Free energy analysis for adsorption-induced lattice transition of flexible coordination framework

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.

Spatiotemporal Design of the Metal-Organic Framework DUT-8(M)

Switchable metal-organic frameworks (MOFs) change their structure in time and selectively open their pores adsorbing guest molecules, leading to highly selective separation, pressure amplification, sensing, and actuation applications. The 3D engineering of MOFs has reached a high level of maturity, but spatiotemporal evolution opens a new perspective toward engineering materials in the 4th dimension (time) by t-axis design, in essence exploiting the deliberate tuning of activation barriers. This work demonstrates the first example in which an explicit temporal engineering of a switchable MOF (DUT-8, [M₁ M₂ (2,6-ndc)₂ dabco]_n , 2,6-ndc = 2,6-naphthalene dicarboxylate, dabco = 1,4diazabicyclo[2.2.2]octane, M₁  = Ni, M₂  = Co) is presented. The temporal response is deliberately tuned by variations in cobalt content. A spectrum of advanced analytical methods is presented for analyzing the switching kinetics stimulated by vapor adsorption using in situ time-resolved techniques ranging from ensemble adsorption and advanced synchrotron X-ray diffraction experiments to individual crystal analysis. A novel analysis technique based on microscopic observation of individual crystals in a microfluidic channel reveals the lowest limit for adsorption switching reported so far. Differences in the spatiotemporal response of crystal ensembles originate from an induction time that varies statistically and widens characteristically with increasing cobalt content reflecting increasing activation barriers.

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.

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.

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.

Effect of gold addition by the recharge method on silver supported catalysts in the catalytic wet air oxidation (CWAO) of phenol

Catalysts Ag/ZrO2-CeO2 and Au/ZrO2-CeO2 were synthesized by a deposition-precipitation method and Ag-Au/ZrO2-CeO2 was prepared using a recharge method for the second metal (Au). The materials were characterized by physisorption of N2, XRD, ICP, UV-vis RDS, H2-TPR, XPS and TEM. The results obtained show that the specific areas for monometallic materials were 29-37 m2 g-1 and 27-74 m2 g-1 for bimetallics. The tetragonal crystal phase of ZrO2 stabilizes when CeO2 quantity increases. Using XPS an increment in Ce3+ species abundance was determined for bimetallic catalysts in contrast to the monometallic ones; according to the Ag 3d region, this metal oxidation was observed when augmenting the content of CeO2 in the materials, and with Au the opposite effect was produced. It was determined by TEM, that the average size of the metallic particles was smaller at bimetallic catalysts due the preparation method. Catalytic activity was evaluated by CWAO of phenol, the Ag-Au/ZrO2-CeO2 catalyst with 20% wt of cerium reached a degradation of 100% within an hour, being the most active catalyst. Maleic, formic and oxalic acid were identified as reaction intermediates; and at the end of the reaction acetic acid was identified as the main by-product, because it is the most refractory and the conditions for oxidation must be more severe.

Double-Step Gate Phenomenon in CO2 Sorption of an Elastic Layer-Structured MOF

A double-step CO2 sorption by [Cu(4,4'-bpy)2(BF4)2] (ELM-11) was observed during isothermal measurements at 195, 253, 273, and 298 K and was accompanied by interlayer expansion in the layered structure of ELM-11. The first step occurred in the range of the relative pressure (P/P0) from 10(-3) to 10(-2). The second step was observed at P/P0 ≈ 0.3 at the four temperatures. Structural changes in ELM-11 during the CO2 sorption process were examined by X-ray diffraction (XRD) measurements. The structural change for the first step was well understood from a detailed structural analysis, as reported previously. The XRD results showed further expansion of the layers during the second step as compared to the already expanded structure in the first step, and both steps were found to be caused by the gate phenomenon. The energy for the expansion of the layer structure was estimated from experimental and simulated data.

Structures of Metal-Organic Frameworks with Rod Secondary Building Units

Rod MOFs are metal-organic frameworks in which the metal-containing secondary building units consist of infinite rods of linked metal-centered polyhedra. For such materials, we identify the points of extension, often atoms, which define the interface between the organic and inorganic components of the structure. The pattern of points of extension defines a shape such as a helix, ladder, helical ribbon, or cylinder tiling. The linkage of these shapes into a three-dimensional framework in turn defines a net characteristic of the original structure. Some scores of rod MOF structures are illustrated and deconstructed into their underlying nets in this way. Crystallographic data for all nets in their maximum symmetry embeddings are provided.

A generalized adsorption-phase transition model to describe adsorption rates in flexible metal organic framework RPM3-Zn

The rate of adsorption to a flexible metal-organic framework is described via generalization of the Avrami theory of phase transition kinetics.

Role of crystal size on swing-effect and adsorption induced structure transition of ZIF-8

The flexibility and structure transition behaviour of ZIF-8 in a series of samples with different particle size has been studied using a combination of high-resolution N₂ gas adsorption isotherms and, for the first time, a broad in situ PXRD and Rietveld analysis.

Understanding gate adsorption behaviour of CO2 on elastic layer-structured metal–organic framework-11

We demonstrate that CO₂ gate adsorption behaviour of elastic layer-structured metal–organic framework-11 can be described by a thermodynamic model by free energy analysis with the aid of an adsorption experiment and a molecular simulation.

