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.

Solute interaction-driven and solvent interaction-driven liquid-liquid phase separation induced by molecular size difference.

We conducted molecular dynamics (MD) simulations in a binary Lennard-Jones system as a model system for molecular solutions and investigated the mechanism of liquid-liquid phase separation (LLPS), which has recently been recognized as a fundamental step in crystallization and organelle formation. Our simulation results showed that LLPS behavior varied drastically with the size ratio of solute to solvent molecules. Interestingly, increasing the size ratio can either facilitate or inhibit LLPS, depending on the combination of interaction strengths. We demonstrated that the unique behavior observed in MD simulation could be reasonably explained by the free energy barrier height calculated using our thermodynamic model based on the classical nucleation theory. Our model proved that the molecular size determines the change in number of interaction pairs through LLPS. Varying the size ratio changes the net number of solute-solvent and solvent-solvent interaction pairs that are either broken or newly generated per solute-solute pair generation, thereby inducing a complicated trend in LLPS depending on the interaction parameters. As smaller molecules have more interaction pairs per unit volume, their contribution is more dominant in the promotion of LLPS. Consequently, as the size ratio of the solute to the solvent increased, the LLPS mode changed from solute-related interaction-driven to solvent-related interaction-driven.

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.

Flow Microreactor Synthesis of Zeolitic Imidazolate Framework (ZIF)@ZIF Core-Shell Metal-Organic Framework Particles and Their Adsorption Properties.

Metal-organic frameworks (MOFs) with core-shell structures enable to enhance intrinsic properties of constituent MOFs and impart additional functional activities. Although shell thickness is a key factor for regulating the properties of core-shell MOF particles, controlling it has been challenging. The widely used batch reactor synthesis cannot produce core-shell particles with uniform shell thickness because of poor reactant mixing. A microreactor could ensure excellent mixing, and that would allow to control shell thickness. In this study, we synthesized zeolitic imidazolate framework-8 (ZIF-8)@ZIF-67 and ZIF-67@ZIF-8 core-shell particles using a microreactor and investigated the effects of the mixing performance on the shell thickness of the obtained particles. Our results demonstrated that rapid mixing was critical for the uniformity of the synthesized particles. The concentration of core particles is another key factor that can preferentially induce heterogeneous nucleation on the surface of the core particles without inducing self-nucleation in the bulk solution, particularly when the self-nucleation rate of the shell MOF is high. The N2 adsorption isotherms of the synthesized particles revealed their unique adsorption properties, which were ascribed to the core-shell structures obtained at low shell formation rates. Our simple and versatile synthesis technique not only allowed the preparation of ZIF@ZIF particles with novel functionalities but also can be extended to synthesize core-shell MOF particles with different combinations of core particles and shells.

Multiple Roles of Polyethylenimine during Synthesis of 10 nm Thick Continuous Silver Nanoshells.

Silica@silver core-shell particles (silver nanoshells) present a wide range of applications, owing to their unique optical, chemical, and surface plasmon resonance (SPR) properties. Because SPR properties are mainly determined by shell thickness, precise shell thickness control is required. However, the synthesis of continuous nanoshells less than 10 nm thickness is still a challenge. In this study, we overcame this challenge by using polyethyleneimine (PEI) during the shell growth step of the seed-mediated growth method. We determined that the addition of PEI significantly slowed the shell growth reaction and facilitated the formation of uniform shells, which allowed us to synthesize 9.8 nm thick complete silver nanoshells. The SPR absorptions of the resultant nanoshell suspensions remained almost unchanged for 15 days. Therefore, we demonstrated that PEI molecules played three different roles during the shell growth process: reaction-rate regulators, shell growth facilitators, and resultant suspension stabilizers. The shell thickness was tuned from 9.8 to 29.5 nm by simply varying the silver-ion concentration. A key factor was the amount of added PEI because excess PEI would result in the formation of silver nanoparticles in the bulk solution phase, while too little PEI would produce incomplete shells. The optimum mass ratio of PEI-to-silica particles was determined to be 1.0 for the experimental conditions in this study. The mixing sequence of the reaction solutions was also important because PEI had to be mixed with silica particles first to ensure that the PEI molecules get adsorbed on the surface of silica and accommodated silver ions via the coordination interactions between the amine groups of the PEI molecules and silver ions. The reaction that involves the use of PEI could lead to establishing a simple and robust synthesis technique for silver nanoshells.

