Origins of Negative Gas Adsorption

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.

The use of collective variables and enhanced sampling in the simulations of existing and emerging microporous materials

Microporous materials, including zeolites, metal-organic frameworks, and cage compounds, offer diverse functionalities due to their unique dynamics and guest confinement properties. These materials play a significant role in separation, catalysis, and sensing, but their complexity hinders exploration using traditional atomistic simulations. This review explores collective variables (CVs) paired with enhanced sampling as a powerful approach to enable efficient investigation of key features in microporous materials. We highlight successful applications of CVs in studying adsorption, diffusion, phase transitions, and mechanical properties, demonstrating their crucial role in guiding material design and optimisation. The future of CVs lies in integration with techniques like machine learning, allowing for enhanced efficiency and accuracy. By tailoring CVs to specific materials and developing multi-scale approaches we can further unlock the intricacies of these fascinating materials. Simulations are a cornerstone in unravelling the complexities of microporous materials and are crucial for our future understanding.

Simulating the structural phase transitions of metal-organic frameworks with control over the volume of nanocrystallites

Flexible metal-organic frameworks (MOFs) can undergo structural transitions with significant pore volume changes upon guest adsorption or other external triggers while maintaining their porosity. In computational studies of this breathing behavior, molecular dynamics (MD) simulations within periodic boundary conditions (PBCs) are commonly performed. However, to account for the finite size and surface effects affecting the phase transition mechanism, the simulation of non-periodic nanocrystallite (NC) models without the constraint of PBCs is an important alternative. In this study, we present an approach allowing the analysis and control of the volume of finite-size structures during MD simulations by a tetrahedral tessellation of the (deformed) NC's volume. The method allows for defining the current NC's volume during the simulation and manipulating it regarding a particular reference volume to compute free energies for the phase transformation via umbrella sampling. The application on differently sized DMOF-1 and DUT-128 NCs reveals flexible pore closing mechanisms without significant biasing of the transition pathway. The concept provides the theoretical foundation for further research on flexible materials regarding targeted initialization of the structural phase behavior to elucidate the underlying mechanism, which can be used to improve the applications of flexible materials by targeted controlling of the phase 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.

Temperature Driven Transformation of the Flexible Metal-Organic Framework DUT-8(Ni)

DUT-8(Ni) metal-organic framework (MOF) belongs to the family of flexible pillared layer materials. The desolvated framework can be obtained in the open pore form (op) or in the closed pore form (cp), depending on the crystal size regime. In the present work, we report on the behaviour of desolvated DUT-8(Ni) at elevated temperatures. For both, op and cp variants, heating causes a structural transition, leading to a new, crystalline compound, containing two interpenetrated networks. The state of the framework before transition (op vs. cp) influences the transition temperature: the small particles of the op phase transform at significantly lower temperature in comparison to the macroparticles of the cp phase, transforming close to the decomposition temperature. The new compound, confined closed pore phase (ccp), was characterized by powder X-ray diffraction and spectroscopic techniques, such as IR, EXAFS, and positron annihilation lifetime spectroscopy (PALS). Thermal effects of structural transitions were studied using differential scanning calorimetry (DSC), showing an overall exothermic effect of the process, involving bond breaking and reformation. Theoretical calculations reveal the energetics, driving the observed temperature induced phase transition.

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.

Development of the Sequential Binding Model and Application for Anticooperative Protein Adsorption onto Charged Dendrimers

The Langmuir binding model provides one of the simplest and elegant methods for characterizing an adsorption process. Despite its wide-ranging applications, enormous effort has been spent to further integrate complexity onto the standard Langmuir isotherm to incorporate a wide breadth of binding kinetics with the heterogeneity and cooperative effect among ligands and receptors. Here, we use statistical mechanics as a convenient theoretical framework to depict several adsorption processes on a Langmuir-like description. With regard to the system with a two-component mixture of macromolecular binders, we have derived the two-group sequential binding isotherm as an important extension of the original sequential model with more applications, including systems of non-identical binders. Via comparison of the Langmuir equilibrium with the Boltzmann equilibrium, for the first time the binding free energy defined in the Langmuir-like models can be meaningfully compared with simulations. In a practical example of the adsorption between the lysozyme protein and charged dendrimer, we have demonstrated how the calorimetry data of this system could be interpreted by the binding models described above, with an accurate description of the adsorption process, including the cooperative effect and dendrimer heterogeneity. Using the computer simulation as a benchmark, we also reveal and discuss the strengths and limitations of the proposed binding models. The entire analysis serves as a starting point for extending the standard Langmuir model to access more complicated binding processes.

