Self-Diffusion of Chain Molecules in the Metal-Organic Framework IRMOF-1: Simulation and Experiment

Elucidating the Competitive Adsorption of H2O and CO2 in CALF-20: New Insights for Enhanced Carbon Capture Metal-Organic Frameworks

In light of the pressing need for efficient carbon capture solutions, our study investigates the simultaneous adsorption of water (H2O) and carbon dioxide (CO2) as a function of relative humidity in CALF-20, a highly scalable and stable metal-organic framework (MOF). Advanced computer simulations reveal that due to their similar interactions with the framework, H2O and CO2 molecules compete for the same binding sites, occupying similar void regions within the CALF-20 pores. This competition results in distinct thermodynamic and dynamical behaviors of H2O and CO2 molecules, depending on whether one or both guest species are present. Notably, the presence of CO2 molecules forces the H2O molecules to form more connected hydrogen-bond networks within smaller regions, slowing water reorientation dynamics and decreasing water entropy. Conversely, the presence of water speeds up the reorientation of CO2 molecules, decreases the CO2 entropy, and increases the propensity for CO2 to be adsorbed within the framework due to stronger water-mediated interactions. Due to the competition for the same void spaces, both H2O and CO2 molecules exhibit slower diffusion when molecules of the other guest species are present. These findings offer valuable strategies and insights into enhancing the differential affinity of H2O and CO2 for MOFs specifically designed for carbon capture applications.

Insights and Heuristics for Predicting Diffusion Rates of Chemical Warfare Agents in Zirconium Metal-Organic Frameworks

Designing nanoporous catalysts to destroy chemical warfare agents (CWAs) and environmental contaminants requires consideration of both intrinsic catalytic activity and the mass transfer of molecules in and out of the pores. Polar adsorbates such as CWAs experience a heterogeneous environment in many metal-organic frameworks (MOFs) due to the arrangement of the metal nodes and organic linkers of the MOF. However, quantitative relationships between the pore architecture and the resulting diffusion properties of polar molecules have not been established. We used molecular dynamics simulations to calculate the diffusion coefficients of the CWA simulant dimethyl methyl phosphonate (DMMP) in a diverse set of 776 MOFs with Zr₆ nodes. We developed a 4-parameter machine learning model to predict DMMP diffusivities in Zr₆ MOFs and found the model to be transferable to the CWA sarin. We then developed a simplified heuristic based on the machine learning model that the node-node distance and accessible surface area should be maximized to find MOFs with rapid CWA diffusion.

Adsorption and Self-Diffusion of R32/R1234yf in MOF-200 Nanoparticles by Molecular Dynamics Simulation

The thermophysical properties of a refrigerant can be modified via adding metal organic frameworks (MOF) to it. Understanding the adsorption–diffusion process of the mixture in MOFs at the molecular level is important to further improve the efficiency of the organic Rankine cycle. The adsorption and diffusion of R32/R1234yf in MOF-200 was investigated by molecular dynamics simulation in the present work. The results show that the number of adsorbed molecules of R32 in MOF-200 per unit mass is higher than that of R1234yf in the pure fluid adsorption system. The adsorption capacity of the mixture is lower than that of a pure working medium due to competitive adsorption. For both pure and mixed refrigerants, the adsorption heat of R32 in MOF-200 is smaller than that of R1234yf. Compared with R1234yf, the self-diffusion coefficient of R32 in MOF-200 is larger because of the lower diffusion activation energy.

Mass transfer of toluene in a series of metal-organic frameworks: molecular clusters inside the nanopores cause slow and step-like release

The mass transfer of the guest molecules in the pores is fundamental for the application of nanoporous materials like metal-organic frameworks, MOFs. In the present work, we explore the uptake and release of toluene in a series of Zr-based MOFs with different pore sizes. We find that intermolecular guest-guest interaction, sterically controlled by the pore size, has a substantial impact on the release kinetics. While the adsorption is rather fast, the desorption process is many orders of magnitude slower. Depending on the pore size, molecular clusters form, here (most likely) toluene dimers, which are rather stable and their break-up is rate-limiting during the desorption process. This results in a step-like desorption kinetics, deviating from the plain Fickian-diffusion-controlled release. Temperature-dependent experiments show that the minimum and maximum of the release rates are obtained at the same toluene loadings, independent of the temperature. Moreover, the activation energy for the release coincides with the binding energy of a toluene dimer. The work shows the importance of intermolecular guest-guest interaction, controlled by the MOF-nanoconfinement, for the uptake and release from nanoporous materials.

Nanoconfinement and mass transport in metal-organic frameworks

The ubiquity of metal-organic frameworks in recent scientific literature underscores their highly versatile nature. MOFs have been developed for use in a wide array of applications, including: sensors, catalysis, separations, drug delivery, and electrochemical processes. Often overlooked in the discussion of MOF-based materials is the mass transport of guest molecules within the pores and channels. Given the wide distribution of pore sizes, linker functionalization, and crystal sizes, molecular diffusion within MOFs can be highly dependent on the MOF-guest system. In this review, we discuss the major factors that govern the mass transport of molecules through MOFs at both the intracrystalline and intercrystalline scale; provide an overview of the experimental and computational methods used to measure guest diffusivity within MOFs; and highlight the relevance of mass transfer in the applications of MOFs in electrochemical systems, separations, and heterogeneous catalysis.

