Recent developments in the molecular modeling of diffusion in nanoporous materials

Computational and Machine Learning Methods for CO2 Capture Using Metal-Organic Frameworks

Machine learning (ML) using data sets of atomic and molecular force fields (FFs) has made significant progress and provided benefits in the fields of chemistry and material science. This work examines the interactions between chemistry and materials computational science at the atomic and molecular scales for metal-organic framework (MOF) adsorbent development toward carbon dioxide (CO2) capture. Herein, a connection will be drawn between atomic forces predicted by ML algorithms and the structures of MOFs for CO2 adsorption. Our study also takes into account the successes of atomic computational screening in the field of materials science, especially quantum ML, and its relationship to ML algorithms that clarify advancements in the area of CO2 adsorption by MOFs. Additionally, we reviewed the processes for supplying data to ML algorithms for algorithm training, including text mining from scientific articles, and MOF's formula processing linked to the chemical properties of MOFs. To create ML algorithms for future research, we recommend that the digitization of scientific records can help efficiently synthesize advanced MOFs. Finally, a future vision for developing pioneer MOF synthesis routes for CO2 capture is presented in this review article.

Probing Self-Diffusion of Guest Molecules in a Covalent Organic Framework: Simulation and Experiment

Covalent organic frameworks (COFs) are a class of porous materials whose sorption properties have so far been studied primarily by physisorption. Quantifying the self-diffusion of guest molecules inside their nanometer-sized pores allows for a better understanding of confinement effects or transport limitations and is thus essential for various applications ranging from molecular separation to catalysis. Using a combination of pulsed field gradient nuclear magnetic resonance measurements and molecular dynamics simulations, we have studied the self-diffusion of acetonitrile and chloroform in the 1D pore channels of two imine-linked COFs (PI-3-COF) with different levels of crystallinity and porosity. The higher crystallinity and porosity sample exhibited anisotropic diffusion for MeCN parallel to the pore direction, with a diffusion coefficient of Dpar = 6.1(3) × 10-10 m2 s-1 at 300 K, indicating 1D transport and a 7.4-fold reduction in self-diffusion compared to the bulk liquid. This finding aligns with molecular dynamics simulations predicting 5.4-fold reduction, assuming an offset-stacked COF layer arrangement. In the low-porosity sample, more frequent diffusion barriers result in isotropic, yet significantly reduced diffusivities (DB = 1.4(1) × 10-11 m2 s-1). Diffusion coefficients for chloroform at 300 K in the pores of the high- (Dpar = 1.1(2) × 10-10 m2 s-1) and low-porosity (DB = 4.5(1) × 10-12 m2 s-1) samples reproduce these trends. Our multimodal study thus highlights the significant influence of real structure effects such as stacking faults and grain boundaries on the long-range diffusivity of molecular guest species while suggesting efficient intracrystalline transport at short diffusion times.

Reaching Quantum Accuracy in Predicting Adsorption Properties for Ethane/Ethene in Zeolitic Imidazolate Framework-8 at Low Pressure Regime

Nanoporous materials in the form of metal-organic frameworks such as zeolitic imidazolate framework-8 (ZIF-8) are promising membrane materials for the separation of hydrocarbon mixtures. To compute the adsorption isotherms in such adsorbents, grand canonical Monte Carlo simulations have proven to be very useful. The quality of these isotherms depends on the accuracy of adsorbate-adsorbent interactions, which are mostly described using force fields owing to their low computational cost. However, force field predictions of adsorption uptake often show discrepancies from experiments at low pressures, providing the need for methods that are more accurate. Hence, in this work, we propose and validate two novel methodologies for the ZIF-8/ethane and ethene systems; a benchmarking methodology to evaluate the performance of any given force field in describing adsorption in the low-pressure regime and a refinement procedure to rescale the parameters of a force field to better describe the host-guest interactions and provide for simulation isotherms with close agreement to experimental isotherms. Both methodologies were developed based on a reference Henry coefficient, computed with the PBE-MBD functional using the importance sampling technique. The force field rankings predicted by the benchmarking methodology involve the comparison of force field derived Henry coefficients with the reference Henry coefficients and ranking the force fields based on the disparities between these Henry coefficients. The ranking from this methodology matches the rankings made based on uptake disparities by comparing force field derived simulation isotherms to experimental isotherms in the low-pressure regime. The force field rescaling methodology was proven to refine even the worst performing force field in UFF/TraPPE. The uptake disparities of UFF/TraPPE improved from 197% and 194% to 11% and 21% for ethane and ethene, respectively. The proposed methodology is applicable to predict adsorption across nanoporous materials and allows for rescaled force fields to reach quantum accuracy without the need for experimental input.