The role of thermodynamically stable configuration in enhancing crystallographic diffraction quality of flexible MOFs

Single-crystal X-ray diffraction (SCXRD) is a widely used method for structural characterization. Generally, low temperature is of great significance for improving the crystallographic diffraction quality. Herein we observe that this practice is not always effective for flexible metal-organic frameworks (f-MOFs). An abnormal crystallography, that is, more diffraction spots at a high angle and better resolution of diffraction data as the temperature increases in the f-MOF (1-g), is observed. XRD results reveal that 1-g has a reversible anisotropic thermal expansion behavior with a record-high c-axial positive expansion coefficient of 1,401.8 × 10-6 K-1. Calculation results indicate that the framework of 1-g has a more stable thermodynamic configuration as the temperature increases. Such configuration has lower-frequency vibration and may play a key role in promoting higher Bragg diffraction quality at room temperature. This work is of great significance for how to obtain high-quality SCXRD diffraction data.

Enhanced Electromagnetic Wave Absorption for Y2O3-Doped SiBCN Ceramics

Polymer-derived SiBCN ceramics (PDCs-SiBCN) are promising ultrahigh-temperature ceramics owing to their excellent high-temperature oxidation resistance and electromagnetic wave (EMW)-absorbing capability. In this paper, the microstructure evolutions, the dielectric properties, and EMW absorption properties of Y₂O₃-doped SiBCN ceramics were investigated. The results reveal that Y₂O₃ acting as a catalyst promotes the formation of SiC, BN(C), and graphite crystalline phases in the SiBCN ceramics, and these crystalline phases are constructed as conduction phases and polarization phases to enhance the EMW-adsorbing properties. The minimum reflection loss (RL_min) reaches -42.22 dB at 15.28 GHz, and the effective absorption bandwidth is 4.72 GHz (13.28-18.00 GHz). In addition, there is only 0.56 wt % mass loss for the Y₂O₃-doped SiBCN ceramics when they are heated from ambient temperature to 1500 °C in air, indicating that the Y₂O₃-doped SiBCN ceramics obtain excellent oxidation resistance at high temperature. We believe that rare metal oxidation is beneficial for the growth of crystalline phases in the PDCs, resulting in high EMW-absorbing properties and oxidation resistance. Thus, the research extends a novel method and design strategy for microstructure regulation and property enhancement of PDCs.

Integration of Fluorescent Functionality into Pressure-Amplifying Metal-Organic Frameworks

The flexibility of soft porous crystals, i.e., their ability to respond to external stimuli with structural changes, is one of the most fascinating features of metal-organic frameworks (MOFs). In addition to breathing and swelling phenomena of flexible MOFs, negative gas adsorption (NGA) and pressure amplification (PA) are the more recent discoveries in this field initially observed in the cubic DUT-49 framework. In recent years, the structural contraction was monitored by physisorption, X-ray diffraction, nuclear magnetic resonance (NMR), and electron paramagnetic resonance (EPR) techniques, providing only limited information about the electronic structure of the ligand. In this work, we designed a new ligand with a fluorescent core in the linker backbone and synthesized three new MOFs, isoreticular to DUT-49, denoted as DUT-140(M) (M-Cu, Co, Zn), crystallizing in the space group Fm3̅m. DUT-140(Cu) can be desolvated and is highly porous with an accessible apparent surface area of 4870 m² g^-1 and a pore volume of 2.59 cm³ g^-1. Furthermore, it shows flexibility and NGA upon adsorption of subcritical gases. DUT-140(Zn), synthesized using postsynthetic metal exchange, could only be studied with guests in the pores. In addition to the investigation of the adsorption behavior of DUT-140(Cu), spectroscopic and computational methods were used to study the light absorption properties.

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.

