Charting the Complete Thermodynamic Landscape of Gas Adsorption for a Responsive Metal-Organic Framework

Atomic Force Microscopy Strategies for Capturing Guest-Induced Structural Transitions in Single Flexible Metal-Organic Framework Particles

Flexible metal-organic frameworks (MOFs) exhibit stepped adsorption isotherms due to structural transitions between narrow-pore (np) and large-pore (lp) states. This characteristic stepwise uptake at a certain pressure results in adsorptive high working capacities, making these materials highly effective for energy-efficient gas storage and separation processes. The transition pressure, which is key to enhancing separation efficiency, can be tuned by varying the particle size of flexible MOFs. However, a comprehensive understanding of size-dependent effects has been limited due to particle size distribution in samples. Conventional adsorption measurements provide only averaged isotherms for powder samples, and analyzing the size effect at the single-particle level requires experimental techniques that can capture transition behavior of individual particles separately. This study utilized atomic force microscopy coupled with thermodynamic analysis to investigate guest-induced structural transitions. Force application to a MOF particle triggered a structural change from the lp to np state, generating force profiles that were analyzed to uncover the underlying transition mechanisms and calculate transition pressures using free energy analysis. The evaluation revealed distinct transition mechanisms for two flexible MOFs: ELM-12 exhibited a step-by-step mechanism, while DUT-8(Ni) displayed an all-at-once transition. Force profile analysis enabled precise determination of the free energy changes and transition pressures for individual particles. This approach provided detailed insights into the transition mechanisms and their impact on overall adsorption isotherms, offering a novel perspective on how single-particle behavior influences bulk material performance.

Negative gas adsorption transitions and pressure amplification phenomena in porous frameworks

Nanoporous solids offer a wide range of functionalities for industrial, environmental, and energy applications. However, only a limited number of porous materials are responsive, i.e. the nanopore dynamically alters its size and shape in response to external stimuli such as temperature, pressure, light or the presence of specific molecular stimuli adsorbed inside the voids deforming the framework. Adsorption-induced structural deformation of porous solids can result in unique counterintuitive phenomena. Negative gas adsorption (NGA) is such a phenomenon which describes the spontaneous release of gas from an "overloaded" nanoporous solid via adsorption-induced structural contraction leading to total pressure amplification (PA) in a closed system. Such pressure amplifying materials may open new avenues for pneumatic system engineering, robotics, damping, or micromechanical actuators. In this review we illustrate the discovery of NGA in DUT-49, a mesoporous metal-organic framework (MOF), and the subsequent examination of conditions for its observation leading to a rationalization of the phenomenon. We outline the development of decisive experimental and theoretical methods required to establish the mechanism of NGA and derive key criteria for observing NGA in other porous solids. We demonstrate the application of these design principles in a series of DUT-49-related model compounds of which several also exhibit NGA. Furthermore, we provide an outlook towards applying NGA as a pressure amplification material and discuss possibilities to discover novel NGA materials and other counterintuitive adsorption phenomena in porous solids in the future.

Ab Initio Predictions of Adsorption in Flexible Metal-Organic Frameworks for Water Harvesting Applications

Metal-organic frameworks such as MOF-303 and MOF-LA2-1 have demonstrated exceptional performance for water harvesting applications. To enable a reticular design of such materials, an accurate prediction of the adsorption properties with chemical accuracy and fully accounting for the flexibility is crucial. The computational prediction of water adsorption properties in MOFs has become standard practice, but current methods lack the predictive power needed to design new materials. Limitations stem from the way the interatomic potential is described and the inadequate consideration of the framework flexibility. Herein, we showcase a methodology to obtain chemically accurate adsorption isotherms that fully account for framework flexibility. The method relies on very accurate and efficiently trained machine learning potentials and transition matrix Monte Carlo simulations to account for framework flexibility. For MOF-303, quantitatively accurate adsorption isotherms are obtained, provided an accurately benchmarked electronic structure method is used to train the machine learning potential, and local and global framework flexibility is accounted for. The broader applicability is shown through the study of MOF-333 and MOF-LA2-1. Analysis of the water density profiles in the MOFs gives insight into the factors governing the shape and origin of the isotherm. An optimal water harvester should have initial seeding sites with intermediate adsorption strength to prevent detrimental low-pressure water uptake. To increase the working capacity, linker extension strategies can be used while maintaining the initial seeding sites, as was done in MOF-LA2-1. The methodology can be applied to other guest molecules and MOFs, enabling the future design of MOFs with specific adsorption properties.