Impact of unrecovered shale gas reserve on methane emissions from abandoned shale gas wells

Shale gas, with its abundance and lower carbon footprint compared to other fossil fuels, is an important bridge fuel in the ongoing energy transition. However, a notable concern in shale gas exploration is fugitive methane emissions during the extraction, development, and transport of natural gas. While most existing works evaluate methane emissions released by well fracking, completion and operation, the greenhouse footprint of unproductive shale gas wells (often abandoned or orphaned) has received little scrutiny. A large fraction of these emissions from abandoned shale gas wells are due to the diffusive transport of methane trapped in nanoporous shale matrix, which is poorly understood. Here, we develop a theoretical kinetic approach to predict methane diffusive flux from heterogeneous shale matrix. Our theoretical model is based on a layer sequence formulation and accurately considers multiple flow mechanisms, including viscous flow, gas slippage, and Knudsen diffusion and their mutual interactions. The model is validated against the observed methane diffusion data obtained from high-pressure and high-temperature experimental measurements on Marcellus shale. We find that methane diffusive flux increases as reservoir pressure decreases. We estimate methane emission due to diffusive transport up to 20 × 103 m3 per well per day, which is comparable to emissions from flowback fluid. For the first time, unrecovered natural gas in the shale matrix is demonstrated to be the main source of methane emissions from abandoned shale gas wells. Given the long-lasting nature of diffusive transport to shale gas seepage, it is suggested that regulatory requirements should be implemented to provide long-term monitoring of methane emissions from abandoned shale gas wells.

Dependence of Methane Transport on Pore Informatics in the Amorphous Nanoporous Kerogen Matrix

Fluid transport in kerogen is mainly diffusion-driven, while its dependence on pore informatics is still poorly understood. It is challenging for experiments to identify the effect of pore informatics (such as pore connectivity and tortuosity) on fluid transport therein. Therefore, in this work, we use molecular dynamics simulations to study methane transport behaviors in amorphous kerogen matrices with broad pore properties. The pore properties including porosity, pore connectivity, pore size, and diffusive tortuosity are characterized. Next, self-diffusion coefficients in the connected pores (DeffS) and in the total pores without distinguishing its connectivity (DtotS) are calculated in all the kerogen matrices based on the free volume theory. We find that both DeffS and DtotS exponentially decreases with methane loading with two controlled parameters: fitting constant αeff and DeffS(0) (DeffS at infinitely small loading) for DeffS and fitting constant αtot and DtotS(0) (DtotS at infinitely small loading) for DtotS. However, in the kerogen models with relatively low pore connectivity, αeff and αtot as well as DeffS(0) and DtotS(0) can be quite different, inducing the different estimations of DeffS and DtotS. Since methane in the unconnected pores does not contribute to the actual transport, it is important to recognize connected pores when evaluating the fluid transport in kerogen. On the other hand, DeffS(0) strongly depends on the effective limiting pore size (rlim_eff) of the dominant flow path and effective diffusive tortuosity (τeff), in which DeffS(0) linearly increases with (rlim_eff/τeff)2. We also find that αeff is a multivariable function of ϕeff, τeff, and rlim_eff, but their generalized relation requires more data to obtain. This work provides important insights into fluid transport in kerogen based on the kerogen pore informatics, which are important to shale gas development.

Cooperative Catalytic Alkyne Hydrosilylation by a Porphyrinic Metal-Organic Framework Composite

Vinylsilanes are valuable building blocks and important structural units in organic chemistry. Herein, catalytic alkyne hydrosilylation was reported to be promoted by a porphyrin metal-organic framework with the incorporation of Pd nanoparticles (Pd@Ir-PCN-222). Catalytic results showed that Pd@Ir-PCN-222 displayed high catalytic efficiency, giving rise to the E isomer vinylsilane with an excellent turnover frequency (TOF) of 2564 h-1. The mechanism studies revealed that the enhancement of the catalytic activity originated from the cooperation between iridium porphyrin and the Pd nanoparticle in confined spaces. The iridium porphyrin was prone to absorb and condense the hydrosilane and alkyne in the inner cavities of Ir-PCN-222, not only accelerating the reaction but also promoting the Pd nanoparticle to activate the Si-H and C≡C bonds of hydrosilane and alkyne, respectively.

