Thermodynamics of Guest-Induced Structural Transitions in Hybrid Organic−Inorganic Frameworks

High-Pressure Molecular Sieving of High-Humidity C2H4/C2H6 Mixture by a Hydrophobic Flexible Metal-Organic Framework

Molecular sieving is an ideal separation mechanism, but controlling pore size, restricting framework flexibility, and avoiding strong adsorption are all very challenging. Here, we report a flexible adsorbent showing molecular sieving at ambient temperature and high pressure, even under high humidity. While typical guest-induced transformations are observed, a high transition pressure of 16.6 atm is observed for C2H4 at 298 K because of very weak C2H4 adsorption (~16 kJ mol-1). Also, C2H6 is completely excluded below the pore-opening pressure of 7.7 atm, giving single-component selectivity of ca. 300. Quantitative high-pressure column breakthrough experiments using 1 : 1 C2H4/C2H6 mixtures at 10 atm as input confirm molecular sieving with C2H4 adsorption of 0.73 mmol g-1 or 32 cm3(STP) cm-3 and negligible C2H6 adsorption of 0.001(2) mmol g-1, and the adsorbent can be completely regenerated by inert gas purging. Furthermore, it is highly hydrophobic with negligible water adsorption, and the C2H4/C2H6 separation performance is unaffected at high humidity.

Bubbles enable volumetric negative compressibility in metastable elastocapillary systems

Although coveted in applications, few materials expand when subject to compression or contract under decompression, i.e., exhibit negative compressibility. A key step to achieve such counterintuitive behaviour is the destabilisations of (meta)stable equilibria of the constituents. Here, we propose a simple strategy to obtain negative compressibility exploiting capillary forces both to precompress the elastic material and to release such precompression by a threshold phenomenon - the reversible formation of a bubble in a hydrophobic flexible cavity. We demonstrate that the solid part of such metastable elastocapillary systems displays negative compressibility across different scales: hydrophobic microporous materials, proteins, and millimetre-sized laminae. This concept is applicable to fields such as porous materials, biomolecules, sensors and may be easily extended to create unexpected material susceptibilities.

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.

Selective sorting of hexane isomers by anion-functionalized metal-organic frameworks with optimal energy regulation

Extensive efforts have been made to improve the separation selectivity of hydrocarbon isomers with nearly distinguishable boiling points; however, how to balance the high regeneration energy consumption remains a daunting challenge. Here we describe the efficient separation of hexane isomers by constructing and exploiting the rotational freedom of organic linkers and inorganic SnF62- anions within adaptive frameworks, and reveal the nature of flexible host-guest interactions to maximize the gas-framework interactions while achieving potential energy storage. This approach enables the discrimination of hexane isomers according to the degree of branching along with high capacity and record mono-/di-branched selectivity (6.97), di-branched isomers selectivity (22.16), and upgrades the gasoline to a maximum RON (Research Octane Number) of 105. Benefitting from the energy regulation of the flexible pore space, the material can be easily regenerated only through a simple vacuum treatment for 15 minutes at 25 °C with no temperature fluctuation, saving almost 45% energy compared to the commercialized zeolite 5 A. This approach could potentially revolutionize the whole scenario of alkane isomer separation processes.

The role of carboxylate ligand orbitals in the breathing dynamics of a metal-organic framework by resonant X-ray emission spectroscopy

Metal-organic frameworks (MOFs) exhibit structural flexibility induced by temperature and guest adsorption, as demonstrated in the structural breathing transition in certain MOFs between narrow-pore and large-pore phases. Soft modes were suggested to entropically drive such pore breathing through enhanced vibrational dynamics at high temperatures. In this work, oxygen K-edge resonant X-ray emission spectroscopy of the MIL-53(Al) MOF was performed to selectively probe the electronic perturbation accompanying pore breathing dynamics at the ligand carboxylate site for metal-ligand interaction. It was observed that the temperature-induced vibrational dynamics involves switching occupancy between antisymmetric and symmetric configurations of the carboxylate oxygen lone pair orbitals, through which electron density around carboxylate oxygen sites is redistributed and metal-ligand interactions are tuned. In turn, water adsorption involves an additional perturbation of π orbitals not observed in the structural change solely induced by temperature.

Hydrocarbon Sorption in Flexible MOFs-Part III: Modulation of Gas Separation Mechanisms

Single gas sorption experiments with the C4-hydrocarbons n-butane, iso-butane, 1-butene and iso-butene on the flexible MOFs Cu-IHMe-pw and Cu-IHEt-pw were carried out with both thermodynamic equilibrium and overall sorption kinetics. Subsequent static binary gas mixture experiments of n-butane and iso-butane unveil a complex dependence of the overall selectivity on sorption enthalpy, rate of structural transition as well as steric effects. A thermodynamic separation favoring iso-butane as well as kinetic separation favoring n-butane are possible within Cu-IHMe-pw while complete size exclusion of iso-butane is achieved in Cu-IHEt-pw. This proof-of-concept study shows that the structural flexibility offers additional levers for the precise modulation of the separation mechanisms for complex mixtures with similar chemical and physical properties with real selectivities of >10.