Direct observation of the attachment behavior of hydrophobic colloidal particles onto a bubble surface.

The attachment of solid particles to the surface of immersed gas bubbles plays a fundamental role in surface science, and hence plays key roles in various engineering fields ranging from industrial separation processes to the fabrication of functional materials. However, detailed investigation from a microscopic view on how a single particle attaches to a bubble surface and how the particle properties affect the attachment behavior has been so far scarcely addressed. Here, we observed the attachment of a single particle to a bubble surface using a high-speed camera and systematically investigated the effects of the wettability and shape of particles. We found that hydrophobic particles abruptly "jumped into" the bubble while sliding down the bubble surface to eventually satisfy their static contact angles, the behavior of which induced a much stronger attachment to the bubble surface. Interestingly, the determinant factor for the attachment efficiency of spherical particles was not the wettability of the spherical particles but the location of the initial collision with the bubble surface. In contrast, the attachment efficiency of anisotropically-shaped particles was found to increase with the hydrophobicity caused by a larger contact area to the bubble surface. Last but not least, a simple formulation is suggested to recover the contact angle based on the jump-in behavior.

On the Convective Self-Assembly of Colloidal Particles in Nanofluid Based on in Situ Measurements of Interaction Forces.

While the currently available techniques for the self-assembly of colloidal particles show great promise owing to their simplicity and high efficiency, they are plagued by the fact that they result in colloidal crystals with defects. Here, in order to overcome this problem, we propose a strategy that uses a suspension of nanoparticles (i.e., a nanofluid) as the "solvent" for the colloidal particles. We fabricated colloidal films of microspheres using such a nanofluid suspension and performed in situ measurements of the interaction forces between the microspheres in the nanofluid. This was done in order to systematically elucidate the effects of the nanoparticle size and the thickness of the electric double layer (Debye length) on the self-assembly process. The obtained results confirm that the use of the nanofluid results in a monolayer with a higher degree of order than that in the case of films formed using pure water. Further, the optimal size of the nanoparticles is determined based on the balance between their physical size and the Debye length. We also show that the lodging of the nanoparticles between the microspheres decreases both the lubrication force and the friction force between them. Thus, in this study, we show, for the first time, that a nanofluid can be used in the self-assembly process for improving the regularity of the fabricated colloidal particle arrays, as it inhibits the aggregation of the particles and limits the lubrication and friction forces between them.

Critical energy barrier for capillary condensation in mesopores: Hysteresis and reversibility.

Capillary condensation in the regime of developing hysteresis occurs at a vapor pressure, Pcond, that is less than that of the vapor-like spinodal. This is because the energy barrier for the vapor-liquid transition from a metastable state at Pcond becomes equal to the energy fluctuation of the system; however, a detailed mechanism of the spontaneous transition has not been acquired even through extensive experimental and simulation studies. We therefore construct accurate atomistic silica mesopore models for MCM-41 and perform molecular simulations (gauge cell Monte Carlo and grand canonical Monte Carlo) for argon adsorption on the models at subcritical temperatures. A careful comparison between the simulation and experiment reveals that the energy barrier for the capillary condensation has a critical dimensionless value, Wc (*) = 0.175, which corresponds to the thermal fluctuation of the system and depends neither on the mesopore size nor on the temperature. We show that the critical energy barrier Wc (*) controls the capillary condensation pressure Pcond and also determines a boundary between the reversible condensation/evaporation regime and the developing hysteresis regime.

In situ observation of meniscus shape deformation with colloidal stripe pattern formation in convective self-assembly.

