Efficient Modeling of Water Adsorption in MOFs Using Interpolated Transition Matrix Monte Carlo.

With the specter of accelerating climate change, securing access to potable water has become a critical global challenge. Atmospheric water harvesting (AWH) through metal-organic frameworks (MOFs) emerges as one of the promising solutions. The standard numerical methods applied for rapid and efficient screening for optimal sorbents face significant limitations in the case of water adsorption (slow convergence and inability to overcome high energy barriers). To address these challenges, we employed grand canonical transition matrix Monte Carlo (GC-TMMC) methodology and proposed an efficient interpolation scheme that significantly reduces the number of required simulations while maintaining accuracy of the results. Through the example of water adsorption in three MOFs: MOF-303, MOF-LA2-1, and NU-1000, we show that the extrapolation of the free energy landscape allows for prediction of the adsorption properties over a continuous range of pressure and temperature. This innovative and versatile method provides rich thermodynamic information, enabling rapid, large-scale computational screening of sorbents for adsorption, applicable for a variety of sorbents and gases. As the presented methodology holds strong applicative potential, we provide alongside this paper a modified version of the RASPA2 code with a ghost swap move implementation and a Python library designed to minimize the user's input for analyzing data derived from the TMMC simulations.

Quasicontinuous Cooperative Adsorption Mechanism in Crystalline Nanoporous Materials.

The hase behavior of confined fluids adsorbed in nanopores differs significantly from their bulk counterparts and depends on the chemical and structural properties of the confining structures. In general, phase transitions in nanoconfined fluids are reflected in stepwise adsorption isotherms with a pronounced hysteresis. Here, we show experimental evidence and an in silico interpretation of the reversible stepwise adsorption isotherm which is observed when methane is adsorbed in the rigid, crystalline metal-organic framework IRMOF-1 (MOF-5). In a very narrow range of pressures, the adsorbed fluid undergoes a structural and highly cooperative reconstruction and transition between low-density and high-density nanophases, as a result of the competition between the fluid-framework and fluid-fluid interactions. This mechanism evolves with temperature: below 110 K, a reversible stepwise isotherm is observed, which is a result of the bimodal distribution of the coexisting nanophases. This temperature may be considered as a critical temperature of methane confined to nanopores of IRMOF-1. Above 110 K, as the entropy contribution increases, the isotherm shape transforms to a common continuous S-shaped form that is characteristic to a gradual densification of the adsorbed phase as the pressure increases.

Hydrogen Storage in Pure and Boron-Substituted Nanoporous Carbons-Numerical and Experimental Perspective.

Nanoporous carbons remain the most promising candidates for effective hydrogen storage by physisorption in currently foreseen hydrogen-based scenarios of the world's energy future. An optimal sorbent meeting the current technological requirement has not been developed yet. Here we first review the storage limitations of currently available nanoporous carbons, then we discuss possible ways to improve their storage performance. We focus on two fundamental parameters determining the storage (the surface accessible for adsorption and hydrogen adsorption energy). We define numerically the values nanoporous carbons have to show to satisfy mobile application requirements at pressures lower than 120 bar. Possible necessary modifications of the topology and chemical compositions of carbon nanostructures are proposed and discussed. We indicate that pore wall fragmentation (nano-size graphene scaffolds) is a partial solution only, and chemical modifications of the carbon pore walls are required. The positive effects (and their limits) of the carbon substitutions by B and Be atoms are described. The experimental 'proof of concept' of the proposed strategies is also presented. We show that boron substituted nanoporous carbons prepared by a simple arc-discharge technique show a hydrogen adsorption energy twice as high as their pure carbon analogs. These preliminary results justify the continuation of the joint experimental and numerical research effort in this field.

Pore opening and breathing transitions in metal-organic frameworks: Coupling adsorption and deformation.

Soft porous crystals undergo large structural transformations under a variety of physical stimuli. Breathing-like transformations, occurring with a large volume change, have been associated with an existence of bi-stable or multi-stable crystal structures. Understanding of the mechanism of these transformations is essential for their potential applications in gas adsorption, separation and storage. However, the generic description is still missing. Here, we provide a detailed, multiscale qualitative and quantitative analysis of the adsorption-induced "breathing" transformations in two metal organic frameworks (MOFs): MIL-53(Al) which is a reference case of our approach, and recently synthesized JUK-8, which does not show any bistability without adsorbate. The proposed approach is based on atomistic simulations and does not require any empirical or adjustable parameters. It allows for a prediction of potential structural transformations in MOFs including the adsorption induced deformations derived from adsorption stress model. We also show that the quantitative agreement between calculated and experimental results critically depends on the quality of the dispersion energy correction. Our methodology represents a new, powerful tool for designing and screening of flexible materials, alternative and complimentary to experimental approaches.