Reticular Synthesis of Flexible Rare-Earth Metal-Organic Frameworks: Control of Structural Dynamics and Sorption Properties Through Ligand Functionalization

An exciting direction in metal-organic frameworks involves the design and synthesis of flexible structures which can reversibly adapt their structure when triggered by external stimuli. Controlling the extent and nature of response in such solids is critical in order to develop custom dynamic materials for advanced applications. Towards this, it is highly important to expand the diversity of existing flexible MOFs, generating novel materials and gain an in-depth understanding of the associated dynamic phenomena, eventually unlocking key structure-property relationships. In the present work, we successfully utilized reticular chemistry for the construction of two novel series of highly crystalline, flexible rare-earth MOFs, RE-thc-MOF-2 and RE-teb-MOF-1. Extensive single-crystal to single-crystal structural analyses coupled with detailed gas and vapor sorption studies, shed light onto the unique responsive behavior. The development of these series is related to the reported RE-thc-MOF-1 solids which were found to display a unique continuous breathing and gas-trapping property. The synthesis of RE-thc-MOF-2 and RE-teb-MOF-1 materials represents an important milestone as they provide important insights into the key factors that control the responsive properties of this fascinating family of flexible materials and demonstrates that it is possible to control their dynamic behavior and the associated gas and vapor sorption properties.

Quasi-open Cu(I) sites for efficient CO separation with high O2/H2O tolerance

Carbon monoxide (CO) separation relies on chemical adsorption but suffers from the difficulty of desorption and instability of open metal sites against O2, H2O and so on. Here we demonstrate quasi-open metal sites with hidden or shielded coordination sites as a promising solution. Possessing the trigonal coordination geometry (sp2), Cu(I) ions in porous frameworks show weak physical adsorption for non-target guests. Rational regulation of framework flexibility enables geometry transformation to tetrahedral geometry (sp3), generating a fourth coordination site for the chemical adsorption of CO. Quantitative breakthrough experiments at ambient conditions show CO uptakes up to 4.1 mmol g-1 and CO selectivity up to 347 against CO2, CH4, O2, N2 and H2. The adsorbents can be completely regenerated at 333-373 K to recover CO with a purity of >99.99%, and the separation performances are stable in high-concentration O2 and H2O. Although CO leakage concentration generally follows the structural transition pressure, large amounts (>3 mmol g-1) of ultrahigh-purity (99.9999999%, 9N; CO concentration < 1 part per billion) gases can be produced in a single adsorption process, demonstrating the usefulness of this approach for separation applications.

Trajectory-Extending Kinetic Monte Carlo Simulations to Evaluate Pure and Gas Mixture Diffusivities through a Dense Polymeric Membrane

With renewed interest in CO2 separations, carbon molecular sieving (CMS) membrane performance evaluation requires diffusion coefficients as inputs to have a reliable estimate of the permeability. An optimal material is desired to have both high selectivity and permeability. Gases diffusing through dense CMS and polymeric membranes experience extended subdiffusive regimes, which hinders reliable extraction of diffusion coefficients from mean squared displacement data. We improve the sampling of the diffusive landscape by implementing the trajectory-extending kinetic Monte Carlo (TEKMC) technique to efficiently extend molecular dynamics (MD) trajectories from ns to μs time scales. The obtained self-diffusion coefficient of pure CO2 in CMS membranes derived from a 6FDA/BPDA-DAM precursor polymer melt is found to linearly increase from 0.8-1.3 × 10-6 cm2 s-1 in the pressure range of 1-20 bar, which supports previous experimental findings. We also extended the TEKMC algorithm to evaluate the mixture diffusivities in binary mixtures to determine the permselectivity of CO2 in CH4 and N2 mixtures. The mixture diffusion coefficient of CO2 ranges from 1.3-7 × 10-6 cm2 s-1 in the binary mixture CO2/CH4, which is significantly higher than the pure gas diffusion coefficient. Robeson plot comparisons show that the permselectivity obtained from pure gas diffusion data is significantly lower than that predicted using mixture diffusivity data. Specifically, in the case of the CO2/N2 mixture, we find that using mixture diffusivities led to permselectivities lying above the Robeson limit highlighting the importance of using mixture diffusivity data for an accurate evaluation of the membrane performance. Combined with gas solubilities obtained from grand canonical Monte Carlo (GCMC) simulations, our work shows that simulations with the TEKMC method can be used to reliably evaluate the performance of materials for gas separations.