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

New nanoporous materials have the ability to revolutionize adsorption and separation processes. In particular, materials with adaptive cavities have high selectivity and may display previously undiscovered phenomena, such as negative gas adsorption (NGA), in which gas is released from the framework upon an increase in pressure. Although the thermodynamic driving force behind this and many other counterintuitive adsorption phenomena have been thoroughly investigated in recent years, several experimental observations remain difficult to explain. This necessitates a comprehensive analysis of gas adsorption akin to the conformational free energy landscapes used to understand the function of proteins. We have constructed the complete thermodynamic landscape of methane adsorption on DUT-49. Traversing this complex landscape reproduces the experimentally observed structural transitions, temperature dependence, and the hysteresis between adsorption and desorption. The complete thermodynamic description presented here provides unparalleled insight into adsorption and provides a framework to understand other adsorbents that challenge our preconceptions.

The role of temperature and adsorbate on negative gas adsorption transitions of the mesoporous metal-organic framework DUT-49

Unusual adsorption phenomena, such as breathing and negative gas adsorption (NGA), are rare and challenge our thermodynamic understanding of adsorption in deformable porous solids. In particular, NGA appears to break the rules of thermodynamics in these materials by exhibiting a spontaneous release of gas accompanying an increase in pressure. This anomaly relies on long-lived metastable states. A fundamental understanding of this process is desperately required for the discovery of new materials with this exotic property. Interestingly, NGA was initially observed upon adsorption of methane at relatively low temperature, close to the respective standard boiling point of the adsorptive, and no NGA was observed at elevated temperatures. In this contribution, we present an extensive investigation of adsorption of an array of gases at various temperatures on DUT-49, a material which features an NGA transition. Experiments, featuring a wide range of gases and vapors at temperatures ranging from 21-308 K, were used to identify for each guest a critical temperature range in which NGA can be detected. The experimental results were complemented by molecular simulations that help to rationalize the absence of NGA at elevated temperatures, and the non-monotonic behavior present upon temperature decrease. Furthermore, this in-depth analysis highlights the crucial thermodynamic and kinetic conditions for NGA, which are unique to each guest and potentially other solids with similar effects. We expect this exploration to provide detailed guidelines for experimentally discovering NGA and related "rule breaking" phenomena in novel and already known materials, and provide the conditions required for the application of this effect, for example as pressure amplifying materials.

Elucidating pore chemistry within metal–organic frameworks via single crystal X-ray diffraction; from fundamental understanding to application

The application of metal–organic frameworks (MOFs) to diverse chemical sectors is aided by their crystallinity, which permits the use of X-ray crystallography to characterise their pore chemistry and provides invaluable insight into their properties.

Statistical Mechanical Model of Gas Adsorption in a Metal-Organic Framework Harboring a Rotaxane Molecular Shuttle

Metal-organic frameworks (MOFs) are modular and tunable nanoporous materials with applications in gas storage, separations, and sensing. Integrating flexible/dynamic, gas-responsive components into MOFs can give them unique or enhanced adsorption properties. Here, we explore the adsorption properties that could be imparted to a MOF by a rotaxane molecular shuttle (RMS) in its pores. In the unit cell of an RMS-MOF, a macrocyclic wheel is mechanically interlocked with a strut of the MOF scaffold. The wheel shuttles between stations on the strut that are also gas adsorption sites. At a level of abstraction similar to the seminal Langmuir adsorption model, we pose and analyze a simple statistical mechanical model of gas adsorption in an RMS-MOF that accounts for (i) wheel/gas competition for sites on the strut and (ii) gas-induced changes in the configurational entropy of the shuttling wheel. We determine how the amount of gas adsorbed, the position of the wheel, and the differential energy of adsorption depend on temperature, pressure, and the interactions of the gas and wheel with the stations on the strut. Our model reveals that, compared to a rigid, Langmuir material, the chemistry of the RMS-MOF can be tuned to render gas adsorption more or less temperature sensitive and to release more or less heat upon adsorption. The model also uncovers that, if gas-wheel competition for a station is fierce, temperature influences the position of the wheel differently depending on the amount of gas adsorbed.