Vertical convective self-assembly is capable of fabricating stripe-patterned structures of colloidal particles with well-ordered periodicity. To unveil the mechanism of the stripe pattern formation, in the present study, we focus on the meniscus shape and conduct in situ observations of shape deformation associated with particulate line evolution. The results reveal that the meniscus is elongated downward in a concave fashion toward the substrate in accordance with solvent evaporation, while the concave deformation is accelerated by solvent flow, resulting in the rupture of the liquid film at the thinnest point of the meniscus. The meniscus rupture triggers the meniscus to slide off from the particulate line, followed by the propagation of the sliding motion of the three-phase contact line, resulting in the formation of stripe spacing.

Dependence of adsorption-induced structural transition on framework structure of porous coordination polymers.

Porous coordination polymers (PCPs) with soft frameworks show a gate phenomenon consisting of an abrupt structural transition induced by adsorption of guest molecules. To understand the dependence of the gating behavior on the host framework structure, we conduct grand canonical Monte Carlo simulations and a free-energy analysis of a simplified model of a stacked-layer PCP. The interlayer width of the rigid layers composing the simplified model can be changed by guest adsorption and by varying the initial interlayer width h0, which is controlled by the length of pillars between the layers. We introduce three types of gating behavior, one-step gating, filling and gating, and double gating, which depend on three parameters: the initial interlayer width h0; the interaction parameter ɛss, which determines the host-guest framework interaction as well as the inter-framework interaction; and the elastic modulus of the framework, which depends on the stiffness of the pillars. We show that the one-step gating and the filling and gating behaviors depend strongly on h0 rather than on ɛss, and thus a transformation from filling and gating to double gating can be achieved by reducing the stiffness of the host framework. This study should be a guideline for controlling the gating pressure of PCPs by modifying their chemical components.

Modeling order-disorder boundaries of colloidal dispersions in organic solvents using interaction force measurements.

HYPOTHESIS: The formation of soft colloidal crystals, which are nonclose-packed ordered arrays of colloidal particles suspended in a solvent, is dictated by a single physical factor that yields a fixed threshold at order-disorder boundaries for different experimental conditions such as ion concentration, solvent type, and particle size. Identifying the determinant factor and its threshold value should enable the prediction of the critical concentrations of colloidal particles to form soft colloidal crystals. EXPERIMENTS: Soft colloidal crystals were fabricated using a series of monohydric alcohols as dispersion media and reflectance spectra were measured to locate order-disorder boundaries. The interaction forces acting between particles were also measured by employing atomic force microscopy. FINDINGS: The interparticle forces at the order-disorder boundaries exhibited a universal threshold that was independent of the solvent types including alcohols and water. Therefore, the determinant factor for the formation of soft colloidal crystals was determined to be the force acting between the particles. Furthermore, a priori calculation of this critical force and consequently the critical particle concentration in colloidal systems was demonstrated by referring to the pressure at the liquid-to-solid transition in a hard sphere system (Alder transition).

Reversible pore size control of elastic microporous material by mechanical force.

Nanoporous materials, such as zeolites, activated carbons, and metal-organic frameworks (MOFs), are peculiar platforms in which a variety of guest molecules are stored, reacted, and/or separated. The size of the nanopores is essential to realize advanced functions. In this work, we demonstrate a very simple but innovative method for the control of nanopore size, that is, reversible and continuous control by mechanical force loaded to soft nanoporous materials. The elastic properties of several microporous materials, including zeolites, zeolite-templated carbon (ZTC), activated carbon, and MOFs (e.g., ZIF-8), are examined and it is found that ZTC is a material that is suitable for the aforementioned idea thanks to its extraordinary soft properties compared to the others. The original pore size of ZTC (1.2 nm) can be contracted to 0.85 nm by using a relatively weak loading force of 135 MPa, whereas the other microporous materials barely contracted. To demonstrate the change in the physical properties induced by such artificial deformation, in situ gas adsorption measurements were performed on ZTC with and without loading mechanical force, by using CO2, CH4, and H2, as adsorbates. Upon the contraction by loading 69 or 135 MPa, CO2 adsorption amount is increased, due to the deepening of the physisorption potential well inside the micropores, as proved by the increase of the heat of adsorption. Moreover, the adsorption amount is completely restored to the original one after releasing the mechanical force, indicating the fully reversible contraction/recovery of the ZTC framework against mechanical force. The experimental results are theoretically supported by a simulation using Grand Canonical Monte Carlo method. The similar adsorption enhancement is observed also on CH4, whereas H2 is found as an exception due to the weak interaction potential.

