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).

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.

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.

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.

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.

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.

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.

High-Performance Carbon Molecular Sieves for the Separation of Propylene and Propane.

High-performance carbon molecular sieves (CMSs) for the separation of propylene (C3H6) and propane (C3H8) were synthesized in this study by chemical vapor deposition (CVD) of benzene on the pore entrances of activated carbon. The C3H6 and C3H8 separation characteristics of the CMSs were controlled by altering the amount of carbon deposited during CVD, and the resulting characteristic curve featuring the kinetic selectivity of C3H6 over C3H8 as a function of the adsorption rate constant of C3H6 is considered to be the upper bound of the C3H6-C3H8 separation factor for current CMSs because of the presence of previously reported CMS data under this curve. Additionally, CMS models were constructed using grand canonical molecular dynamics (GCMD) simulations mimicking the process of CVD, which revealed that the kinetic selectivity of C3H6 over C3H8 strongly depended on the size of the pore entrances at the level of 0.01 nm, and that strict control of the pore-entrance size was crucial for obtaining high-performance CMSs for C3H6-C3H8 separation. This was essentially achieved by controlling the duration of CVD, which led to the experimental realization of CMSs with a C3H6 selectivity over C3H8 of >2000 and a high uptake rate of C3H6. A design guideline for the development of high-performance CMSs for C3H6-C3H8 separation was proposed based on theoretical calculations performed using idealized carbon structures, which extracted the characteristics of the CMS models obtained from the GCMD simulations.

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.

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.

High-throughput gas separation by flexible metal-organic frameworks with fast gating and thermal management capabilities.

Establishing new energy-saving systems for gas separation using porous materials is indispensable for ensuring a sustainable future. Herein, we show that ELM-11 ([Cu(BF4)2(4,4'-bipyridine)2]n), a member of flexible metal-organic frameworks (MOFs), exhibits rapid responsiveness to a gas feed and an 'intrinsic thermal management' capability originating from a structural deformation upon gas adsorption (gate-opening). These two characteristics are suitable for developing a pressure vacuum swing adsorption (PVSA) system with rapid operations. A combined experimental and theoretical study reveals that ELM-11 enables the high-throughput separation of CO2 from a CO2/CH4 gas mixture through adiabatic operations, which are extreme conditions in rapid pressure vacuum swing adsorption. We also propose an operational solution to the 'slipping-off' problem, which is that the flexible MOFs cannot adsorb target molecules when the partial pressure of the target gas decreases below the gate-opening pressure. Furthermore, the superiority of our proposed system over conventional systems is demonstrated.

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.

Low-temperature hydrogen-graphite system revisited: Experimental study and Monte Carlo simulation.

Hydrogen adsorption by microporous carbon materials attracts much attention for the past few decades, which has been stimulated by growing interest in hydrogen storage. Numerous studies of this topic based on molecular simulation technique have been reported. However, in many cases, the reliability of the results obtained with numerical methods is insufficient, which is a consequence of poor reference data used for fitting parameters of the fluid-fluid and fluid-solid potentials. This study is devoted to a detailed experimental investigation of the hydrogen-graphite system and its modeling with a kinetic Monte Carlo method at temperatures from 20 to 77 K and the bulk pressure from 0.1 Pa to 100 kPa. We found that the best fit of the bulk hydrogen equation of state corresponds to the 10-6 Lennard-Jones potential with the temperature dependent parameters to account for the quantum effects. The experimental hydrogen adsorption isotherms on the graphite surface were fitted with a high accuracy, which constitutes a firm basis of subsequent simulation of hydrogen adsorption in various nanoporous carbons and their pore size distribution analysis using a kernel generated with the developed approach.

Force-driven reversible liquid-gas phase transition mediated by elastic nanosponges.

Nano-confined spaces in nanoporous materials enable anomalous physicochemical phenomena. While most nanoporous materials including metal-organic frameworks are mechanically hard, graphene-based nanoporous materials possess significant elasticity and behave as nanosponges that enable the force-driven liquid-gas phase transition of guest molecules. In this work, we demonstrate force-driven liquid-gas phase transition mediated by nanosponges, which may be suitable in high-efficiency heat management. Compression and free-expansion of the nanosponge afford cooling upon evaporation and heating upon condensation, respectively, which are opposite to the force-driven solid-solid phase transition in shape-memory metals. The present mechanism can be applied to green refrigerants such as H2O and alcohols, and the available latent heat is at least as high as 192 kJ kg-1. Cooling systems using such nanosponges can potentially achieve high coefficients of performance by decreasing the Young's modulus of the nanosponge.

Central metal dependent modulation of induced-fit gas uptake in molecular porphyrin solids.

The induced-fit accommodation of a variety of gaseous molecules including non-polar molecules has been demonstrated in porphyrin-based supramolecular architectures for the first time. Moreover, the gas uptake behaviour can be modulated by changing the central cation of porphyrin.

Intrinsic Thermal Management Capabilities of Flexible Metal-Organic Frameworks for Carbon Dioxide Separation and Capture.

We show that flexible metal-organic frameworks (MOFs) exhibiting "gate openings/closings" for CO2 can intrinsically suppress the exothermic heat released by adsorption and the endothermic heat gained by desorption, both of which reduce the working capacity of CO2 in a separation process under near-adiabatic conditions. We use the elastic layer-structured metal-organic framework-11 (ELM-11) [Cu(4,4'-bipyridine)2(BF4)2], which exhibits a two-step gate-adsorption isotherm, as a model system for flexible MOFs, and perform free energy analyses with the aid of grand canonical Monte Carlo simulations for ELM-11 structures that were determined by the Rietveld method using in situ synchrotron X-ray powder diffraction data. We demonstrate that the thermal management capabilities of ELM-11 showing the two-step gating for CO2 at lower and higher pressures are nearly identical and quite effective (41% and 44% at 298 K, respectively). Moreover, we show that ELM-11 has an extremely high CO2 selectivity for both CO2/N2 and CO2/CH4 mixtures at 298 K that, in addition to the intrinsic thermal management capability, is a crucial factor for application to carbon capture and storage (CCS). The multigate closing pressures of ELM-11 are not necessarily matched to the operating pressures used in CCS; however, our findings, and perspectives based on free energy analyses regarding modification of the host framework structure to tune the gating pressure, suggest that flexible MOFs exhibiting multigate openings/closings are promising materials for further development into systems with intrinsic thermal management mechanisms for CCS applications.

Mechanism of Kinetically Controlled Capillary Condensation in Nanopores: A Combined Experimental and Monte Carlo Approach.

We find the rule of capillary condensation from the metastable state in nanoscale pores based on the transition state theory. The conventional thermodynamic theories cannot achieve it because the metastable capillary condensation inherently includes an activated process. We thus compute argon adsorption isotherms on cylindrical pore models and atomistic silica pore models mimicking the MCM-41 materials by the grand canonical Monte Carlo and the gauge cell Monte Carlo methods and evaluate the rate constant for the capillary condensation by the transition state theory. The results reveal that the rate drastically increases with a small increase in the chemical potential of the system, and the metastable capillary condensation occurs for any mesopores when the rate constant reaches a universal critical value. Furthermore, a careful comparison between experimental adsorption isotherms and the simulated ones on the atomistic silica pore models reveals that the rate constant of the real system also has a universal value. With this finding, we can successfully estimate the experimental capillary condensation pressure over a wide range of temperatures and pore sizes by simply applying the critical rate constant.