Influence of flexible side-chains on the breathing phase transition of pillared layer MOFs: a force field investigation

The prototypical pillared layer MOFs, formed by a square lattice of paddle-wheel units and connected by dinitrogen pillars, can undergo a breathing phase transition by a "wine-rack" type motion of the square lattice. We studied this behavior, which is not yet fully understood, using an accurate first principles parameterized force field (MOF-FF) for larger nanocrystallites on the example of Zn₂(bdc)₂(dabco) [bdc: benzenedicarboxylate, dabco: (1,4-diazabicyclo[2.2.2]octane)], and found clear indications for an interface between a closed and an open pore phase traveling through the system during the phase transformation [J. Keupp and R. Schmid, Adv. Theory Simul., 2019, 2, 1900117]. In conventional simulations in small supercells this mechanism is prevented by periodic boundary conditions (PBCs), enforcing a synchronous transformation of the entire crystal. Here, we extend this investigation to pillared layer MOFs with flexible side-chains, attached to the linker. Such functionalized (fu-)MOFs are experimentally known to have different properties with the side-chains acting as fixed guest molecules. First, in order to extend the parameterization for such flexible groups, a new parameterization strategy for MOF-FF had to be developed, using a multi-structure force based fit method. The resulting parameterization for a library of fu-MOFs is then validated with respect to a set of reference systems and shows very good accuracy. In the second step, a series of fu-MOFs with increasing side-chain length is studied with respect to the influence of the side-chains on the breathing behavior. For small supercells in PBCs a systematic trend of the closed pore volume with the chain length is observed. However, for a nanocrystallite model a distinct interface between a closed and an open pore phase is visible only for the short chain length, whereas for longer chains the interface broadens and a nearly concerted transformation is observed. Only by molecular dynamics simulations using accurate force fields can such complex phenomena can be studied on a molecular level.

Engineering micromechanics of soft porous crystals for negative gas adsorption

Framework materials at the molecular level, such as metal-organic frameworks (MOF), were recently found to exhibit exotic and counterintuitive micromechanical properties. Stimulated by host-guest interactions, these so-called soft porous crystals can display counterintuitive adsorption phenomena such as negative gas adsorption (NGA). NGA materials are bistable frameworks where the occurrence of a metastable overloaded state leads to pressure amplification upon a sudden framework contraction. How can we control activation barriers and energetics via functionalization of the molecular building blocks that dictate the frameworks' mechanical response? In this work we tune the elastic and inelastic properties of building blocks at the molecular level and analyze the mechanical response of the resulting frameworks. From a set of 11 frameworks, we demonstrate that widening of the backbone increases stiffness, while elongation of the building blocks results in a decrease in critical yield stress of buckling. We further functionalize the backbone by incorporation of sp3 hybridized carbon atoms to soften the molecular building blocks, or stiffen them with sp2 and sp carbons. Computational modeling shows how these modifications of the building blocks tune the activation barriers within the energy landscape of the guest-free bistable frameworks. Only frameworks with free energy barriers in the range of 800 to 1100 kJ mol-1 per unit cell, and moderate yield stress of 0.6 to 1.2 nN for single ligand buckling, exhibit adsorption-induced contraction and negative gas adsorption. Advanced experimental in situ methodologies give detailed insights into the structural transitions and the adsorption behavior. The new framework DUT-160 shows the highest magnitude of NGA ever observed for nitrogen adsorption at 77 K. Our computational and experimental analysis of the energetics and mechanical response functions of porous frameworks is an important step towards tuning activation barriers in dynamic framework materials and provides critical design principles for molecular building blocks leading to pressure amplifying materials.

Structural Transitions of the Metal-Organic Framework DUT-49(Cu) upon Physi- and Chemisorption Studied by in Situ Electron Paramagnetic Resonance Spectroscopy

Flexible metal-organic frameworks (MOFs) exhibit a variety of phenomena attractive for basic and applied science. DUT-49(Cu) is one of the remarkable representatives of such MOFs, where phase transitions are coupled to pressure amplification and "negative gas adsorption". In this work we report important insights into structural transitions of DUT-49(Cu) upon physi- and chemisorption of gases and volatile liquids obtained by in situ electron paramagnetic resonance (EPR) spectroscopy. In this method, phase transitions are detected via the zero-field splitting in dimeric copper(II) units. First, a new approach was validated upon physisorption of n-butane. Then, using diethyl ether, we for the first time demonstrated that chemisorption can also trigger phase transition in DUT-49(Cu). On the basis of the EPR results, the transition appears completely reversible. The developed EPR-based approach can also be extended to other flexible MOFs containing paramagnetic metal paddlewheels, where high sensitivity and spectral resolution allow in situ studies of stimuli-induced structural variability.