Generalised analytical method unravels framework-dependent kinetics of adsorption-induced structural transition in flexible metal-organic frameworks

Flexible metal-organic frameworks (MOFs) exhibiting adsorption-induced structural transition can revolutionise adsorption separation processes, including CO2 separation, which has become increasingly important in recent years. However, the kinetics of this structural transition remains poorly understood despite being crucial to process design. Here, the CO2-induced gate opening of ELM-11 ([Cu(BF4)2(4,4'-bipyridine)2]n) is investigated by time-resolved in situ X-ray powder diffraction, and a theoretical kinetic model of this process is developed to gain atomistic insight into the transition dynamics. The thus-developed model consists of the differential pressure from the gate opening (indicating the ease of structural transition) and reaction model terms (indicating the transition propagation within the crystal). The reaction model of ELM-11 is an autocatalytic reaction with two pathways for CO2 penetration of the framework. Moreover, gas adsorption analyses of two other flexible MOFs with different flexibilities indicate that the kinetics of the adsorption-induced structural transition is highly dependent on framework structure.

Crossover Sorption of C2 H2 /CO2 and C2 H6 /C2 H4 in Soft Porous Coordination Networks

Porous sorbents are materials that are used for various applications, including storage and separation. Typically, the uptake of a single gas by a sorbent decreases with temperature, but the relative affinity for two similar gases does not change. However, in this study, we report a rare example of "crossover sorption," in which the uptake capacity and apparent affinity for two similar gases reverse at different temperatures. We synthesized two soft porous coordination polymers (PCPs), [Zn2 (L1)(L2)2 ]n (PCP-1) and [Zn2 (L1)(L3)2 ]n (PCP-2) (L1= 1,4-bis(4-pyridyl)benzene, L2=5-methyl-1,3-di(4-carboxyphenyl)benzene, and L3=5-methoxy-1,3-di(4-carboxyphenyl)benzene). These PCPs exhibits structural changes upon gas sorption and show the crossover sorption for both C2 H2 /CO2 and C2 H6 /C2 H4 , in which the apparent affinity reverse with temperature. We used in situ gas-loading single-crystal X-ray diffraction (SCXRD) analysis to reveal the guest inclusion structures of PCP-1 for C2 H2 , CO2 , C2 H6 , and C2 H4 gases at various temperatures. Interestingly, we observed three-step single-crystal to single-crystal (sc-sc) transformations with the different loading phases under these gases, providing insight into guest binding positions, nature of host-guest or guest-guest interactions, and their phase transformations upon exposure to these gases. Combining with theoretical investigation, we have fully elucidated the crossover sorption in the flexible coordination networks, which involves a reversal of apparent affinity and uptake of similar gases at different temperatures. We discovered that this behaviour can be explained by the delicate balance between guest binding and host-guest and guest-guest interactions.

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.

Elastic heterogeneity governs asymmetric adsorption-desorption in a soft porous crystal

Metal-organic frameworks (MOFs), which possess a high degree of crystallinity and a large surface area with tunable inorganic nodes and organic linkers, exhibit high stimuli-responsiveness and molecular adsorption selectivity that enable various applications. The adsorption in MOFs changes the crystalline structure and elastic moduli. Thus, the coexistence of adsorbed/desorbed sites makes the host matrices elastically heterogeneous. However, the role of elastic heterogeneity in the adsorption-desorption transition has been overlooked. Here, we show the asymmetric role of elastic heterogeneity in the adsorption-desorption transition. We construct a minimal model incorporating adsorption-induced lattice expansion/contraction and an increase/decrease in the elastic moduli. We find that the transition is hindered by the entropic and energetic effects which become asymmetric in the adsorption process and desorption process, leading to the strong hysteretic nature of the transition. Furthermore, the adsorbed/desorbed sites exhibit spatially heterogeneous domain formation, implying that the domain morphology and interfacial area between adsorbed/desorbed sites can be controlled by elastic heterogeneity. Our results provide a theoretical guideline for designing soft porous crystals with tunable adsorption hysteresis and the dispersion and domain morphology of adsorbates using elastic heterogeneity.