Interplay of Hydropathy and Heterogeneous Diffusion in the Molecular Transport within Lamellar Lipid Mesophases

Lipid mesophases are being intensively studied as potential candidates for drug-delivery purposes. Extensive experimental characterization has unveiled a wide palette of release features depending on the nature of the host lipids and of the guest molecule, as well as on the environmental conditions. However, only a few simulation works have addressed the matter, which hampers a solid rationalization of the richness of outcomes observed in experiments. Particularly, to date, there are no theoretical works addressing the impact of hydropathy on the transport of a molecule within lipid mesophases, despite the significant fraction of hydrophobic molecules among currently-available drugs. Similarly, the high heterogeneity of water mobility in the nanoscopic channels within lipid mesophases has also been neglected. To fill this gap, we introduce here a minimal model to account for these features in a lamellar geometry, and systematically study the role played by hydropathy and water-mobility heterogeneity by Brownian-dynamics simulations. We unveil a fine interplay between the presence of free-energy barriers, the affinity of the drug for the lipids, and the reduced mobility of water in determining the net molecular transport. More in general, our work is an instance of how multiscale simulations can be fruitfully employed to assist experiments in release systems based on lipid mesophases.

Molecular and Artificial Neural Networks Modeling of Sorption and Diffusion of Small Alkanes, Alkenes and Their Ternary Mixtures in ZIF-8 at Different Temperatures

Numerical computations comprising of Grand Canonical-Monte Carlo (GCMC) and Canonical Statistical Ensemble (NVT) Molecular Dynamics (MD) simulations were used to study the diffusion and sorption characteristics primarily for methane, ethane, and ethene molecules and for their ternary mixtures at different temperatures in ZIF-8 porous material. Methane as pure component or in mixture proved to be the sorbed hydrocarbon with the higher molecular mobility at the temperature range of 273-373 K among alkanes and alkenes. In addtion, alkenes were the hydrocarbons with the higher self-diffusion coefficients compared to the respective alkanes. In the ternary mixtures ethane was preferentially sorbed in ZIF-8 at all temperatures studied. Direct comparisons of the self-diffusivity data obtained from the NVT-MD simulations with recently reported Magic Angle Spinning Pulsed Field Gradient Nuclear Magnetic Resonance (MAS PFG NMR) measurements showed reasonable agreement. Furthermore, the NVT-MD self-diffusivity coefficients in conjunction with the aforementioned MAS PFG NMR experimental measurements, and sorption thermodynamic data obtained from the present GCMC simulations were utilized for the development of individual Artificial Neural Networks (ANNs) predictive modeling procedures in order to provide additional quantitative and qualitative information regarding the diffusion and sorption of small alkanes, alkenes in ZIF-8. The ANNs predictions were in good agreement with the experimental measurements and with the molecular simulation data. The modeling and analysis capabilities of ANNs along with their fast computations using moderate computer resources can significantly assist the irreplaceable molecular simulation and experimental approaches to cope with complicated problems at the molecular level.

Interlayer Expansion in a Layered Metal-Organic Framework Enhances CO2 Capture and CO2/N2 Separation

Developing efficient CO 2 adsorbent materials and technologies is significant to reduce the increasing greenhouse gases concentration in the atmosphere. Herein, a layered MOF with a porous kagomé lattice (kgm), which owned three phases (kgm-1, kgm-2, and kgm-3) via interlayer expansion, was evaluated as a promising CO 2 capture and separation material by using grand canonical Monte Carlo simulations. Results showed that the interlayer expansion provided additional pore volume, which played a considerable role in CO 2 adsorption and separation. The CO 2 adsorption capacity and CO 2 /N 2 selectivity followed the sequence kgm-3 > kgm-2 > kgm-1, and kgm-3 exhibited an excellent CO 2 adsorption capacity of 8.7 mmol g -1 at 1 bar with a CO 2 /N 2 selectivity of 130.3 at 20 bar and 298 K. Gas distribution analysis showed that CO 2 and N 2 are adsorbed only in the channels in kgm-1, whereas they could be adsorbed between layers in kgm-2 and kgm-3 due to the interlayer expansion. The adsorption heat and interactions between CO 2 and frameworks were analyzed to elucidate the effect of interlayer expansion. Results of this work highlighted that appropriate interlayer expansion can be an effective approach for framework adsorbents to improve CO 2 capture ability and separation performance at the same time.

Energy-efficient recovery of fermented butyric acid using octyl acetate extraction

Background

A butyric acid recovery process using octyl acetate is proposed, and the design details of the extraction and subsequent distillation processes were investigated. Ternary equilibrium data for the extractor design were derived from molecular simulations and experimental measurements.

Results

A new procedure for estimating the thermodynamic parameters was introduced to determine the effect of the parameters on extractor design by comparison with previously reported parameters. Using the proposed recovery process with the newly estimated thermodynamic model, 99.8% butyric acid was recovered from the fermentation broth at a recovery rate of 99%. The energy demand for the proposed process was found to be lower than the average demand for several reported butyric acid recovery processes.