Impact of Defects and Crystal Size on Negative Gas Adsorption in DUT-49 Analyzed by In Situ 129Xe NMR Spectroscopy

The origin of crystal-size-dependent adsorption behavior of flexible metal-organic frameworks is increasingly studied. In this contribution, we probe the solid-fluid interactions of DUT-49 crystals of different size by in situ 129Xe NMR spectroscopy at 200 K. With decreasing size of the crystals, the average solid-fluid interactions are found to decrease reflected by a decrease in chemical shift of adsorbed xenon from 230 to 200 ppm, explaining the lack of adsorption-induced transitions for smaller crystals. However, recent studies propose that these results can also originate from the presence of lattice defects. To investigate the influence of defects on the adsorption behavior of DUT-49, we synthesized a series of samples with tailored defect concentrations and characterized them by in situ 129Xe NMR. In comparison to the results obtained for crystals with different size, we find pronounced changes of the adsorption behavior and influence of the chemical shift only for very high concentrations of defects, which further emphasizes the important role of particle size phenomena.

Four-dimensional metal-organic frameworks

Recognising timescale as an adjustable dimension in porous solids provides a new perspective to develop novel four-dimensional framework materials. The deliberate design of three-dimensional porous framework architectures is a developed field; however, the understanding of dynamics in open frameworks leaves a number of key questions unanswered: What factors determine the spatiotemporal evolution of deformable networks? Can we deliberately engineer the response of dynamic materials along a time-axis? How can we engineer energy barriers for the selective recognition of molecules? Answering these questions will require significant methodological development to understand structural dynamics across a range of time and length scales.

Low Temperature Calorimetry Coupled with Molecular Simulations for an In-Depth Characterization of the Guest-Dependent Compliant Behavior of MOFs

In this study adsorption microcalorimetry is employed to monitor the adsorption of four probes (argon, oxygen, nitrogen, and carbon monoxide) on a highly flexible mesoporous metal-organic framework (DUT-49, DUT = Dresden University of Technology), precisely measuring the differential enthalpy of adsorption alongside high-resolution isotherms. This experimental approach combined with force field Monte Carlo simulations reveals distinct pore filling adsorption behaviors for the selected probes, with argon and oxygen showing abrupt adsorption in the open pore form of DUT-49, in contrast with the gradual filling for nitrogen and carbon monoxide. A complex structural transition behavior of DUT-49 observed upon nitrogen adsorption is elucidated through an isotherm deconvolution in order to quantify the fractions of the open pore, contracted pore, and intermediate pore forms that coexist at a given gas pressure. Finally, the heat flow measured during the guest-induced structural contraction of DUT-49 allowed an exploration of complex open-contracted pore transition energetics, leading to a first assessment of the energy required to induce this spectacular structural change.

Tunable Flexibility and Porosity of the Metal-Organic Framework DUT-49 through Postsynthetic Metal Exchange

As a prominent and representative example of flexible metal-organic frameworks (MOFs), DUT-49(Cu) has gained attention due to the unique phenomenon of negative gas adsorption (NGA), originating from an unprecedented structural contraction during the gas adsorption. Herein, postsynthetic metal exchange is demonstrated to afford DUT-49 frameworks with a wide variety of metal cations, e.g., Mn²⁺, Fe²⁺, Ni²⁺, Zn²⁺, Cu²⁺, and Cd²⁺. The single-crystal-to-single-crystal conversion allowed characterization of the new MOFs by single crystal X-ray diffraction, indicating identical structure and topology compared with that of previously explored DUT-49(Cu) framework. This approach is proven successful in achieving Mn-Mn and Cd-Cd dimers, which are rare examples of M-M paddle-wheel SBUs. The relative stability and flexibility of the resulted frameworks are observed to be highly sensitive to the metal ion of the framework, following the trends predicted by the Irving-Williams series. DUT-49(Ni) was recognized as a second material from the DUT-49 series showing adsorption-induced transitions. A sequential increase in framework flexibility from rigid to flexible and from flexible to NGA has been achieved through selective incorporation of metal centers into the structure. Finally, heterometallic structures are formed by selective and controlled exchange of metal ions to finely tune the flexibility and NGA phenomenon of the framework.