Molecular Simulation of Argon Adsorption and Diffusion in a Microporous Carbon with Poroelastic Couplings

Neglected for a long time in molecular simulations of fluid adsorption and transport in microporous carbons, adsorption-induced deformations of the matrix have recently been shown to have important effects on both sorption isotherms and diffusion coefficients. Here we investigate in detail the behavior of a recently proposed 3D-connected mature kerogen model, as a generic model of aromatic microporous carbon with atomic H/C ∼ 0.5, in both chemical and mechanical equilibrium with argon at 243 K over an extended pressure range. We show that under these conditions the material exhibits some viscoelasticity, and simulations of hundreds of nanoseconds are required to accurately determine the equilibrium volumes and sorption loadings. We also show that neglecting matrix internal deformations and swelling can lead to underestimations of the loading by up to 19% (swelling only) and 28% (swelling and internal deformations). The volume of the matrix is shown to increase up to about 8% at the largest pressure considered (210 MPa), which induces an increase of about 33% of both pore volume and specific surface area via the creation of additional pores, yet does not significantly change the normalized pore size distribution. Volume swelling is also rationalized by using a well-known linearized microporomechanical model. Finally, we show that self-diffusivity decreases with applied pressure, following an almost perfectly linear evolution with the free volume. Quantitatively, neglecting swelling and internal deformations tends to reduce the computed self-diffusivities.

One Atom Can Make All the Difference: Gas-Induced Phase Transformations in Bisimidazole-Linked Diamondoid Coordination Networks

Coordination networks (CNs) that undergo gas-induced transformation from closed (nonporous) to open (porous) structures are of potential utility in gas storage applications, but their development is hindered by limited control over their switching mechanisms and pressures. In this work, we report two CNs, [Co(bimpy)(bdc)]_n (X-dia-4-Co) and [Co(bimbz)(bdc)]_n (X-dia-5-Co) (H₂bdc = 1,4-benzendicarboxylic acid; bimpy = 2,5-bis(1H-imidazole-1-yl)pyridine; bimbz = 1,4-bis(1H-imidazole-1-yl)benzene), that both undergo transformation from closed to isostructural open phases involving at least a 27% increase in cell volume. Although X-dia-4-Co and X-dia-5-Co only differ from one another by one atom in their N-donor linkers (bimpy = pyridine, and bimbz = benzene), this results in different pore chemistry and switching mechanisms. Specifically, X-dia-4-Co exhibited a gradual phase transformation with a steady increase in the uptake when exposed to CO₂, whereas X-dia-5-Co exhibited a sharp step (type F-IV isotherm) at P/P₀ ≈ 0.008 or P ≈ 3 bar (195 or 298 K, respectively). Single-crystal X-ray diffraction, in situ powder XRD, in situ IR, and modeling (density functional theory calculations, and canonical Monte Carlo simulations) studies provide insights into the nature of the switching mechanisms and enable attribution of pronounced differences in sorption properties to the changed pore chemistry.

Propagating MOF flexibility at the macroscale: the case of MOF-based mechanical actuators

Shapeshifting materials have captured the imagination of researchers for their myriad potential applications, yet their practical development remains challenging. These materials operate by mechanical actuation: their structural responses to external stimuli generate mechanical work. Here, we review progress on the use of flexible metal-organic frameworks (MOFs) in composite actuators that shapeshift in a controlled fashion. We highlight the dynamic behaviour of flexible MOFs, which are unique among materials, even other porous ones, and introduce the concept of propagation, which involves the efficient transmission of flexible MOF deformations to the macroscale. Furthermore, we explain how researchers can observe, measure, and induce such effects in MOF composites. Next, we review pioneering first-generation MOF-composite actuators that shapeshift in response to changes in humidity, temperature, pressure, or to other stimuli. Finally, we allude to recent developments, identify remaining R & D hurdles, and suggest future directions in this field.

On the Role of Flexibility for Adsorptive Separation

Chemical separations, mostly based on heat-driven techniques such as distillation, account for a large portion of the world's energy consumption. In principle, differential adsorption is a more energy-efficient separation method, but conventional adsorbent materials are still not effective for many industry-relevant mixtures. Porous coordination polymers (PCPs), or metal-organic frameworks (MOFs), are attractive for their well-defined, designable, modifiable, and flexible structures connecting to various potential applications. While the importance of the structural flexibility of MOFs in adsorption-based functions has been demonstrated, the understanding of this special feature is still in its infancy and mostly stays at the periodic structural transformation at the equilibrium state and the special shapes of single-component adsorption isotherms. There are many confusions about the categorization and roles of various types of flexibility. This Account discusses the role of flexibility of MOFs for adsorptive separation, mainly from the thermodynamic and kinetic points of view.As the classic type of framework flexibility, guest-driven structural transformations and the corresponding adsorption isotherms can be thermodynamically described by the energies of the host-guest system. The highly guest-specific pore-opening action showing contrasting single-component adsorption isotherms is regarded as a strategy for achieving molecular sieving without the need for aperture size control, but its effect and role for mixture separation are still controversial. Quantitative mixture adsorption/separation experiments showed that the common periodic (cooperative) pore-opening action leads to coadsorption of molecules smaller than the opened aperture, while the aperiodic (noncooperative) one can achieve inversed molecular sieving under a thermodynamic mechanism.The energy barrier and structure in the nonequilibrium state are also important for flexibility and adsorption/separation. With suitable energy barriers between metastable structures, new types of framework flexibility such as aperture gating can be realized. While kinetically controlled gating flexibility is usually ignored because of the difficulty of characterization or considered as disadvantageous for separation because of the variable aperture size, it plays a critical role in most kinetic separation systems, including adsorbents conventionally regarded as rigid. With the concept of gating flexibility, the meanings of aperture and guest sizes for judging molecular sieving need to be reconsidered. Gating flexibility depends on not only the host itself but also the guest, the host-guest interaction, and the external environment such as temperature, which can be rationally tuned to achieve special adsorption/separation behaviors such as inversed temperature dependence, molecular sieving, and even inversed thermodynamic selectivity. The comprehensive understanding of the thermodynamic and kinetic bases of flexibility will give a new horizon for next-generation separation materials beyond MOFs and adsorbents.