Conclusions

The investment cost is projected to be lower than that of other butyric acid processes due to the high efficiency of extraction solvent. The recovery cost of butyric acid was comparable to its selling price.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13068-022-02146-6.

Use of Boundary-Driven Nonequilibrium Molecular Dynamics for Determining Transport Diffusivities of Multicomponent Mixtures in Nanoporous Materials

The boundary-driven molecular modeling strategy to evaluate mass transport coefficients of fluids in nanoconfined media is revisited and expanded to multicomponent mixtures. The method requires setting up a simulation with bulk fluid reservoirs upstream and downstream of a porous media. A fluid flow is induced by applying an external force at the periodic boundary between the upstream and downstream reservoirs. The relationship between the resulting flow and the density gradient of the adsorbed fluid at the entrance/exit of the porous media provides for a direct path for the calculation of the transport diffusivities. It is shown how the transport diffusivities found this way relate to the collective, Onsager, and self-diffusion coefficients, typically used in other contexts to describe fluid transport in porous media. Examples are provided by calculating the diffusion coefficients of a Lennard-Jones (LJ) fluid and mixtures of differently sized LJ particles in slit pores, a realistic model of methane in carbon-based slit pores, and binary mixtures of methane with hypothetical counterparts having different attractions to the solid. The method is seen to be robust and particularly suited for the study of study of transport of dense fluids and liquids in nanoconfined media.

In Silico Prediction of Food Properties: A Multiscale Perspective

Several open software packages have popularized modeling and simulation strategies at the food product scale. Food processing and key digestion steps can be described in 3D using the principles of continuum mechanics. However, compared to other branches of engineering, the necessary transport, mechanical, chemical, and thermodynamic properties have been insufficiently tabulated and documented. Natural variability, accented by food evolution during processing and deconstruction, requires considering composition and structure-dependent properties. This review presents practical approaches where the premises for modeling and simulation start at a so-called “microscopic” scale where constituents or phase properties are known. The concept of microscopic or ground scale is shown to be very flexible from atoms to cellular structures. Zooming in on spatial details tends to increase the overall cost of simulations and the integration over food regions or time scales. The independence of scales facilitates the reuse of calculations and makes multiscale modeling capable of meeting food manufacturing needs. On one hand, new image-modeling strategies without equations or meshes are emerging. On the other hand, complex notions such as compositional effects, multiphase organization, and non-equilibrium thermodynamics are naturally incorporated in models without linearization or simplifications. Multiscale method’s applicability to hierarchically predict food properties is discussed with comprehensive examples relevant to food science, engineering and packaging. Entropy-driven properties such as transport and sorption are emphasized to illustrate how microscopic details bring new degrees of freedom to explore food-specific concepts such as safety, bioavailability, shelf-life and food formulation. Routes for performing spatial and temporal homogenization with and without chemical details are developed. Creating a community sharing computational codes, force fields, and generic food structures is the next step and should be encouraged. This paper provides a framework for the transfer of results from other fields and the development of methods specific to the food domain.

Performance-Based Screening of Porous Materials for Carbon Capture

Computational screening methods have changed the way new materials and processes are discovered and designed. For adsorption-based gas separations and carbon capture, recent efforts have been directed toward the development of multiscale and performance-based screening workflows where we can go from the atomistic structure of an adsorbent to its equilibrium and transport properties at different scales, and eventually to its separation performance at the process level. The objective of this work is to review the current status of this new approach, discuss its potential and impact on the field of materials screening, and highlight the challenges that limit its application. We compile and introduce all the elements required for the development, implementation, and operation of multiscale workflows, hence providing a useful practical guide and a comprehensive source of reference to the scientific communities who work in this area. Our review includes information about available materials databases, state-of-the-art molecular simulation and process modeling tools, and a complete catalogue of data and parameters that are required at each stage of the multiscale screening. We thoroughly discuss the challenges associated with data availability, consistency of the models, and reproducibility of the data and, finally, propose new directions for the future of the field.

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.