High-Pressure in Situ 129Xe NMR Spectroscopy: Insights into Switching Mechanisms of Flexible Metal-Organic Frameworks Isoreticular to DUT-49

Flexible metal-organic frameworks (MOFs) are capable of changing their crystal structure as a function of external stimuli such as pressure, temperature, and type of adsorbed guest species. DUT-49 is the first MOF exhibiting structural transitions accompanied by the counterintuitive phenomenon of negative gas adsorption. Here, we present high-pressure in situ ¹²⁹Xe NMR spectroscopic studies of a novel isoreticular MOF family based on DUT-49. These porous materials differ only in the length of their organic linkers causing changes in pore size and elasticity. The series encompasses both, purely microporous materials as well as materials with both micropores and small mesopores. The chemical shift of the adsorbed xenon depends on xenon-wall interactions and thus on the pore size of the material. The xenon adsorption behavior of different MOFs can be observed over the whole range of relative pressure. Chemical shift adsorption/desorption isotherms closely resembling the conventional, uptake-measurement-based isotherms were obtained at 237 K where all materials are rigid. The comparable chemical environment of the adsorbed xenon in these isoreticular MOFs allows to establish a correlation between the chemical shift at a relative pressure of p/p ₀ = 1.0 and the mean pore diameter. Furthermore, the xenon adsorption behavior of MOFs is studied also at 200 K. Here, structural flexibility is found for DUT-50, a material with an even longer linker than that of the previously known DUT-49. Its structural transitions are monitored by ¹²⁹Xe NMR spectroscopy. This compound is the second known MOF showing the phenomenon of negative gas adsorption. Further increase in the linker length results in DUT-151, a material with an interpenetrated network topology. In situ ¹²⁹Xe NMR spectroscopy proves that this material exhibits another type of flexibility compared to DUT-49 and DUT-50. Further surprising observations are made for DUT-46. Volumetric xenon adsorption measurements show that this nonflexible microporous material does not exhibit any hysteresis. In contrast, the in situ ¹²⁹Xe NMR spectroscopically detected xenon chemical shift isotherms exhibit a hysteresis even after longer equilibration times than in the volumetric experiments. This indicates kinetically hindered redistribution processes and long-lived metastable states of adsorbed xenon within the MOF persisting at the time scale of hours or longer.

Towards general network architecture design criteria for negative gas adsorption transitions in ultraporous frameworks

Switchable metal-organic frameworks (MOFs) have been proposed for various energy-related storage and separation applications, but the mechanistic understanding of adsorption-induced switching transitions is still at an early stage. Here we report critical design criteria for negative gas adsorption (NGA), a counterintuitive feature of pressure amplifying materials, hitherto uniquely observed in a highly porous framework compound (DUT-49). These criteria are derived by analysing the physical effects of micromechanics, pore size, interpenetration, adsorption enthalpies, and the pore filling mechanism using advanced in situ X-ray and neutron diffraction, NMR spectroscopy, and calorimetric techniques parallelised to adsorption for a series of six isoreticular networks. Aided by computational modelling, we identify DUT-50 as a new pressure amplifying material featuring distinct NGA transitions upon methane and argon adsorption. In situ neutron diffraction analysis of the methane (CD4) adsorption sites at 111 K supported by grand canonical Monte Carlo simulations reveals a sudden population of the largest mesopore to be the critical filling step initiating structural contraction and NGA. In contrast, interpenetration leads to framework stiffening and specific pore volume reduction, both factors effectively suppressing NGA transitions.

Exploring the thermodynamic criteria for responsive adsorption processes

We describe a general model to explore responsive adsorption processes in flexible porous materials. This model combines mean field formalism of the osmotic potential, classical density functional theory of adsorption in slit pore models and generic potential functions which represent the Helmholtz free energy landscape of a porous system. Using this model, we focus on recreating flexible adsorption phenomena observed in prototypical metal-organic frameworks, especially the recently discovered effect of negative gas adsorption (NGA). We identify the key characteristics required for the model to generate unusual adsorption processes and subsequently employ an extensive parametric study to outline conditions under which gate-opening and NGA are observed. This powerful approach will guide the design of responsive porous materials and the discovery of entirely new adsorption processes.

Langmuir's Theory of Adsorption: A Centennial Review

The 100th anniversary of Langmuir's theory of adsorption is a significant landmark for the physical chemistry and chemical engineering communities. Despite its simplicity, the Langmuir adsorption model captures the key physics of molecular interactions at interfaces and laid the foundation for further progress in understanding interfacial phenomena, developing new adsorbent materials, and designing engineering processes. The Langmuir model has had an exceptional impact on diverse fields within the chemical sciences (ranging from chemical biology to materials science), an impact that became clearer with the development of modified adsorption theories and continues to be relevant today.