Metal-Organic Framework with Structural Flexibility Responding Specifically to Acetylene and Its Adsorption Behavior

Flexible metal-organic frameworks (MOFs) are one kind of stimuli-responsive materials that exhibit reversible structural transformations in response to external stimuli. Exploring and understanding the stimuli response behavior of flexible MOFs is challenging, as it involves weak host-guest interaction. We report here the unique flexibility of MOF Zn(int)(Ad) (TIF-A1, Hint = isonicotinic acid, Had = adenine) induced by acetylene adsorption. TIF-A1 is rigid toward most gas molecules, while only C₂H₂ can induce the flexibility of TIF-A1. C₂H₂-loaded TIF-A1 is characterized by single-crystal X-ray diffraction and molecular modeling. It is revealed that the flexibility of TIF-A1 originates from the strong interaction between acetylene and the framework, which pushes the rotation of the int ligand and the expansion of the framework simultaneously. This work is helpful in deeply understanding the flexibility of MOFs and guides exploring new flexible MOFs in the future.

Large breathing effect in ZIF-65(Zn) with expansion and contraction of the SOD cage

The flexibility and guest-responsive behavior of some metal-organic frameworks (MOFs) indicate their potential in the fields of sensors and molecular recognition. As a subfamily of MOFs, the flexible zeolitic imidazolate frameworks (ZIFs) typically feature a small displacive transition due to the rigid zeolite topology. Herein, an atypical reversible displacive transition (6.4 Å) is observed for the sodalite (SOD) cage in flexible ZIF-65(Zn), which represents an unusually large breathing effect compared to other ZIFs. ZIF-65(Zn) exhibits a stepwise II → III → I expansion between an unusual ellipsoidal SOD cage (8.6 Å × 15.9 Å for II) and a spherical SOD cage (15.0 Å for I). The breathing behavior of ZIF-65(Zn) varies depending on the nature of the guest molecules (polarity and shape). Computational simulations are employed to rationalize the differences in the breathing behavior depending on the structure of the ZIF-65(Zn) cage and the nature of the guest-associated host–guest and guest–guest interactions.

Flexible metal-organic frameworks have potential applications in the development of sensors and switching materials. Here, the authors report a large breathing effect in a zeolitic imidazolate framework upon guest adsorption.

Hydrocarbon Sorption in Flexible MOFs—Part I: Thermodynamic Analysis with the Dubinin-Based Universal Adsorption Theory (D‑UAT)

The analysis of empirical sorption equilibrium datasets is still vital to gain insights into material–property relationships as computational methods remain in development, especially for complex materials such as flexible MOFs. Therefore, the Dubinin-based universal adsorption theory (D-UAT) was revisited and evaluated as a simple visualization, analysis, and prediction tool for sorption equilibrium data. Within the theory, gas properties are normalized into corresponding states using the critical temperatures of the respective sorptives. The study shows theoretically and experimentally that the D-UAT is able to condense differences of sorption data visualized in reduced Dubinin plots to just three governing parameters: (a) the accessible pore volume, (b) the reduced enthalpy of sorption, and (c) the framework’s reduced free energy differences (in case of flexible behavior). This makes the theory a fast visualization and analysis tool, the use as a prediction tool depends on rough assumptions, and thus is not recommended.

Tunable acetylene sorption by flexible catenated metal-organic frameworks

The safe storage of flammable gases, such as acetylene, is essential for current industrial purposes. However, the narrow pressure (P) and temperature range required for the industrial use of pure acetylene (100 < P < 200 kPa at 298 K) and its explosive behaviour at higher pressures make its storage and release challenging. Flexible metal-organic frameworks that exhibit a gated adsorption/desorption behaviour-in which guest uptake and release occur above threshold pressures, usually accompanied by framework deformations-have shown promise as storage adsorbents. Herein, the pressures for gas uptake and release of a series of zinc-based mixed-ligand catenated metal-organic frameworks were controlled by decorating its ligands with two different functional groups and changing their ratio. This affects the deformation energy of the framework, which in turn controls the gated behaviour. The materials offer good performances for acetylene storage with a usable capacity of ~90 v/v (77% of the overall amount) at 298 K and under a practical pressure range (100-150 kPa).