Self-Assembled Two-Dimensional Nanoporous Crystals as Molecular Sieves: Molecular Dynamics Studies of 1,3,5-Tristyrilbenzene-Cn Superstructures.

Due to their unique geometry complex, self-assembled nanoporous 2D molecular crystals offer a broad landscape of potential applications, ranging from adsorption and catalysis to optoelectronics, substrate processes, and future nanomachine applications. Here we report and discuss the results of extensive all-atom Molecular Dynamics (MD) investigations of self-assembled organic monolayers (SAOM) of interdigitated 1,3,5-tristyrilbenzene (TSB) molecules terminated by alkoxy peripheral chains Cn containing n carbon atoms (TSB3,5-Cn) deposited onto highly ordered pyrolytic graphite (HOPG). In vacuo structural and electronic properties of the TSB3,5-Cn molecules were initially determined using ab initio second order Møller-Plesset (MP2) calculations. The MD simulations were then used to analyze the behavior of the self-assembled superlattices, including relaxed lattice geometry (in good agreement with experimental results) and stability at ambient temperatures. We show that the intermolecular disordering of the TSB3,5-Cn monolayers arises from competition between decreased rigidity of the alkoxy chains (loss of intramolecular order) and increased stabilization with increasing chain length (afforded by interdigitation). We show that the inclusion of guest organic molecules (e.g., benzene, pyrene, coronene, hexabenzocoronene) into the nanopores (voids formed by interdigitated alkoxy chains) of the TSB3,5-Cn superlattices stabilizes the superstructure, and we highlight the importance of alkoxy chain mobility and available pore space in the dynamics of the systems and their potential application in selective adsorption.

Tailoring the separation properties of flexible metal-organic frameworks using mechanical pressure.

Metal-organic frameworks are widely considered for the separation of chemical mixtures due to their adjustable physical and chemical properties. However, while much effort is currently devoted to developing new adsorbents for a given separation, an ideal scenario would involve a single adsorbent for multiple separations. Porous materials exhibiting framework flexibility offer unique opportunities to tune these properties since the pore size and shape can be controlled by the application of external stimuli. Here, we establish a proof-of-concept for the molecular sieving separation of species with similar sizes (CO2/N2 and CO2/CH4), via precise mechanical control of the pore size aperture in a flexible metal-organic framework. Besides its infinite selectivity for the considered gas mixtures, this material shows excellent regeneration capability when releasing the external mechanical constraint. This strategy, combining an external stimulus applied to a structurally compliant adsorbent, offers a promising avenue for addressing some of the most challenging gas separations.

Collective Breathing in an Eightfold Interpenetrated Metal-Organic Framework: From Mechanistic Understanding towards Threshold Sensing Architectures.

Functional materials that respond to chemical or physical stimuli through reversible structural transformations are highly desirable for the integration into devices. Now, a new stable and flexible eightfold interpenetrated three-dimensional (3D) metal-organic framework (MOF) is reported, [Zn(oba)(pip)]n (JUK-8) based on 4,4'-oxybis(benzenedicarboxylate) (oba) and 4-pyridyl functionalized benzene-1,3-dicarbohydrazide (pip) linkers, featuring distinct switchability in response to guest molecules (H2 O and CO2 ) or temperature. Single-crystal X-ray diffraction (SC-XRD), combined with density functional theory (DFT) and grand canonical Monte Carlo (GCMC) simulations, reveal a unique breathing mechanism involving collective motions of eight mixed-linker diamondoid subnetworks with only minor displacements between them. The pronounced stepwise volume change of JUK-8 during water adsorption is used to construct an electron conducting composite film for resistive humidity sensing.

Computer modeling of 2D supramolecular nanoporous monolayers self-assembled on graphite.