Molecular dynamics study of water confined in MIL-101 metal-organic frameworks

Molecular dynamics simulations of water adsorbed in Material Institute Lavoisier MIL-101(Cr) metal-organic frameworks are performed to analyze the kinetic properties of water molecules confined in the framework at 298.15 K and under different vapor pressures and clarify the water adsorption mechanism in MIL-101(Cr). The terahertz frequency-domain spectra (THz-FDS) of water are calculated by applying fast Fourier transform to the configurational data of water molecules. According to the characteristic frequencies in the THz-FDS, the dominant motions of water molecules in MIL-101(Cr) can be categorized into three types: (1) low-frequency translational motion (0-0.5 THz), (2) medium-frequency vibrational motion (2-2.5 THz), and (3) high-frequency vibrational motion (>6 THz). Each type of water motion is confirmed by visualizing the water configuration in MIL-101(Cr). The ratio of the number of water molecules with low-frequency translational motion to the total number of water molecules increases with the increase in vapor pressure. In contrast, that with medium-frequency vibrational motion is found to decrease with vapor pressure, exhibiting a pronounced decrease after water condensation has started in the cavities. That with the high-frequency vibrational motion is almost independent of the vapor pressure. The interactions between different types of water molecules affect the THz-FDS. Furthermore, the self-diffusion coefficient and the velocity auto-correlation function are calculated to clarify the adsorption state of the water confined in MIL-101(Cr). To confirm that the general trend of the THz-FDS does not depend on the water model, the simulations are performed using three water models, namely, rigid SPC/E, flexible SPC/E, and rigid TIP5PEw.

Simulation of the Adsorption and Release of Large Drugs by ZIF-8

The adsorption and release of two drugs 5FU (5-fluorouracil) and CAF (caffeine) into and from the ZIF-8 framework were simulated by the Gibbs-ensemble Monte Carlo approach employing two models for representing the sorbent: one without surface (ZIF-8P) and another with surface (ZIF-8S). The inner pores of ZIF-8S were inaccessible to the drugs, but accessible to the solvents (methanol or water). The ZIF-8P model is not recommended to describe the actual sorption processes because it lacks surface and solvent effects, which are reflected in the poor quantitative agreement with experimental results. The ZIF-8S model yielded results for the sorption of CAF in very close agreement with the experimental loading from methanol solution and release of the drug into water. For 5FU, the computer simulations provided qualitative agreements, which suggests that the sorbent-5FU interaction potentials should be improved. The excellent performance of the ZIF-8S model is due to its adequate description of the surface and by exposing adsorption sites such as undercoordinated zinc ions to interactions with large molecules. This was achieved by applying periodic conditions to a ZIF-8 nanocrystal, instead of an elementary cell, which is easy to generalize and used to describe several surface defects. Furthermore, the combination of this ZIF-8S model with the Monte Carlo method provides a very simple and efficient approach to simulate the inaccessibility of the ZIF-8 inner porosity to large molecules. Namely, any trial moves that inserted the drug within the pore were disregarded. This is a quite simple and general approach that can be promptly applied to a large number of MOF sorbents and of drugs that cannot access the inner pores.

Understanding the Loading Dependence of Adsorbate Diffusivities in Hierarchical Metal-Organic Frameworks

Using atomistic simulations, we studied the diffusion of n-hexane in a series of isoreticular hierarchical metal-organic frameworks (MOFs) NU-100x. Nonmonotonic diffusivity-loading relationships that depend on the pore sizes were observed, which can be explained by the spatial distribution of adsorbates at different loadings. For one of the MOFs in the series, NU-1000-M, the diffusivity-loading relationship is almost identical to the previously reported results of n-hexane diffusion in the hierarchical self-pillared pentasil (SPP) zeolite. Detailed analysis revealed that the similarity results from their similar micropore and window sizes, which was confirmed by free-energy mapping. The effects of temperature and adsorbate chain length on the diffusion were also studied, which supported our conclusion that the diffusivity in hierarchical nanoporous materials is primarily controlled by the sizes of the micropores and the connecting windows, particularly at relatively low loadings.

Progress in supercapacitors: roles of two dimensional nanotubular materials

Overcoming the global energy crisis due to vast economic expansion with the advent of human reliance on energy-consuming labor-saving devices necessitates the demand for next-generation technologies in the form of cleaner energy storage devices. The technology accelerates with the pace of developing energy storage devices to meet the requirements wherever an unanticipated burst of power is indeed needed in a very short time. Supercapacitors are predicted to be future power vehicles because they promise faster charging times and do not rely on rare elements such as lithium. At the same time, they are key nanoscale device elements for high-frequency noise filtering with the capability of storing and releasing energy by electrostatic interactions between the ions in the electrolyte and the charge accumulated at the active electrode during the charge/discharge process. There have been several developments to increase the functionality of electrodes or finding a new electrolyte for higher energy density, but this field is still open to witness the developments in reliable materials-based energy technologies. Nanoscale materials have emerged as promising candidates for the electrode choice, especially in 2D sheet and folded tubular network forms. Due to their unique hierarchical architecture, excellent electrical and mechanical properties, and high specific surface area, nanotubular networks have been widely investigated as efficient electrode materials in supercapacitors, while maintaining their inherent characteristics of high power and long cycling life. In this review, we briefly present the evolution, classification, functionality, and application of supercapacitors from the viewpoint of nanostructured materials to apprehend the mechanism and construction of advanced supercapacitors for next-generation storage devices.