Multi- and instabilities in gas partitioning between nanoporous materials and rubber balloons

In the two-balloon experiment, two rubber balloons are connected and allowed to exchange gas. Owing to the non-monotonic relationship between the radius of the balloon and the pressure of gas inside it, the two-balloon system presents multi- and in-stabilities. Herein, we consider a two-adsorbent system, where two different adsorbents are allowed to exchange gas. We show that, for rigid adsorbents, the thermodynamic equilibrium state is unique. Then, we consider an adsorbent-balloon system, where an adsorbent exchanges gas with a rubber balloon. This system can exhibit multiple states at thermodynamic equilibrium- two (meta)stable and one unstable. The size of the balloon, pressure of gas in the balloon, and partitioning of gas between the adsorbent and the balloon differ among the equilibrium states. Temperature changes and the addition/removal of gas into/from the adsorbent-balloon system can induce catastrophe bifurcations and show hysteresis. Furthermore, the adsorbent-balloon system exhibits a critical temperature where, when approached from below, the discrepancy of balloon size between the two (meta)stable states decreases and, beyond, bistability is impossible. Practically, our findings preclude multiple partitions of adsorbed gas in rigid, mixed-linker or stratified metal-organic frameworks and may inspire new soft actuator and sensor designs.

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.

Novel metal–organic framework materials: blends, liquids, glasses and crystal–glass composites

This Feature Article reviews a range of amorphisation mechanisms of Metal–Organic Frameworks (MOFs) and presents recent advances to produce novel MOF materials including porous MOF glasses, MOF crystal–glass composites, flux melted MOF glasses and blended zeolitic imidazolate framework glasses.

Protocol for Identifying Accurate Collective Variables in Enhanced Molecular Dynamics Simulations for the Description of Structural Transformations in Flexible Metal-Organic Frameworks

Various kinds of flexibility have been observed in metal-organic frameworks, which may originate from the topology of the material or the presence of flexible ligands. The construction of free energy profiles describing the full dynamical behavior along the phase transition path is challenging since it is not trivial to identify collective variables able to identify all metastable states along the reaction path. In this work, a systematic three-step protocol to uniquely identify the dominant order parameters for structural transformations in flexible metal-organic frameworks and subsequently construct accurate free energy profiles is presented. Methodologically, this protocol is rooted in the time-structure based independent component analysis (tICA), a well-established statistical modeling technique embedded in the Markov state model methodology and often employed to study protein folding, that allows for the identification of the slowest order parameters characterizing the structural transformation. To ensure an unbiased and systematic identification of these order parameters, the tICA decomposition is performed based on information from a prior replica exchange (RE) simulation, as this technique enhances the sampling along all degrees of freedom of the system simultaneously. From this simulation, the tICA procedure extracts the order parameters-often structural parameters-that characterize the slowest transformations in the material. Subsequently, these order parameters are adopted in traditional enhanced sampling methods such as umbrella sampling, thermodynamic integration, and variationally enhanced sampling to construct accurate free energy profiles capturing the flexibility in these nanoporous materials. In this work, the applicability of this tICA-RE protocol is demonstrated by determining the slowest order parameters in both MIL-53(Al) and CAU-13, which exhibit a strongly different type of flexibility. The obtained free energy profiles as a function of this extracted order parameter are furthermore compared to the profiles obtained when adopting less-suited collective variables, indicating the importance of systematically selecting the relevant order parameters to construct accurate free energy profiles for flexible metal-organic frameworks, which is in correspondence with experimental findings. The method succeeds in mapping the full free energy surface in terms of appropriate collective variables for MOFs exhibiting linker flexibility. For CAU-13, we show the decreased stability of the closed pore phase by systematically adding adsorbed xylene molecules in the framework.