Adsorption and Separation by Flexible MOFs

Flexible metal-organic frameworks (MOFs) offer unique opportunities due to their dynamic structural adaptability. This review explores the impact of flexibility on gas adsorption, highlighting key concepts for gas storage and separation. Specific examples demonstrate the principal effectiveness of flexible frameworks in enhancing gas uptake and working capacity. Additionally, mixed gas adsorption and separation of mixtures are reviewed, showcasing their potential in selective gas separation. The review also discusses the critical role of the single gas isotherms analysis and adsorption conditions in designing separation experiments. Advanced combined characterization techniques are crucial for understanding the behavior of flexible MOFs, including monitoring of phase transitions, framework-guest and guest-guest interactions. Key challenges in the practical application of flexible adsorbents are addressed, such as the kinetics of switching, volume change, and potential crystal damage during phase transitions. Furthermore, the effects of additives and shaping on flexibility and the "slipping off effect" are discussed. Finally, the benefits of phase transitions beyond improved working capacity and selectivity are outlined, with a particular focus on the advantages of intrinsic thermal management. This review highlights the potential and challenges of using flexible MOFs in gas storage and separation technologies, offering insights for future research and application.

Computational Modeling of Reticular Materials: The Past, the Present, and the Future

Reticular materials rely on a unique building concept where inorganic and organic building units are stitched together giving access to an almost limitless number of structured ordered porous materials. Given the versatility of chemical elements, underlying nets, and topologies, reticular materials provide a unique platform to design materials for timely technological applications. Reticular materials have now found their way in important societal applications, like carbon capture to address climate change, water harvesting to extract atmospheric moisture in arid environments, and clean energy applications. Combining predictions from computational materials chemistry with advanced experimental characterization and synthesis procedures unlocks a design strategy to synthesize new materials with the desired properties and functions. Within this review, the current status of modeling reticular materials is addressed and supplemented with topical examples highlighting the necessity of advanced molecular modeling to design materials for technological applications. This review is structured as a templated molecular modeling study starting from the molecular structure of a realistic material towards the prediction of properties and functions of the materials. At the end, the authors provide their perspective on the past, present of future in modeling reticular materials and formulate open challenges to inspire future model and method developments.

Metal-Organic Frameworks through the Lens of Artificial Intelligence: A Comprehensive Review

Metal-organic frameworks (MOFs) are a class of hybrid porous materials that have gained prominence as a noteworthy material with varied applications. Currently, MOFs are in extensive use, particularly in the realms of energy and catalysis. The synthesis of these materials poses considerable challenges, and their computational analysis is notably intricate due to their complex structure and versatile applications in the field of material science. Density functional theory (DFT) has helped researchers in understanding reactions and mechanisms, but it is costly and time-consuming and requires bigger systems to perform these calculations. Machine learning (ML) techniques were adopted in order to overcome these problems by implementing ML in material data sets for synthesis, structure, and property predictions of MOFs. These predictions are fast, efficient, and accurate and do not require heavy computing. In this review, we discuss ML models used in MOF and their incorporation with artificial intelligence (AI) in structure and property predictions. The advantage of AI in this field would accelerate research, particularly in synthesizing novel MOFs with multiple properties and applications oriented with minimum information.