Isotope-selective pore opening in a flexible metal-organic framework

Flexible metal-organic frameworks that show reversible guest-induced phase transitions between closed and open pore phases have enormous potential for highly selective, energy-efficient gas separations. Here, we present the gate-opening process of DUT-8(Ni) that selectively responds to D₂, whereas no response is observed for H₂ and HD. In situ neutron diffraction directly reveals this pressure-dependent phase transition. Low-temperature thermal desorption spectroscopy measurements indicate an outstanding D₂-over-H₂ selectivity of 11.6 at 23.3 K, with high D₂ uptake. First-principles calculations coupled with statistical thermodynamics predict the isotope-selective gate opening, rationalized by pronounced nuclear quantum effects. Simulations suggest DUT-8(Ni) to remain closed in the presence of HT, while it also opens for DT and T₂, demonstrating gate opening as a highly effective approach for isotopolog separation.

Gating effect for gas adsorption in microporous materials-mechanisms and applications

In the past two decades, various microporous materials have been developed as useful adsorbents for gas adsorption for a wide range of industries. Considerable efforts have been made to regulate the pore accessibility in microporous materials for the manipulation of guest molecules' admission and release. It has long been known that some microporous adsorbents suddenly become highly accessible to guest molecules at specific conditions, e.g., above a threshold pressure or temperature. This anomalous adsorption behavior results from a gating effect, where a structural variation of the adsorbent leads to an abrupt change in the gas admission. This review summarizes the mechanisms of the gating effect, which can be a result of the deformation of the framework (e.g., expansion, contraction, reorientation, and sliding of the unit cells), the vibration of the pore-keeping groups (e.g., rotation, swing, and collapse of organic linkers), and the oscillation of the pore-keeping ions (e.g. cesium, potassium, etc.). These structural variations are induced either by the host-guest interaction or by an external stimulus, such as temperature or light, and account for the gating effect at a threshold value of the stimulus. Emphasis is given to the temperature-regulated gating effect, where the critical admission temperature is dictated by the combined effect of the gate opening and thermodynamic factors and plays a key role in regulating guest admission. Molecular simulations can improve our understanding of the gate opening/closing transitions at the atomic scale and enable the construction of quantitative models to describe the gated adsorption behaviour at the macroscale level. The gating effect in porous materials has been widely applied in highly selective gas separation and offers great potential for gas storage and sensing.

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.

Models of adsorption-induced deformation: ordered materials and beyond

Adsorption-induced deformation is a change in geometrical dimensions of an adsorbent material caused by gas or liquid adsorption on its surface. This phenomenon is universal and sensitive to adsorbent properties, which makes its prediction a challenging task. However, the pure academic interest is complemented by its importance in a number of engineering applications with porous materials characterization among them. Similar to classical adsorption-based characterization methods, the deformation-based ones rely on the quality of the underlying theoretical framework. This fact stimulates the recent development of qualitative and quantitative models toward the more detailed description of a solid material, e.g. account of non-convex and corrugated pores, calculations of adsorption stress in realistic three-dimension solid structures, the extension of the existing models to new geometries, etc. The present review focuses on the theoretical description of adsorption-induced deformation in micro and mesoporous materials. We are aiming to cover recent theoretical works describing the deformation of both ordered and disordered porous bodies.

Concluding remarks: current and next generation MOFs

This paper describes the content of my "Concluding remarks" talk at the Faraday Discussion meeting on "MOFs for energy and the environment" (online, 23-25 June 2021). The panel consisted of sessions on the design of MOFs and MOF hybrids (synthetic chemistry), their applications (e.g., capture, storage, separation, electrical devices, photocatalysis), advanced characterization (e.g., transmission electron microscopy, solid-state nuclear magnetic resonance), theory and modeling, and commercialization. MOF chemistry is undergoing a significant evolution from simply network chemistry to the chemistry of synergistic integration with heterogeneous materials involving other disciplines (we call this the fourth generation type). As reflected in the papers of the invited speakers and discussions with the participants, the present and future of this field will be described in detail.