Nano-porous two-dimensional molecular crystals, self-assembled on atomically flat host surfaces offer a broad range of possible applications, from molecular electronics to future nano-machines. Computer-assisted designing of such complex structures requires numerically intensive modeling methods. Here we present the results of extensive, fully atomistic simulations of self-assembled monolayers of interdigitated molecules of 1,3,5-tristyrilbenzene substituted by C6 alkoxy peripheral chains (TSB3,5-C6), deposited onto highly-ordered pyrolytic graphite. Structural and electronic properties of the TSB3,5-C6 molecules were determined from ab initio calculations, then used in Molecular Dynamics simulations to analyze the mechanism of formation, epitaxy, and stability of the TSB3,5-C6 nanoporous superlattice. We show that the monolayer disordering results from the competition between flexibility of the C6 chains and their stabilization by interdigitation. The inclusion of guest molecules (benzene and pyrene) into superlattice nanopores stabilizes the monolayer. The alkoxy chain mobility and available pore space defines the systems dynamics, essential for potential application.

Boron-neutron Capture on Activated Carbon for Hydrogen Storage.

This work investigates the effects of neutron irradiation on nitrogen and hydrogen adsorption in boron-doped activated carbon. Boron-neutron capture generates an energetic lithium nucleus, helium nucleus, and gamma photons, which can alter the surface and structure of pores in activated carbon. The defects introduced by fission tracks are modeled assuming the slit-shaped pores geometry. Sub-critical nitrogen adsorption shows that nitrogen molecules cannot probe the defects created by fission tracks. Hydrogen adsorption isotherms of irradiated samples indicate higher binding energies compared to their non-irradiated parent samples.

Intermediate states approach for adsorption studies in flexible metal-organic frameworks.

Adsorption studies in flexible metal-organic frameworks are challenging and time-consuming. It is mainly because the mechanism of adsorption, defined by structural framework properties, is constantly modified during the process, as the framework transformation depends on the adsorption uptake. We propose here a new approach to investigate adsorption in such complex systems, in which the simulations of adsorption in a deforming framework are replaced by the analysis of adsorption in intermediate rigid structures. As a proof of concept we analyze carbon dioxide, hexane, and methane adsorption in MIL-53. 19 intermediate structures were generated using geometrical interpolation between the open and the closed MOF forms and optimized with quantum DFT calculations. The grand canonical Monte Carlo method was applied to calculate adsorption isotherms in all intermediate structures. The comparison with experimental results enabled the identification of the intermediate adsorption states. The analysis of the microscopic configurations of the adsorbed molecules in these structures allowed us to propose a new mechanism of adsorbate evolution over the entire process.

Benchmarking of GGA density functionals for modeling structures of nanoporous, rigid and flexible MOFs.

The adequate choice of the interaction model is essential to reproduce qualitatively and estimate quantitatively the experimentally observed characteristics of materials or phenomena in computer simulations. Here we present the results of a benchmarking of density-functional theory calculations of rigid and flexible metal-organic frameworks (MOFs). The stability of these systems depends on the dispersion interactions. We compare the performance of two functionals, Perdew-Burke-Ernzerhof (PBE) and PBE designed for solids, with and without the dispersion corrections (D2 and TS), in reproducing the high-accuracy low-temperature X-ray and neutron diffraction data for both groups of MOFs. We focus our analysis on the key structural parameters: the lattice parameters, bond lengths, and angles. We show that the dispersion long range correction is essential to stabilize the structures and, in some cases, to converge the system to a geometry that is in line with the experimentally observed structure, especially for breathing MIL-53 structures or zeolitic imidazolate frameworks. We find that for all structures and all analyzed parameters, the D2-corrected PBE functional performs the best, except for bonds involving the metal ions; however, even for these bonds the difference between the experimentally observed and calculated lengths is small. Therefore, we recommend the use of the PBE-D2 functional in further numerical analyses of rigid and flexible nanoporous MOFs.

Adsorption-Induced Structural Phase Transformation in Nanopores.

We report a new type of structural transformation occurring in methane adsorbed in micropores. The observed methane structures are defined by probability distributions of molecular positions. The mechanism of the transformation has been modeled using Monte Carlo method. The transformation is totally determined by a reconstruction of the probability distribution functions of adsorbed molecules. The methane molecules have some freedom to move in the pore but most of the time they are confined to the positions around the high probability adsorption sites. The observed high-probability structures evolve as a function of temperature and pressure. The transformation is strongly discontinuous at low temperature and becomes continuous at high temperature. The mechanism of the transformation is influenced by a competition between different components of the interaction and the thermal energy. The methane structure represents a new state of matter, intermediate between solid and liquid.