Understanding adsorption-induced structural transitions in metal-organic frameworks: from the unit cell to the crystal

Breathing transitions represent recently discovered adsorption-induced structural transformations between large-pore and narrow-pore conformations in bi-stable metal-organic frameworks such as MIL-53. We present a multiscale physical mechanism of the dynamics of breathing transitions. We show that due to interplay between host framework elasticity and guest molecule adsorption, these transformations on the crystal level occur via layer-by-layer shear. We construct a simple Hamiltonian that describes the physics of host-host and host-guest interactions on the level of unit cells and reduces to one effective dimension due to the long-range elastic cell-cell interactions. We then use this Hamiltonian in Monte Carlo simulations of adsorption-desorption cycles to study how the behavior of unit cells is linked to the transition mechanism at the crystal level through three key physical parameters: the transition energy barrier, the cell-cell elastic coupling, and the system size.

Selective separation of water, methanol, and ethanol by a porous coordination polymer built with a flexible tetrahedral ligand

A novel porous coordination polymer, Cu(II)(mtpm)Cl(2) [mtpm = tetrakis(m-pyridyloxy methylene)methane], has been synthesized, and its crystal structure has been determined. Its adsorption isotherms for water, methanol, and ethanol are totally different from each other. It adsorbs water at low humidity and shows gate-open behavior for methanol, but it does not adsorb ethanol. This compound has the capacity to separate both methanol and water from bioethanol, which is a mixture of water, methanol, and ethanol.

Adsorption-induced structural transition of an interpenetrated porous coordination polymer: detailed exploration of free energy profiles

Specific types of coordination polymers show an adsorption-induced structural transition, or so-called "gate adsorption", in which a host framework is said to change its structure from a "closed" nonporous phase to an "open" porous one for guest molecules. To identify the pathway for such a structural transition, we perform grand canonical Monte Carlo simulations for the adsorption of guest molecules in a host interpenetrated framework and calculate the free energy profiles of the structural changes in a complete three-dimensional space. In addition to the open phase found in our previous analyses along a fixed one-dimensional path, we reveal the existence of another open configuration. Each of the two open phases yields the status of global minimum to the other depending on the external pressure, resulting in a two-step isotherm. Moreover, the shape of adsorption hysteresis associated with the structural transition can change depending on the energy barrier between a metastable and a stable state that the system can overcome. Our simulations not only give a comprehensive understanding of stepped isotherms observed empirically but also suggest that isotherms with hysteretic gate adsorption is closely related to the thermal fluctuation of the system.

Thermodynamic methods and models to study flexible metal-organic frameworks

Much attention has recently been focused on a fascinating subclass of metal-organic frameworks that behave in a remarkable stimuli-responsive fashion. These soft porous crystals feature dynamic crystalline frameworks displaying reversible, large-amplitude structural deformations under external physical constraints such as temperature, electric field or gas exposure. The number of reported syntheses of such materials is rapidly growing and they are promising for practical applications, such as gas capture, purification and fluid separation. Herein, we summarize the recently developed thermodynamic tools that can help understand the process of fluid adsorption and fluid mixture coadsorption in these flexible nanoporous materials. These tools, which include both molecular simulation methods and analytical models, can help rationalize experimental results and predict adsorption properties over a wide range of thermodynamic conditions. A particular focus is given on how these methods can guide the experimental exploration of a large number of materials and working conditions (temperature, pressure, composition) to help design efficient processes relying on fluid adsorption in soft porous crystals.

Unveiling thermal transitions of polymers in subnanometre pores

The thermal transitions of confined polymers are important for the application of polymers in molecular scale devices and advanced nanotechnology. However, thermal transitions of ultrathin polymer assemblies confined in subnanometre spaces are poorly understood. In this study, we show that incorporation of polyethylene glycol (PEG) into nanochannels of porous coordination polymers (PCPs) enabled observation of thermal transitions of the chain assemblies by differential scanning calorimetry. The pore size and surface functionality of PCPs can be tailored to study the transition behaviour of confined polymers. The transition temperature of PEG in PCPs was determined by manipulating the pore size and the pore–polymer interactions. It is also striking that the transition temperature of the confined PEG decreased as the molecular weight of PEG increased.

Understanding the thermal transitions of confined polymers is important for the design of molecular scale devices. In this study, unusual thermal transitions are observed in polyethylene glycol chains incorporated in nanochannels of porous coordination polymers.

Soft porous crystals

The field of host-guest complexation is intensely attractive from diverse perspectives, including materials science, chemistry and biology. The uptake and encapsulation of guest species by host frameworks are being investigated for a wide variety of purposes, including separation and storage using zeolites, and recognition and sensing by enzymes in solution. Here we focus on the concept of the cooperative integration of 'softness' and 'regularity'. Recent developments on porous coordination polymers (or metal-organic frameworks) have provided the inherent properties that combine these features. Such soft porous crystals exhibit dynamic frameworks that are able to respond to external stimuli such as light, electric fields or the presence of particular species, but they are also crystalline and can change their channels reversibly while retaining high regularity. We discuss the relationship between the structures and properties of these materials in view of their practical applications.