Determination of phase equilibria in confined systems by open pore cell Monte Carlo method.

We present a modification of the molecular dynamics simulation method with a unit pore cell with imaginary gas phase [M. Miyahara, T. Yoshioka, and M. Okazaki, J. Chem. Phys. 106, 8124 (1997)] designed for determination of phase equilibria in nanopores. This new method is based on a Monte Carlo technique and it combines the pore cell, opened to the imaginary gas phase (open pore cell), with a gas cell to measure the equilibrium chemical potential of the confined system. The most striking feature of our new method is that the confined system is steadily led to a thermodynamically stable state by forming concave menisci in the open pore cell. This feature of the open pore cell makes it possible to obtain the equilibrium chemical potential with only a single simulation run, unlike existing simulation methods, which need a number of additional runs. We apply the method to evaluate the equilibrium chemical potentials of confined nitrogen in carbon slit pores and silica cylindrical pores at 77 K, and show that the results are in good agreement with those obtained by two conventional thermodynamic integration methods. Moreover, we also show that the proposed method can be particularly useful for determining vapor-liquid and vapor-solid coexistence curves and the triple point of the confined system.

Simulation study for adsorption-induced structural transition in stacked-layer porous coordination polymers: equilibrium and hysteretic adsorption behaviors.

We conduct grand canonical Monte Carlo simulations and a free-energy analysis for a simplified model of a stacked-layer porous coordination polymer to understand the gate phenomenon, which is a structural transition of a host framework induced by the adsorption of guest particles. Our calculations demonstrate that stabilization of the system due to the guest adsorption causes host deformation under thermodynamic equilibrium. We also investigate spontaneous transition behaviors (gate opening and closing under metastable conditions). The structural transition should occur when the required activation energy, which is determined using the free-energy analysis, becomes equal to the system energy fluctuation. To estimate the system energy fluctuation, we construct a kinetic transition model based on the transition state theory. In this model, the system energy fluctuation can be calculated by setting the adsorption time and transition domain size of the host framework. The model demonstrates that a smaller domain size results in a gate-opening transition at lower pressure. Furthermore, we reveal that the slope of the logarithm of the equilibrium structural transition pressure versus reciprocal temperature shows transition enthalpy, and that slopes of the gate-opening and -closing transition pressures versus reciprocal temperature show activation enthalpies.

Validating the Mechanism Underlying the Slacking of the Gate-Opening Behavior in Flexible Metal-Organic Frameworks Arising from the Application of External Force.

Flexible metal-organic frameworks (MOFs) are innovative adsorbents expected to revolutionize conventional separation systems as they exhibit stepwise adsorption arising from structural transitions, commonly known as "gate opening." However, because MOFs are typically obtained in powder form, they require shaping for industrial applications. In our previous study, we reported that the stepwise uptake observed in the CO2 gate opening of ELM-11 ([Cu(BF4)2(4,4'-bipyridine)2]) became less distinct when molded with polymer binders and found that this slacking phenomenon could be caused by the polymer binder inhibiting the structural change of the ELM-11 particles. In this study, we aimed to fully validate and generalize the mechanism behind the slacking of gate adsorption from both theoretical and experimental perspectives. First, we conducted grand canonical molecular dynamics simulations for a simplified MOF model to directly calculate free energy profiles of the particle to validate the slacking theory without any assumptions. The results confirmed the fundamental assumption made in our previous study that the deformation of the flexible motifs within the MOF particles occurs sequentially, which is a key factor contributing to the slacking phenomenon. The second part of the study focused on the relationship between the volume expansion ratio of MOFs and the degree of slacking. The relationship predicted by the theory was experimentally validated by comparing ELM-11, which exhibits 30% volume expansion, to another MOF with a mutually interpenetrating jungle-gym structure, which exhibits 10% volume expansion. These findings strengthened and generalized the understanding of the mechanism underlying the slacking of gate adsorption induced upon the application of external force, which could guide the fabrication of molded MOFs while maintaining a high adsorption efficiency for various industrial applications.