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.

Transport Diffusion of Linear Alkanes (C5-C16) through Thin Films of ZIF-8 as Assessed by Quartz Crystal Microgravimetry

We report uptake capacities and transport diffusivities, D, for each of eight linear alkanes (ranging from C₅ to C₁₆) in quartz crystal-supported films of solvent-evacuated ZIF-8. Analyses of the alkane uptake profiles revealed that the transport dynamics are governed by guest diffusion through metal-organic framework (MOF) (ZIF-8) crystallites rather than by rates of entry into films at the MOF/vapor interface. The obtained diffusivities range from just over 10^-18 m²/s to just under 10^-14 m²/s. Notably, minimum cross-sectional widths for all guests exceed the crystallographically measured width of ZIF-8's largest apertures and imply consistently with previous experimental and computational studies that apertures expand to accommodate guest uptake. On average, each additional carbon decreases the transport diffusivity of an alkane by twofold. Closer examination, however, reveals an odd-even effect such that linear alkanes having even numbers of carbons diffuse more rapidly than alkanes featuring one more or one less carbon atom. Thus, ZIF-8's differentiation of transport diffusivities for pairs of alkanes differing in length by only one carbon atom can be significantly greater than the aforementioned factor of 2. Elucidation of the microscopic basis for the odd-even behavior, however, awaits the outcome of molecular dynamics calculations that are beyond the scope of the present study. For compact, solvothermally prepared films, guest transport is dominated by 1D diffusion from the film/vapor interface and toward the underlying quartz crystal. For much lower density, electrophoretically deposited (EPD) films, crystallites behave nearly independently, and guest transport can be adequately modeled by assuming rapid permeation of macroscopic voids between crystallites, followed by entry and rate-limiting radial diffusion into isolated crystallites. One consequence is that EPD films can be much more rapidly infiltrated by molecular guests than can compact, solvothermally grown films. The combined results have potentially favorable implications for the development of kinetic separation schemes for closely related analytes.

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.

Topology-Dependent Alkane Diffusion in Zirconium Metal-Organic Frameworks

Metal-organic frameworks (MOFs) can be designed for chemical applications by modulating the size and shape of intracrystalline pores through selection of their nodes and linkers. Zirconium nodes with variable connectivity to organic linkers allow for a broad range of topological nets that have diverse pore structures even for a consistent set of linkers. Identifying an optimal pore structure for a given application, however, is complicated by the large material space of possible MOFs. In this work, molecular dynamics simulations were used to determine how a MOF's topology affects the diffusion of propane and isobutane over the full range of loadings and to understand how MOFs can be tuned to reduce transport limitations for applications in separations and catalysis. High-throughput simulation techniques were employed to efficiently calculate loading-dependent diffusivities in 38 MOFs. The results show that topologies with higher node connectivity have reduced alkane diffusivities compared to topologies with lower node connectivity. Molecular siting techniques were used to elucidate how the pore structures in different topologies affect adsorbate diffusivities.

Molecular Diffusion in a Flexible Mesoporous Metal-Organic Framework over the Course of Structural Contraction

In situ 1H pulsed field gradient (PFG) NMR was used to investigate the molecular diffusion of n-butane in the pores of the flexible metal-organic framework DUT-49(Cu) at 298 K at different pore loadings, including pressure ranges below and above the negative gas adsorption (NGA) transition caused by structural contraction of the material. Supported by molecular dynamics simulations, the investigation provided crucial insight into confined diffusion within a highly flexible pore environment. The self-diffusion coefficients were derived from the experiment and compared with simulations, capturing the diffusion during n-butane adsorption and desorption. This complementary approach has yielded experimental characterization of molecular diffusion mechanisms during the unique process of NGA. This includes the observation of a 4-fold decrease of diffusivity within a less than 2 kPa gas pressure variation, corresponding to the NGA transition point.

Investigating the Process and Mechanism of Molecular Transport within a Representative Solvent-Filled Metal-Organic Framework

Effective permeation into, and diffusive mass transport within, solvent-filled metal-organic frameworks (MOFs) is critical in applications such as MOF-based chemical catalysis of condensed-phase reactions. In this work, we studied the entry from solution of a luminescent probe molecule, 1,3,5,7-tetramethyl-4,4-difluoroboradiazaindacene (BODIPY), into the 1D channel-type, zirconium-based MOF NU-1008 and subsequent transport of the probe through the MOF. Measurements were accomplished via in situ confocal fluorescence microscopy of individual crystallites, where the evolution of the fluorescence response from the crystallite was followed as functions of both time and location within the crystallite. From the confocal data, intracrystalline transport of BODIPY is well-described by one-dimensional diffusion along the channel direction. Varying the chemical identity of the solvent revealed an inverse dependence of probe-molecule diffusivity on bulk-solvent viscosity, qualitatively consistent with expectations from the Stokes-Einstein equation for molecular diffusion. At a more quantitative level, however, measured diffusion coefficients are about 100-fold smaller than expected from Stokes-Einstein, pointing to substantial channel-confinement effects. Evaluation of the confocal data also reveals a non-negligible mass transport resistance, i.e., surface barrier, associated with the probe molecule leaving the solution and permeating the exterior surface of the MOF. Permeation by the probe entails displacement of solvent from the MOF channels. The magnitude of the resistance increases with the size of the solvent molecule. This work draws attention to the importance of MOF structure, external-surface barriers, and solvent molecule identity to the overall transport process in MOFs, which should assist in understanding the performance of MOFs in applications such as condensed-phase heterogeneous catalysis.