Diffusion in Binary Aqueous Solutions of Alcohols by Molecular Simulation

Based on the molecular dynamics method, the calculations for diffusion coefficients were carried out in binary aqueous solutions of three alcohols: ethanol, isopropanol, and tert-butanol. The intermolecular potential TIP4P/2005 was used for water; and five force fields were analyzed for the alcohols. The force fields providing the best accuracy of calculation were identified based on a comparison of the calculated self-diffusion coefficients of pure alcohols with the experimental data for internal (Einstein) diffusion coefficients of alcohols in solutions. The temperature and concentration dependences of the interdiffusion coefficients were determined using Darken’s Equation. Transport (Fickian) diffusion coefficients were calculated using a thermodynamic factor determined by the non-random two-liquid (NRTL) and Willson models. It was demonstrated that for adequate reproduction of the experimental data when calculating the transport diffusion coefficients, the thermodynamic factor has to be 0.64. Simple approximations were obtained, providing satisfactory accuracy in calculating the concentration and temperature dependences of the transport diffusion coefficients in the studied mixtures.

A thermo-responsive adsorbent-heater-thermometer nanomaterial for controlled drug release: (ZIF-8,EuxTby)@AuNP core-shell

An adsorbent-heater-thermometer nanomaterial, (ZIF-8,Eu_xTb_y)@AuNP, based on ZIF-8 (adsorbent), containing Eu³⁺ and/or Tb³⁺ ions (thermometer) and gold nanoparticles (AuNPs, heater) was designed, synthetized, characterized, and applied to controlled drug release. These composite materials were characterized as core-shell nanocrystals with the AuNPs being the core, around which the crystalline ZIF-8 has grown (shell) and onto which the lanthanide ions have been incorporated or chemosorbed. This shell of ZIF-8 acts as adsorbent of the drugs, the AuNPs act as heaters, while the luminescence intensities of the ligand and the lanthanide ions are used for temperature monitoring. This thermo-responsive material can be activated by visible irradiation to release small molecules in a controlled manner as established for the model pharmaceutical compounds 5-fluorouracil and caffeine. Computer simulations and transition state theory calculations shown that the diffusion of small molecules between neighboring pores in ZIF-8 is severely restricted and involves high-energy barriers. These findings imply that these molecules are uploaded onto and released from the ZIF-8 surface instead of being inside the cavities. This is the first report of ZIF-8 nanocrystals (adsorbents) containing simultaneously lanthanide ions as sensitive nanothermometers and AuNPs as heaters for controlled drug release in a physiological temperature range. These results provide a proof-of-concept that can be applied to other classes of materials, and offer a novel perspective on the design of self-assembly multifunctional thermo-responsive adsorbing materials that are easily prepared and promptly controllable.

The role of molecular modelling and simulation in the discovery and deployment of metal-organic frameworks for gas storage and separation

Metal-organic frameworks (MOFs) are highly tuneable, extended-network, crystalline, nanoporous materials with applications in gas storage, separations, and sensing. We review how molecular models and simulations of gas adsorption in MOFs have informed the discovery of performant MOFs for methane, hydrogen, and oxygen storage, xenon, carbon dioxide, and chemical warfare agent capture, and xylene enrichment. Particularly, we highlight how large, open databases of MOF crystal structures, post-processed to enable molecular simulations, are a platform for computational materials discovery. We discuss how to orient research efforts to routinise the computational discovery of MOFs for adsorption-based engineering applications.

Intermediate states approach for adsorption studies in flexible metal–organic frameworks

Adsorption studies in flexible metal–organic frameworks are challenging and time-consuming.

Improving Olefin Purification Using Metal Organic Frameworks with Open Metal Sites

The separation and purification of light hydrocarbons is challenging in the industry. Recently, a ZJNU-30 metal-organic framework (MOF) has been found to have the potential for adsorption-based separation of olefins and diolefins with four carbon atoms [H. M. Liu et al. Chem.-Eur. J. 2016, 22, 14988-14997]. Our study corroborates this finding but reveals Fe-MOF-74 as a more efficient candidate for the separation because of the open metal sites. We performed adsorption-based separation, transient breakthrough curves, and density functional theory calculations. This combination of techniques provides an extensive understanding of the studied system. Using this MOF, we propose a separation scheme to obtain a high-purity product.