Predicting the Features of Methane Adsorption in Large Pore Metal-Organic Frameworks for Energy Storage

Currently, metal-organic frameworks (MOFs) are receiving significant attention as part of an international push to use their special properties in an extensive variety of energy applications. In particular, MOFs have exceptional potential for gas storage especially for methane and hydrogen for automobiles. However, using theoretical approaches to investigate this important problem presents various difficulties. Here we present the outcomes of a basic theoretical investigation into methane adsorption in large pore MOFs with the aim of capturing the unique features of this phenomenon. We have developed a pseudo one-dimensional statistical mechanical theory of adsorption of gas in a MOF with both narrow and large pores, which is solved exactly using a transfer matrix technique in the Osmotic Ensemble (OE). The theory effectively describes the distinctive features of adsorption of gas isotherms in MOFs. The characteristic forms of adsorption isotherms in MOFs reflect changes in structure caused by adsorption of gas and compressive stress. Of extraordinary importance for gas storage for energy applications, we find two regimes of Negative gas adsorption (NGA) where gas pressure causes the MOF to transform from the large pore to the narrow pore structure. These transformations can be induced by mechanical compression and conceivably used in an engine to discharge adsorbed gas from the MOF. The elements which govern NGA in MOFs with large pores are identified. Our study may help guide the difficult program of work for computer simulation studies of gas storage in MOFs with large pores.

Adsorption Contraction Mechanics: Understanding Breathing Energetics in Isoreticular Metal-Organic Frameworks

A highly porous metal-organic framework DUT-48, isoreticular to DUT-49, is reported with a high surface area of 4560 m2·g-1 and methane storage capacity up to 0.27 g·g-1 (164 cm3·cm-3) at 6.5 MPa and 298 K. The flexibility of DUT-48 and DUT-49 under external and internal (adsorption-induced) pressure is analyzed and rationalized using a combination of advanced experimental and computational techniques. While both networks undergo a contraction by mechanical pressure, only DUT-49 shows adsorption-induced structural transitions and negative gas adsorption of n-butane and nitrogen. This adsorption behavior was analyzed by microcalorimetry measurements and molecular simulations to provide an explanation for the lack of adsorption-induced breathing in DUT-48. It was revealed that for DUT-48, a significantly lower adsorption enthalpy difference and a higher framework stiffness prevent adsorption-induced structural transitions and negative gas adsorption. The mechanical behavior of both DUT-48 and DUT-49 was further analyzed by mercury porosimetry experiments and molecular simulations. Both materials exhibit large volume changes under hydrostatic compression, demonstrating noteworthy potential as shock absorbers with unprecedented high work energies.

On flexible force fields for metal-organic frameworks: Recent developments and future prospects

Classical force field simulations can be used to study structural, diffusion, and adsorption properties of metal-organic frameworks (MOFs). To account for the dynamic behavior of the material, parameterization schemes have been developed to derive force constants and the associated reference values by fitting on ab initio energies, vibrational frequencies, and elastic constants. Here, we review recent developments in flexible force field models for MOFs. Existing flexible force field models are generally able to reproduce the majority of experimentally observed structural and dynamic properties of MOFs. The lack of efficient sampling schemes for capturing stimuli-driven phase transitions, however, currently limits the full predictive potential of existing flexible force fields from being realized. This article is categorized under: Structure and Mechanism > Computational Materials ScienceMolecular and Statistical Mechanics > Molecular Mechanics.

The effect of crystallite size on pressure amplification in switchable porous solids

Negative gas adsorption (NGA) in ordered mesoporous solids is associated with giant contractive structural transitions traversing through metastable states. Here, by systematically downsizing the crystal dimensions of a mesoporous MOF (DUT-49) from several micrometers to less than 200 nm, counterintuitive NGA phenomena are demonstrated to critically depend on the primary crystallite size. Adsorbing probe molecules, such as n-butane or nitrogen, gives insights into size-dependent activation barriers and thermodynamics associated with guest-induced network contraction. Below a critical crystal size, the nitrogen adsorption-induced breathing is completely suppressed as detected using parallelized synchrotron X-ray diffraction–adsorption instrumentation. In contrast, even the smallest particles show NGA in the presence of n-butane, however, associated with a significantly reduced pressure amplification. Consequently, the magnitude of NGA in terms of amount of gas expulsed and pressure amplification can be tuned, potentially paving the way towards innovative concepts for pressure amplification in micro- and macro-system engineering.

Pressure amplification phenomena have recently been observed in ordered mesoporous solids, but little is understood about this counter-intuitive behaviour. Here, Kaskel and colleagues demonstrate that crystal size can play an important role in modulating pressure amplification in metal-organic frameworks.