Adsorption of Carbon Dioxide, Methane, and Nitrogen on Zn(dcpa) Metal-Organic Framework

Adsorption-based processes using metal-organic frameworks (MOFs) are a promising option for carbon dioxide (CO2) capture from flue gases and biogas upgrading to biomethane. Here, the adsorption of CO2, methane (CH4), and nitrogen (N2) on Zn(dcpa) MOF (dcpa (2,6-dichlorophenylacetate)) is reported. The characterization of the MOF by powder X-ray diffraction (PXRD), thermogravimetric analysis (TGA), and N2 physisorption at 77 K shows that it is stable up to 650 K, and confirms previous observations suggesting framework flexibility upon exposure to guest molecules. The adsorption equilibrium isotherms of the pure components (CO2, CH4, and N2), measured at 273–323 K, and up to 35 bar, are Langmuirian, except for that of CO2 at 273 K, which exhibits a stepwise shape with hysteresis. The latter is accurately interpreted in terms of the osmotic thermodynamic theory, with further refinement by assuming that the free energy difference between the two metastable structures of Zn(dcpa) is a normally distributed variable due to the existence of different crystal sizes and defects in a real sample. The ideal selectivities of the equimolar mixtures of CO2/N2 and CO2/CH4 at 1 bar and 303 K are 12.8 and 2.9, respectively, which are large enough for Zn(dcpa) to be usable in pressure swing adsorption.

17 O solid-state NMR at ultrahigh magnetic field of 35.2 T: Resolution of inequivalent oxygen sites in different phases of MOF MIL-53(Al)

MIL-53(Al) is a member of the most extensively studied metal-organic framework (MOF) families owing to its "flexible" framework and superior stability. 17 O solid-state NMR (SSNMR) spectroscopy is an ideal site-specific characterization tool as it probes local oxygen environments. Because oxygen local structure is often altered during phase change, 17 O SSNMR can be used to follow phase transitions. However, 17 O is a challenging nucleus to study via SSNMR due to its low sensitivity and resolution arising from the very low natural abundance of 17 O isotope and its quadrupolar nature. In this work, we describe that by using 17 O isotopic enrichment and performing 17 O SSNMR experiments at an ultrahigh magnetic field of 35.2 T, all chemically and crystallographically inequivalent oxygen sites in two representative MIL-53(Al) (as-made and water adsorbed) phases can be completely resolved. The number of signals in each phase is consistent with that predicted from the space group refined from powder X-ray diffraction data. The 17 O 1D magic-angle spinning (MAS) and 2D triple-quantum MAS (3QMAS) spectra at 35.2 T furnish fine information about the host-guest interactions and the structural changes associated with phase transition. The ability to completely resolve multiple chemically and crystallographically inequivalent oxygen sites in MOFs at very high magnetic field, as illustrated in this work, significantly enhances the potential for using the NMR crystallography approach to determine crystal structures of new MOFs and verify the structures of existing MOFs obtained from refining powder X-ray diffraction data.

Hysteresis curves reveal the microscopic origin of cooperative CO2 adsorption in diamine-appended metal-organic frameworks

Diamine-appended metal-organic frameworks (MOFs) of the form Mg₂(dobpdc)(diamine)₂ adsorb CO₂ in a cooperative fashion, exhibiting an abrupt change in CO₂ occupancy with pressure or temperature. This change is accompanied by hysteresis. While hysteresis is suggestive of a first-order phase transition, we show that hysteretic temperature-occupancy curves associated with this material are qualitatively unlike the curves seen in the presence of a phase transition; they are instead consistent with CO₂ chain polymerization, within one-dimensional channels in the MOF, in the absence of a phase transition. Our simulations of a microscopic model reproduce this dynamics, providing a physical understanding of cooperative adsorption in this industrially important class of materials.

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.

Porous flexible frameworks: origins of flexibility and applications

Porous crystalline frameworks including zeolites, metal-organic frameworks (MOFs), covalent organic frameworks (COFs) and hydrogen-bonded organic frameworks (HOFs) have attracted great research interest in recent years. In addition to their assembly in the solid-state being fundamentally interesting and aesthetically pleasing, their potential applications have now pervaded in different areas of chemistry, biology and materials science. When framework materials are endowed with 'flexibility', they exhibit some properties (e.g., stimuli-induced pore breathing and reversible phase transformations) that are distinct from their rigid counterparts. Benefiting from flexibility and porosity, these framework materials have shown promise in applications that include separation of toxic chemicals, isotopes and hydrocarbons, sensing, and targeted delivery of chemicals. While flexibility in MOFs has been widely appreciated, recent developments of COFs and HOFs have established that flexibility is not just limited to MOFs. In fact, zeolites-that are considered rigid when compared with MOFs-are also known to exhibit dynamic modes. Despite flexibility may be conceived as being detrimental to the formation and stability of periodic structures, the landscape of flexible framework structures continues to expand with discovery of new materials with promising applications. In this review, we make an account of different flexible framework materials based on their framework types with a more focus on recent examples and delve into the origin of flexibility in each case. This systematic analysis of different flexibility types based on their origins enables understanding of structure-property relationships, which should help guide future development of flexible framework materials based on appropriate monomer design and tailoring their properties by bottom-up approach. In essence, this review provides a summary of different flexibility types extant to framework materials and critical analysis of importance of flexibility in emerging applications.