Thermodynamic Route to Efficient Prediction of Gas Diffusivity in Nanoporous Materials

We report an efficient computational procedure for rapid and accurate prediction of the self-diffusivity of gas molecules in nanoporous materials by implementing the transition state theory for intercage hopping at infinite dilution with the string method in conjunction with the excess-entropy scaling for predicting gas diffusion coefficients at finite loadings. The theoretical procedure has been calibrated with molecular dynamics simulations for the diffusion coefficients of methane and hydrogen gases in representative nanoporous materials including metal organic frameworks and zeolites. Combined with the classical density functional theory for calculating the excess entropy of gas molecules in micropores, the theoretical procedure enables efficient computation of both thermodynamic and transport properties important for design and screening of nanostructured materials for gas storage and separation.

Adsorption and Diffusion of C1 to C4 Alkanes in Dual-Porosity Zeolites by Molecular Simulations

We employ grand canonical Monte Carlo and molecular dynamics simulations to systematically study the adsorption and diffusion of C₁ to C₄ alkanes in hierarchical ZSM-5 zeolite with micropores (∼1 nm) and mesopores (>2 nm). The zeolite is characterized by a large surface area of active sites on the microporous scale with high permeability and access to the active sites, which arises from the enhanced transport at the mesoporous scale. We model this zeolite as a microporous Na⁺-exchanged alumino-sillicate zeolite ZSM-5/35 (Si/Al = 35) in which cylindrical mesopores with a diameter of 4 nm have been built by deleting atoms accordingly. We use the TraPPE and Vujić-Lyubartsev force fields along with the Lorentz-Berthelot combining rules to describe adsorbate-adsorbate and adsorbate-adsorbent interactions. The performance of the force fields is assessed by comparing against experimental single-component adsorption isotherms of methane and ethane in microporous ZSM-5/35, which we measured as part of this work. We compare the adsorption isotherms and diffusivities of the adsorbed alkanes in the dual-porosity zeolite with those in microporous ZSM-5/35 and discern the specific behavior at each porosity scale on the overall adsorption, self-diffusion, and transport behavior in zeolites with dual micro/mesoporosities.

Lattice-Gas Modeling of Adsorbate Diffusion in Mixed-Linker Zeolitic Imidazolate Frameworks: Effect of Local Imidazolate Ordering

The rates of adsorbate diffusion in zeolitic imidazolate frameworks (ZIFs) can be varied by several orders of magnitude by incorporating two different imidazolate linkers in the ZIF crystals. Although some prior measurements of short-range order in these mixed-linker materials have been reported, it is unclear how this short-range order impacts the net diffusion of adsorbates. We introduce a lattice diffusion model that treats diffusion in ZIF-8_x-90_100-x crystals as a series of activated hops between cages, allowing us to assess the effects of short-range imidazolate order on molecular diffusion.

Metal–organic frameworks for the removal of toxic industrial chemicals and chemical warfare agents

Toxic gases can be captured or degraded by metal–organic frameworks.

Application of computational methods to the design and characterisation of porous molecular materials

Composed from discrete units, porous molecular materials (PMMs) possess properties not observed for conventional, extended solids. Molecular simulations provide crucial understanding for the design and characterisation of these unique materials.

Selective Adsorption and Selective Transport Diffusion of CO2-CH4 Binary Mixture in Coal Ultramicropores

The adsorption and diffusion of the CO2-CH4 mixture in coal and the underlying mechanisms significantly affect the design and operation of any CO2-enhanced coal-bed methane recovery (CO2-ECBM) project. In this study, bituminous coal was fabricated based on the Wiser molecular model and its ultramicroporous parameters were evaluated; molecular simulations were established through Grand Canonical Monte Carlo (GCMC) and Molecular Dynamic (MD) methods to study the effects of temperature, pressure, and species bulk mole fraction on the adsorption isotherms, adsorption selectivity, three distinct diffusion coefficients, and diffusivity selectivity of the binary mixture in the coal ultramicropores. It turns out that the absolute adsorption amount of each species in the mixture decreases as temperature increases, but increases as its own bulk mole fraction increases. The self-, corrected, and transport diffusion coefficients of pure CO2 and pure CH4 all increase as temperature or/and their own bulk mole fractions increase. Compared to CH4, the adsorption and diffusion of CO2 are preferential in the coal ultramicropores. Adsorption selectivity and diffusivity selectivity were simultaneously employed to reveal that the optimal injection depth for CO2-ECBM is 800-1000 m at 308-323 K temperature and 8.0-10.0 MPa.

Critical Role of Dynamic Flexibility in Ge-Containing Zeolites: Impact on Diffusion

Incorporation of germanium in zeolites is well known to confer static flexibility to their framework, by stabilizing the formation of small rings. In this work, we show that the flexibility associated to Ge atoms in zeolites goes beyond this static effect, manifesting also a clear dynamic nature, in the sense that it leads to enhanced molecular diffusion. Our study combines experimental and theoretical methods providing evidence for this effect, which has not been described previously, as well as a rationalization for it, based on atomistic grounds. We have used both pure‐silica and silico‐germanate ITQ‐29 (LTA topology) zeolites as a case study. Based on our simulations, we identify the flexibility associated to the pore breathing‐like behavior induced by the Ge atoms, as the key factor leading to the enhanced diffusion observed experimentally in Ge‐containing zeolites.