Screening the Effect of Water Vapour on Gas Adsorption Performance: Application to CO2 Capture from Flue Gas in Metal-Organic Frameworks.

A simple laboratory-scale protocol that enables the evaluation of the effect of adsorbed water on CO2 uptake is proposed. 45 metal-organic frameworks (MOFs) were compared against reference zeolites and active carbons. It is possible to classify materials with different trends in CO2 uptake with varying amounts of pre-adsorbed water, including cases in which an increase in CO2 uptake is observed for samples with a given amount of pre-adsorbed water. Comparing loss in CO2 uptake between "wet" and "dry" samples with the Henry constant calculated from the water adsorption isotherm results in a semi-logarithmic trend for the majority of samples allowing predictions to be made. Outliers from this trend may be of particular interest and an explanation for the behaviour for each of the outliers is proposed. This thus leads to propositions for designing or choosing MOFs for CO2 capture in applications where humidity is present.

Modeling of adsorption of CO2 in the deformed pores of MIL-53(Al).

Molecular simulations were performed to predict CO2 adsorption in flexible metal-organic frameworks (MOFs). A generic force field was fitted to our experimental data to describe the non-bonded (electrostatic and van der Waals) interactions between CO2 molecules and the large pore (lp) and narrow pore (np) forms of the MIL-53(Al) framework. With the new validated force field, it is possible to predict CO2 uptake and enthalpy of adsorption at various applied external pressures that will modify the structure's pore configuration and allow us to have more control over the adsorption/desorption process. A sensitivity analysis of MOF adsorption properties to the variation of the force field parameters was also intensively studied. It was shown that relatively small variations of the adsorbate gas model can improve the quality of the numerical predictions of the experimental data. However, the variations must be kept small enough to not modify the properties of the gas itself.

Modeling of low temperature adsorption of hydrogen in carbon nanopores.

We simulated the low temperature (T = 77 K) hydrogen adsorption in carbon slit-shaped nanopores using consecutively united atom (UA) and all atom (AA) representation of hydrogen molecule. We showed that both approximations give comparable estimation of the amount stored, for the wide range of pore width (0.6-2.5 nm). We also showed that at very high pressure (P = 400 bar, corresponding to the fugacity f used in grand canonical Monte Carlo simulations of f = 800 bar) the density of the adsorbed hydrogen structures is larger than the density of bulk liquid at critical temperature (∼76 kg/m3). This result agrees with the experimental observation of the density of the order of 100 kg/m3 for the hydrogen adsorbed in microporous carbons, reported recently in the literature.

Unique bonding nature of carbon-substituted Be2 dimer inside the carbon (sp(2)) network.

Controlled doping of active carbon materials (viz., graphenes, carbon nanotubes etc.) may lead to the enhancement of their desired properties. The least studied case of C/Be substitution offers an attractive possibility in this respect. The interactions of Be2 with Be or C atoms are dominated by the large repulsive Pauli exchange contributions, which in turn offsets the attractive interactions leading to relatively small binding energies. The Be2 dimer, e.g., after being doped inside a planar carbon network, undergoes orbital adjustments due to charge transfer and unusual intermolecular interactions and is oriented perpendicular to the plane of the carbon network with the Be-Be bond center located inside the plane. The present theoretical investigation on the nature of bonding in C/Be2 exchange complexes, using state of the art quantum chemical techniques, reveals a sp(2) carbon-like bonding scheme in Be2 arising due to the molecular hybridization of σ and two π orbitals. The perturbations imposed by doped Be2 dimers exhibit a local character of the structural and electronic properties of the complexes, and the separation by two carbon atoms between beryllium active centers is sufficient to consider these centers as independent sites.

Understanding universal adsorption limits for hydrogen storage in nano porous systems.

Despite of more than 15 years of research, no materials possess the adsorbing properties required for mobile storage. At this time of state-of-the-art technology, the essential question should be asked: why is it so difficult to prepare a material with the desired properties? Here, we discuss the sources of physical limitations of existing materials and indicate the directions for further material research.