The state of the field: from inception to commercialization of metal–organic frameworks

We provide a brief overview of the state of the MOF field from their inception to their synthesis, potential applications, and finally, to their commercialization.

Flexible Adsorbents at High Pressure: Observations and Correlation of ZIF-7 Stepped Sorption Isotherms for Nitrogen, Argon, and Other Gases

Stepped adsorption isotherms with desorption hysteresis were measured for nitrogen, argon, ethane, carbon dioxide, and methane at pressures up to 17 MPa on zeolitic imidazolate framework-7 (ZIF-7) using a gravimetric sorption analyzer. Such stepped sorption isotherms have not been previously reported for nitrogen or argon on ZIF-7, and required the application of pressures as high as 15 MPa to trigger the ZIF-7 structural phase transition at temperatures around 360 K. The stepped hysteretic sorption isotherms measured for carbon dioxide, methane, and ethane were consistent with previous observations reported in the literature. To correlate these stepped hysteretic sorption isotherms, a semi-empirical model was developed by combining a three-parameter Langmuir equation to describe the Type I aspect of the isotherm, with a model designed to describe the temperature-dependent ZIF-7 structural phase transition. Excellent fits of the combined adsorption and desorption branches were achieved by adjusting nine parameters in the temperature-dependent model, with root-mean-square deviations within 2.5 % of the highest measured adsorption capacity. Each parameter of the new semi-empirical model has a physical basis, allowing them to be estimated or compared independently.

Temperature dependence of adsorption hysteresis in flexible metal organic frameworks

"Breathing" and "gating" are striking phenomena exhibited by flexible metal-organic frameworks (MOFs) in which their pore structures transform upon external stimuli. These effects are often associated with eminent steps and hysteresis in sorption isotherms. Despite significant mechanistic studies, the accurate description of stepped isotherms and hysteresis remains a barrier to the promised applications of flexible MOFs in molecular sieving, storage and sensing. Here, we investigate the temperature dependence of structural transformations in three flexible MOFs and present a new isotherm model to consistently analyse the transition pressures and step widths. The transition pressure reduces exponentially with decreasing temperature as does the degree of hysteresis (c.f. capillary condensation). The MOF structural transition enthalpies range from +6 to +31 kJ·mol^-1 revealing that the adsorption-triggered transition is entropically driven. Pressure swing adsorption process simulations based on flexible MOFs that utilise the model reveal how isotherm hysteresis can affect separation performance.

Pressure-Gradient Sorption Calorimetry of Flexible Porous Materials: Implications for Intrinsic Thermal Management

Thermal management is an important consideration for applications that involve gas sorption by flexible porous materials. A pressure-gradient differential scanning calorimetric method was developed to measure the energetics of adsorption and desorption both directly and continuously. The method was applied to the uptake and release of CO₂ by the well-known flexible metal-organic frameworks MIL-53(Al) and MOF-508b. High-resolution differential enthalpy plots and total integral enthalpy values for sorption allow comprehensive assessment of the thermal behavior of the materials throughout the entire sorption process. During adsorption, the investigated materials display the ability to offset exothermic adsorption enthalpy against endothermic structural transition enthalpy, and vice versa during desorption. The results show that flexible materials offer reduced total integral heat over a working range when compared to rigid materials.

Self-adjusting binding pockets enhance H2 and CH4 adsorption in a uranium-based metal-organic framework

A new, air-stable, permanently porous uranium(iv) metal-organic framework U(bdc)2 (1, bdc2- = 1,4-benzenedicarboxylate) was synthesized and its H2 and CH4 adsorption properties were investigated. Low temperature adsorption isotherms confirm strong adsorption of both gases in the framework at low pressures. In situ gas-dosed neutron diffraction experiments with different D2 loadings revealed a rare example of cooperative framework contraction (ΔV = -7.8%), triggered by D2 adsorption at low pressures. This deformation creates two optimized binding pockets for hydrogen (Q st = -8.6 kJ mol-1) per pore, in agreement with H2 adsorption data. Analogous experiments with CD4 (Q st = -24.8 kJ mol-1) and N,N-dimethylformamide as guests revealed that the binding pockets in 1 adjust by selective framework contractions that are unique for each adsorbent, augmenting individual host-guest interactions. Our results suggest that the strategic combination of binding pockets and structural flexibility in metal-organic frameworks holds great potential for the development of new adsorbents with an enhanced substrate affinity.

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.

Palladium-catalyzed oxidative homocoupling of pyrazole boronic esters to access versatile bipyrazoles and the flexible metal–organic framework Co(4,4′-bipyrazolate)

A facile catalytic protocol achieves the homocoupling of pyrazole boronic esters, enabling access to the structurally-flexible metal–organic framework Co(bpz).