Computational Simulations of Metal-Organic Frameworks to Enhance Adsorption Applications

Metal-organic frameworks (MOFs), renowned for their exceptional porosity and crystalline structure, stand at the forefront of gas adsorption and separation applications. Shortly after their discovery through experimental synthesis, computational simulations quickly become an important method in broadening the use of MOFs by offering deep insights into their structural, functional, and performance properties. This review specifically addresses the pivotal role of molecular simulations in enlarging the molecular understanding of MOFs and enhancing their applications, particularly for gas adsorption. After reviewing the historical development and implementation of molecular simulation methods in the field of MOFs, high-throughput computational screening (HTCS) studies used to unlock the potential of MOFs in CO2 capture, CH4 storage, H2 storage, and water harvesting are visited and recent advancements in these adsorption applications are highlighted. The transformative impact of integrating artificial intelligence with HTCS on the prediction of MOFs' performance and directing the experimental efforts on promising materials is addressed. An outlook on current opportunities and challenges in the field to accelerate the adsorption applications of MOFs is finally provided.

Amplification of negative gas adsorption in a multivariate framework

The approach of employing multivariate MOFs was used to fine-tune the mechanical properties of the flexible framework DUT-49. In situ XRD, NMR and physisorption studies showed that the partial incorporation of a more rigid linker into the DUT-49 framework enables stabilization of the metastable open pore phase, which led to a two-fold amplification of the expelled gas amount upon the "negative gas adsorption" transition.

Theoretical isotherm equation for adsorption-induced structural transition on flexible metal-organic frameworks

Flexible metal-organic frameworks (MOFs) exhibit an adsorption-induced structural transition known as "gate opening" or "breathing," resulting in an S-shaped adsorption isotherm. This unique feature of flexible MOFs offers significant advantages, such as a large working capacity, high selectivity, and intrinsic thermal management capability, positioning them as crucial candidates for revolutionizing adsorption separation processes. Therefore, the interest in the industrial applications of flexible MOFs is increasing, and the adsorption engineering for flexible MOFs is becoming important. However, despite the establishment of the theoretical background for adsorption-induced structural transitions, no theoretical equation is available to describe S-shaped adsorption isotherms of flexible MOFs. Researchers rely on various empirical equations for process simulations that can lead to unreliable outcomes or may overlook insights into improving material performance owing to parameters without physical meaning. In this study, we derive a theoretical equation based on statistical mechanics that could be a standard for the structural transition type adsorption isotherms, as the Langmuir equation represents type I isotherms. The versatility of the derived equation is shown through four examples of flexible MOFs that exhibit gate opening and breathing. The consistency of the formula with existing theories, including the osmotic free energy analysis and intrinsic thermal management capabilities, is also discussed. The developed theoretical equation may lead to more reliable and insightful outcomes in adsorption separation processes, further advancing the direction of industrial applications of flexible MOFs.

On the role of history-dependent adsorbate distribution and metastable states in switchable mesoporous metal-organic frameworks

A unique feature of metal-organic frameworks (MOFs) in contrast to rigid nanoporous materials is their structural switchabilty offering a wide range of functionality for sustainable energy storage, separation and sensing applications. This has initiated a series of experimental and theoretical studies predominantly aiming at understanding the thermodynamic conditions to transform and release gas, but the nature of sorption-induced switching transitions remains poorly understood. Here we report experimental evidence for fluid metastability and history-dependent states during sorption triggering the structural change of the framework and leading to the counterintuitive phenomenon of negative gas adsorption (NGA) in flexible MOFs. Preparation of two isoreticular MOFs differing by structural flexibility and performing direct in situ diffusion studies aided by in situ X-ray diffraction, scanning electron microscopy and computational modelling, allowed assessment of n-butane molecular dynamics, phase state, and the framework response to obtain a microscopic picture for each step of the sorption process.

Cutting-edge molecular modelling to unveil new microscopic insights into the guest-controlled flexibility of metal-organic frameworks

Metal-organic frameworks are a class of porous solids that exhibit intriguing flexibility under stimuli, leading often to reversible giant structural changes upon guest adsorption. DUT-49(Cu) and MIL-53(Cr) are fascinating flexible MOFs owing to their guest-induced breathing and negative gas adsorption behaviors respectively. Molecular simulation is one of the most relevant tools to examine these phenomena at the atomistic scale and gain a unique understanding of the physics behind them. Although molecular dynamics and Monte Carlo simulations are widely used in the field of porous materials, these methods hardly consider the structural deformation of a soft material upon guest adsorption. In this work, a cutting-edge osmotic molecular dynamics approach is developed to consider simultaneously the fluid adsorption process and material flexibility. We demonstrate that this newly developed computational strategy offers a unique opportunity to gain unprecedented molecular insights into the flexibility of this class of materials.

