure of the material and can range from 8 to 23 kJ mol(-1). The different models we have developed are aimed to determine how this optimal heat of adsorption is related to the molecular structure of the material.

Large-scale computational screening of zeolites for ethane/ethene separation

Large-scale computational screening of thirty thousand zeolite structures was conducted to find optimal structures for separation of ethane/ethene mixtures. Efficient grand canonical Monte Carlo (GCMC) simulations were performed with graphics processing units (GPUs) to obtain pure component adsorption isotherms for both ethane and ethene. We have utilized the ideal adsorbed solution theory (IAST) to obtain the mixture isotherms, which were used to evaluate the performance of each zeolite structure based on its working capacity and selectivity. In our analysis, we have determined that specific arrangements of zeolite framework atoms create sites for the preferential adsorption of ethane over ethene. The majority of optimum separation materials can be identified by utilizing this knowledge and screening structures for the presence of this feature will enable the efficient selection of promising candidate materials for ethane/ethene separation prior to performing molecular simulations.

Micro-Imaging by Interference Microscopy: A Case Study of Orientation-Dependent Guest Diffusion in MFI-Type Zeolite Host Crystals

Because of the small particle size, orientation-dependent diffusion measurements in microporous materials remains a challenging task. We highlight here the potential of micro-imaging by interference microscopy in a case study with MFI-type crystals in which, although with different accuracies, transient concentration profiles in all three directions can be observed. The measurements, which were performed with “rounded-boat” shaped crystals, reproduce the evolution patterns of the guest profiles recorded in previous studies with the more common “coffin-shaped” MFI crystals. The uptake and release patterns through the four principal faces (which in the coffin-shaped crystals extend in the longitudinal direction) are essentially coincident and there is no perceptible mass transfer in the direction of the long axis. The surface resistances of the four crystal faces through which mass transfer occurs are relatively small and have only a minor effect on the mass transfer rate. As a result of the pore structure, diffusion in the crystallographic c direction (which corresponds to the direction of the long axis) is expected to be much slower than in the transverse directions. This could explain the very low rate of mass transfer observed in the direction of the long axis, but it is also possible that the small end faces of the crystal may have high surface resistance. It is not possible to distinguish unequivocally between these two possibilities. All guest molecules studied (methyl-butane, benzene and 4-methyl-2-pentyne) show the same orientation dependence of mass transfer. The long 4-methyl-2-pentyne molecules would be expected to propagate at very different rates through the straight and sinusoidal channels. The coinciding patterns for uptake through the mutually perpendicular crystal faces therefore provide clear evidence that both the coffin shaped crystals and the rounded-boat-shaped crystals considered in this study, must be intergrowths rather than pure single crystals.

Comparative molecular simulation study of CO2/N2 and CH4/N2 separation in zeolites and metal-organic frameworks

In this work, a systematic molecular simulation study was performed to compare the separation of CO2/N2 and CH4/N2 mixtures in two different classes of nanoporous materials, zeolites, and metal-organic frameworks (MOFs). For this purpose, three zeolites (MFI, LTA, and DDR) and seven MOFs (Cu-BTC, MIL-47 (V), IRMOF-1, IRMOF-12, IRMOF-14, IRMOF-11, and IRMOF-13) were chosen as the representatives to compare. On the basis of the validated force fields, both adsorption selectivity and pure CO2 and CH4 adsorption isotherms were simulated. The results show that although MOFs perform much better for gas storage, their separation performance is comparable to zeolites; for the systems with the preferable component having a larger quadrupolar moment, both zeolites and MOFs can enhance the separation selectivity, and in contrast they both reduce the selectivity. In addition, we show that ideal adsorbed solution theory (IAST) gives a very reasonable prediction of the mixture adsorption isotherms both in zeolites and in MOFs if the pure component isotherms are known. We demonstrate that the difference in quadrupolar moment of the components is an important property that has to be considered in the selection of a membrane material.

Molecular simulation study of the stepped behaviors of gas adsorption in two-dimensional covalent organic frameworks

In this work, grand canonical Monte Carlo simulations were performed to investigate the adsorption behaviors of three important gases (CO2, CH4 and H2) in two two-dimensional (2D) covalent organic frameworks (COFs) with different pore sizes. The simulation results show that stepped behavior is common in gas adsorption in 2D COFs, and multilayer formation is likely to be the underlying mechanism. For CO2 adsorption in 2D COFs, stepped phenomena easily occur, and the electrostatic interactions between CO2-CO2 molecules play a dominant role, while, within the temperature range studied, no stepped behaviors were found in isotherms for H2 adsorption in 2D COFs because of the too weak interactions in the systems. In addition, this work demonstrates that the stepped behaviors are highly affected by temperature, pore size, and the interaction strengths between adsorbates as well as those between adsorbates and adsorbents.

Identification of adsorption sites in Cu-BTC by experimentation and molecular simulation

The adsorption of several quadrupolar and nonpolar gases on the Metal Organic Framework Cu-BTC has been studied by combining experimental measurements and Monte Carlo simulations. Four main adsorption sites for this structure have been identified: site I close to the copper atoms, site I' in the bigger cavities, site II located in the small octahedral cages, and site III at the windows of the four open faces of the octahedral cage. Our simulations identify the octahedral cages (sites II and III) and the big cages (site I') as the preferred positions for adsorption, while site I, near the copper atoms, remains empty over the entire range of pressures analyzed due to its reduced accessibility. The occupation of the different sites for ethane and propane in Cu-BTC proceeds similarly as for methane, and shows small differences for O2 and N2 that can be attributed to the quadrupole moment of these molecules. Site II is filled predominantly for methane (the nonpolar molecule), whereas for N2, the occupation of II and I' can be considered almost equivalent. The molecular sitting for O2 shows an intermediate behavior between those observed for methane and for N2. The differences between simulated and experimental data at elevated temperatures for propane are tentatively attributed to a reversible change in the lattice parameters of Cu-BTC by dehydration and by temperature, blocking the accessibility to site III and reducing that to site I'. Adsorption parameters of the investigated molecules have been determined from the simulations.