Thermodynamic Resistance to Matter Flow at The Interface of a Porous Membrane

Nanoporous materials are important in industrial separation, but their application is subject to strong interfacial barriers to the entry and transport of fluids. At certain conditions the fluid inside and outside the nanoporous material can be viewed as a two-phase system, with an interface between them, which poses an excess resistance to matter flow. We show that there exist two kinds of phenomena which influence the interfacial resistance: hydrodynamic effects and thermodynamic effects, which are independent of each other. Here, we investigate the role of the thermodynamic effects in carbon nanotubes (CNTs) and slit pores and compare the associated thermodynmic resistance with that due to hydrodynamic effects traditionally modeled by the established Sampson expression. Using CH4 and CO2 as model fluids, we show that the thermodynamic resistance is especially important for moderate to high pressures, at which the fluid within the CNT or slit pore is in the condensed state. Further, we show that at such pressures the thermodynamic resistance becomes comparable with the internal resistance to fluid transport at length scales typical of membranes used in fuel cells, and of importance in membrane-based separation, and nanofluidics in general.

Heterogeneous Diffusion of Alkanes in the Hierarchical Metal-Organic Framework NU-1000

The metal-organic framework (MOF) NU-1000 is a hierarchical material that comprises both micropores and mesopores in its crystalline structure. Because the pore structure is perfectly defined, NU-1000 is an interesting material for improving our understanding of diffusion in hierarchically structured materials. Here, we present molecular dynamics simulations aimed at probing the transport properties of n-alkanes in NU-1000 and introduce methods from the microrheology literature for analyzing the mean-squared displacements and their spatial heterogeneity. Adsorption occurs initially in the smaller channels, and diffusion at low loading is limited by interaction between adsorbate and framework atoms. The larger channels provide a region of low density where molecules are able to diffuse at higher rates predominantly along the channel axes. The disparate size of the channels gives rise to heterogeneity in the diffusivity of the guest molecules, whereas the asymmetry of the channels leads to anisotropic diffusion. Together, the channels form a network of "highways" and "side streets" that provide enhanced diffusion in one dimension.

High-throughput computational screening of metal-organic frameworks

There is an almost unlimited number of metal-organic frameworks (MOFs). This creates exciting opportunities but also poses a problem: how do we quickly find the best MOFs for a given application? Molecular simulations have advanced sufficiently that many MOF properties - especially structural and gas adsorption properties - can be predicted computationally, and molecular modeling techniques are now used increasingly to guide the synthesis of new MOFs. With increasing computational power and improved simulation algorithms, it has become possible to conduct high-throughput computational screening to identify promising MOF structures and uncover structure-property relations. We review these efforts and discuss future directions in this new field.

Influence of Structural Heterogeneity on Diffusion of CH4 and CO2 in Silicon Carbide-Derived Nanoporous Carbon

We investigate the influence of structural heterogeneity on the transport properties of simple gases in a Hybrid Reverse Monte Carlo (HRMC) constructed model of silicon carbide-derived carbon (SiC-DC). The energy landscape of the system is determined based on free energy analysis of the atomistic model. The overall energy barriers of the system for different gases are computed along with important properties, such as Henry constant and differential enthalpy of adsorption at infinite dilution, and indicate hydrophobicity of the SiC-DC structure and its affinity for CO₂ and CH₄ adsorption. We also study the effect of molecular geometry, pore structure and energy heterogeneity considering different hopping scenarios for diffusion of CO₂ and CH₄ through ultramicropores using the Nudged Elastic Band (NEB) method. It is shown that the energy barrier of a hopping molecule is very sensitive to the shape of the pore entry. We provide evidence for the influence of structural heterogeneity on self-diffusivity of methane and carbon dioxide using molecular dynamics simulation, based on a maximum in the variation of self-diffusivity with loading. A comparison of the MD simulation results with self-diffusivities from quasi-elastic neutron scattering (QENS) measurements and, with macroscopic uptake-based low-density transport coefficients, reveals the existence of internal barriers not captured in MD simulation and QENS experiments. Nevertheless, the simulation and macroscopic uptake-based diffusion coefficients agree within a factor of 2-3, indicating that our HRMC model structure captures most of the important energy barriers affecting the transport of CH₄ in the nanostructure of SiC-DC.