The importance of crystal size for breathing kinetics in MIL-53(Al)

Herein we analyze the switching kinetics of a breathing framework MIL-53(Al) with respect to different crystallite size regimes. Synchrotron time-resolved powder X-ray diffraction (PXRD) and adsorption rate analysis of n-butane physisorption at 298 K demonstrate the decisive role of crystal size affecting the time domain of breathing transitions in MIL-53(Al).

Cooperative light-induced breathing of soft porous crystals via azobenzene buckling

Although light is a prominent stimulus for smart materials, the application of photoswitches as light-responsive triggers for phase transitions of porous materials remains poorly explored. Here we incorporate an azobenzene photoswitch in the backbone of a metal-organic framework producing light-induced structural contraction of the porous network in parallel to gas adsorption. Light-stimulation enables non-invasive spatiotemporal control over the mechanical properties of the framework, which ultimately leads to pore contraction and subsequent guest release via negative gas adsorption. The complex mechanism of light-gated breathing is established by a series of in situ diffraction and spectroscopic experiments, supported by quantum mechanical and molecular dynamic simulations. Unexpectedly, this study identifies a novel light-induced deformation mechanism of constrained azobenzene photoswitches relevant to the future design of light-responsive materials.

Topological transformations in metal–organic frameworks: a prospective design route?

We apply a topological approach based on the underlying net and transformation pattern concepts as well as on the ‘supernet–subnet’ formalism to uncover mechanisms of solid-state transformations in coordination polymers and metal–organic frameworks.

MOFs in the time domain

Many of the proposed applications of metal-organic framework (MOF) materials may fail to materialize if the community does not fully address the difficult fundamental work needed to map out the 'time gap' in the literature - that is, the lack of investigation into the time-dependent behaviours of MOFs as opposed to equilibrium or steady-state properties. Although there are a range of excellent investigations into MOF dynamics and time-dependent phenomena, these works represent only a tiny fraction of the vast number of MOF studies. This Review provides an overview of current research into the temporal evolution of MOF structures and properties by analysing the time-resolved experimental techniques that can be used to monitor such behaviours. We focus on innovative techniques, while also discussing older methods often used in other chemical systems. Four areas are examined: MOF formation, guest motion, electron motion and framework motion. In each area, we highlight the disparity between the relatively small amount of (published) research on key time-dependent phenomena and the enormous scope for acquiring the wider and deeper understanding that is essential for the future of the field.

The Importance of Highly Connected Building Units in Reticular Chemistry: Thoughtful Design of Metal-Organic Frameworks