Mechanism of Nucleation Pathway Selection in Binary Lennard-Jones Solution: A Combined Study of Molecular Dynamics Simulation and Free Energy Analysis.

The nucleation process, which is the initial step in particle synthesis, determines the properties of the resultant particles. Although recent studies have observed various nucleation pathways, the physical factors that determine these pathways have not been fully elucidated. Herein, we conducted molecular dynamics simulations in a binary Lennard-Jones system as a model solution and found that the nucleation pathway can be classified into four types depending on microscopic interactions. The key parameters are (1) the strength of the solute-solute interaction and (2) the difference between the strengths of the like-pair and unlike-pair interactions. The increment of the former alters the nucleation mechanism from a two-step to a one-step pathway, whereas that of the latter causes quick assembly of solutes. Moreover, we developed a thermodynamic model based on the formation of core-shell nuclei to calculate the free energy landscapes. Our model successfully described the pathway observed in the simulations and demonstrated that the two parameters, (1) and (2), define the degree of supercooling and supersaturation, respectively. Thus, our model interpreted the microscopic insights from a macroscopic point of view. Because the only inputs required for our model are the interaction parameters, our model can a priori predict the nucleation pathway.

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.

Fast Gas-Adsorption Kinetics in Supraparticle-Based MOF Packings with Hierarchical Porosity.

Metal-organic frameworks (MOFs) are microporous adsorbents for high-throughput gas separation. Such materials exhibit distinct adsorption characteristics owing to the flexibility of the crystal framework in a nanoparticle, which can be different from its bulk crystal. However, for practical applications, such particles need to be compacted into macroscopic pellets, creating mass-transport limitations. In this work, this problem is addressed by forming materials with structural hierarchy, using a supraparticle-based approach. Spherical supraparticles composed of nanosized MOF particles are fabricated by emulsion templating and they are used as the structural component forming a macroscopic material. Zeolitic imidazolate framework-8 (ZIF-8) particles are used as a model system and the gas-adsorption kinetics of the hierarchical material are compared with conventional pellets without structural hierarchy. It is demonstrated that a pellet packed with supraparticles exhibits a 30 times faster adsorption rate compared to an unstructured ZIF-8 powder pellet. These results underline the importance of controlling structural hierarchy to maximize the performance of existing materials. In the hierarchical MOFs, large macropores between the supraparticles, smaller macropores between individual ZIF-8 primary particles, and micropores inherent to the ZIF-8 framework collude to combine large surface area, defined adsorption sites, and efficient mass transport to enhance performance.

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.

Spontaneous formation of cluster array of gold particles by convective self-assembly.

Cluster arrays composed of metal nanoparticles are promising for application in sensing devices because of their interesting surface plasmon characteristics. Herein, we report the spontaneous formation of cluster arrays of gold colloids on flat substrates by vertical-deposition convective self-assembly. In this technique, under controlled temperature, a hydrophilic substrate is vertically immersed in a colloid suspension. Cluster arrays form when the particle concentration is extremely low (in the order of 10(-6)-10(-8) v/v). These arrays are arranged in a hierarchically ordered structure, where the particles form clusters that are deposited at a certain separation distance from each other, to form "dotted" lines that are in turn aligned with a constant spacing. The size of the cluster can be controlled by varying the particle concentration and temperature while an equal separation distance is maintained between the lines formed by the clusters. Our technique thus demonstrates a one-step, template-free fabrication method for cluster arrays. In addition, through the direct observation of the assembly process, the spacing between the dotted lines is found to result from the "stick-and-slip" behavior of the meniscus tip, which is entirely different from the formation processes observed for the striped patterns, which we reported previously at higher particle concentrations. The difference in the meniscus behavior possibly comes from the difference in colloidal morphology at the meniscus tip. These results demonstrate the self-regulating characteristics of the convective self-assembly process to produce colloidal patterns, whose structure depends on particle concentration and temperature.