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.

Comparing Geometry and Chemistry When Confined Molecules Diffuse in Monodisperse Metal-Organic Framework Pores

The monodisperse pore structure of MOFs (metal-organic frameworks) is advantageous for investigating how porosity influences diffusion. Here we report translational and rotational diffusion using fluorescence correlation spectroscopy and time-correlated single-photon counting, using the three-dimensional pores of the zeolitic-like metal-organic framework family. We compare the influence of size and electric charge as well as dependence on pore size that we controlled through postsynthetic cation-exchange modifications. Charge-charge interactions with the MOF appeared to produce transient adsorption, manifested as a relatively fast and a slower diffusion process, but diffusants without net electric charge displayed a single diffusion process. Obtained from this family of guest molecules selected to be fluorescent, these findings suggest potentially useful general design rules to predict how pore size, guest size, and host-guest interaction control guest mobility within nanopores. With striking fidelity, diffusion coefficient scales with the ratio of cross-sectional areas of diffusant and host pores when charge is taken into account.

Molecular simulations of MOF membranes for separation of ethane/ethene and ethane/methane mixtures

Metal organic framework (MOF) membranes have been widely investigated for gas separation applications. Several MOFs have been recently examined for selective separation of C2H6. Considering the large number of available MOFs, it is not possible to fabricate and test the C2H6 separation performance of every single MOF membrane using purely experimental methods. In this study, we used molecular simulations to assess the membrane-based C2H6/C2H4 and C2H6/CH4 separation performances of 175 different MOF structures. This is the largest number of MOF membranes studied to date for C2H6 separation. We computed adsorption selectivity, diffusion selectivity, membrane selectivity and gas permeability of MOFs for C2H6/C2H4 and C2H6/CH4 mixtures. Our results show that a significant number of MOF membranes are C2H6 selective for C2H6/C2H4 separation in contrast to traditional nanoporous materials. Selectivity and permeability of MOF membranes were compared with other membrane materials, such as polymers, zeolites, and carbon molecular sieves. Several MOFs were identified to exceed the upper bound established for polymeric membranes and many MOF membranes exhibited higher gas permeabilities than zeolites and carbon molecular sieves. Examining the structure-performance relations of MOF membranes revealed that MOFs with cavity diameters between 6 and 9 Å, porosities lower than 0.50, and surface areas between 500-1000 m2 g-1 have high C2H6 selectivities. The results of this study will be useful to guide the experiments to the most promising MOF membranes for efficient separation of C2H6 and to accelerate the development of new MOFs with high C2H6 selectivities.

Liquid self-diffusion of H2O and DMF molecules in Co-MOF-74: molecular dynamics simulations and dielectric spectroscopy studies

Dielectric spectroscopy, supported by molecular dynamics simulations, is found to be a fast and non-destructive technique to study molecular transport within porous MOFs and related materials.

Nanoporous Materials Can Tune the Critical Point of a Pure Substance

Molecular simulations and NMR relaxometry experiments demonstrate that pure benzene or xylene confined in isoreticular metal–organic frameworks (IRMOFs) exhibit true vapor–liquid phase equilibria where the effective critical point may be reduced by tuning the structure of the MOF. Our results are consistent with vapor and liquid phases extending over many MOF unit cells. These results are counterintuitive since the MOF pore diameters are approximately the same length scale as the adsorbate molecules. As applications of these materials in catalysis, separations, and gas storage rely on the ability to tune the properties of adsorbed molecules, we anticipate that the ability to systematically control the critical point, thereby preparing spatially inhomogeneous local adsorbate densities, could add a new design tool for MOF applications.

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.

On the structural stability of ionic liquid–IRMOF composites: a computational study

IRMOFs become unstable in the presence of ILs due to dramatic structural deformation caused mainly by metal-anion electrostatic interactions.

Recent NMR developments applied to organic-inorganic materials

In this contribution, the latest developments in solid state NMR are presented in the field of organic-inorganic (O/I) materials (or hybrid materials). Such materials involve mineral and organic (including polymeric and biological) components, and can exhibit complex O/I interfaces. Hybrids are currently a major topic of research in nanoscience, and solid state NMR is obviously a pertinent spectroscopic tool of investigation. Its versatility allows the detailed description of the structure and texture of such complex materials. The article is divided in two main parts: in the first one, recent NMR methodological/instrumental developments are presented in connection with hybrid materials. In the second part, an exhaustive overview of the major classes of O/I materials and their NMR characterization is presented.