The prediction of crystal structures assembled in three dimensions has been considered for a long time, simultaneously as a chemical wasteland and a certain growth point of the chemistry of the future. Less than 30 years after Roald Hoffmann's statement, we can categorically affirm that the elevation of reticular chemistry and the introduction of metal-organic frameworks (MOFs) significantly tackled this tridimensional assembly issue. MOFs result from the assembly of organic polytopic organic ligands bridging metal nodes, clusters, chains, or layers together into mostly three-periodic open frameworks. They can exhibit extremely high porosity and offer great potential as revolutionary catalysts, drug carrier systems, sensors, smart materials, and, of course, separation agents. Overall, the progressive development of reticular chemistry has been a game changer in materials chemistry during the last 25 years.Such diverse properties often result not only from the selected organic and inorganic molecular building blocks (MBBs) but also from their distribution within the framework. Indeed, the size and shape of the porous system, as well as the location of active sites influence the overall properties. Therefore, in the continuity of achieving the crystallization of three-periodic structures, chemists and crystal engineers faced the next challenge, as summarized by John Maddox: "it remains in general impossible to predict the structure of even the simplest crystallographic solids from knowledge of their chemical composition". This is where rational design takes place.In this Account, we detail three specific approaches developed by our group to facilitate the design and assembly of finely tuned MOFs. All are based on careful geometrical consideration and a deep study and understanding of the existing nets and topologies. We recognized that highly connected nets, if possible, edge-transitive, are ideal blueprints because their number is limited in contrast to nets with lower connectivity. Therefore, we embarked on taking advantage of existing highly connected MBBs, or, in parallel, promoting their formation to meet our requirements. This is achieved by utilizing externally decorated metal-organic polyhedra as supermolecular building blocks (SBBs), serving as a net-coding building unit, comprising the requisite connectivity and directional information coding for the chosen nets. The SBB approach allowed the synthesis of several families of SBB-based MOFs, including fcu, rht, and gea-MOFs, that are detailed here.The second strategy is directly inherited from the success of the SBB approach. In seeking highly connected building units, our group naturally expanded its research focus to nets that can be deconstructed into layers, pillared in various ways. In the supermolecular building layer (SBL) approach, the layers have an almost infinite connectivity, and the framework backbone is fixed in two dimensions while the third is free for pillar expansion and functionalization. The cases of trigonal pillaring leading to rtl, eea, and apo MOFs as well as the quadrangular pillaring leading to a family of tbo-MOFs are discussed here, along with recent cases of highly connected pillars in pek and aea-MOFs.Finally, our experience with highly coordinated MBBs led us to develop a novel way to use them as secondary building units of lower connectivity and unlock the possibility of assembling a novel class of zeolite-like MOFs (ZMOFs). The case of the Zr-sod-ZMOFs designed through a cantellation strategy is described as a future leading direction of MOF design.

Unraveling the Guest-Induced Switchability in the Metal-Organic Framework DUT-13(Zn)*

The switching mechanism of the flexible framework Zn4 O(benztb)1.5 (benztb=N,N,N',N'-benzidine tetrabenzoate), also known as DUT-13, was studied by advanced powder X-ray diffraction (PXRD) and gas physisorption techniques. In situ synchrotron PXRD experiments upon physisorption of nitrogen (77 K) and n-butane (273 K) shed light on the hitherto unnoticed guest-induced breathing in the MOF. The mechanism of contraction is based on the conformationally labile benztb ligand and accompanied by a reduction in specific pore volume from 2.03 cm3  g-1 in the open-pore phase to 0.91 cm3  g-1 in the contracted-pore phase. The high temperature limit for adsorption-induced contraction of 170 K, determined by systematic temperature variation of methane adsorption isotherms, indicates that the DUT-13 framework is softer than other mesoporous MOFs like DUT-49 and does not support the formation of overloaded metastable states required for negative gas-adsorption transitions.

Slacking of Gate Adsorption Behavior on Metal-Organic Frameworks under an External Force

As flexible metal-organic frameworks (MOFs) and their gate adsorption behaviors are increasingly expected to be used in gas storage and separation systems, evaluating their performance by considering their usage patterns in actual processes is becoming increasingly important. Herein, we show that the shaping of the elastic layer-structured MOF-11 (ELM-11; [Cu(BF₄)₂(4,4'-bipyridine)₂]) into pellet forms using polymer binders smears its stepwise uptake associated with the CO₂ gate adsorption. This is a critical problem because the superior adsorption properties of flexible MOFs are highly dependent on the sharpness of the step. Free energy analysis by molecular simulations revealed that the slacking of the gate adsorption is natural from a thermodynamic point of view. In other words, the external force exerted by the polymer binders, which prevents the expansion of MOF particles upon the gate opening, changes the free energy landscape of the system. This causes the flexible motifs within the MOF particles to undergo a structural transition at slightly different pressures from each other. The force profile dependence of the slacking phenomenon on both adsorption and desorption isotherms was also investigated. It was revealed that controlling the force profile applied to MOF particles is important to mold MOF pellets that satisfy the robustness and sharpness of the gate adsorption. Finally, we examined the coating of pellets to verify the relationship between the force profile and the degree of slacking and discussed possible strategies to improve the sharpness of the gate adsorption on MOF pellets considering the revealed mechanism.

Exploration of structural transition phenomenon in flexible metal–organic framework formed on polymer substrate

We investigate the structural transition of directly formed flexible MOF crystals on a polymer substrate.