Adsorption-induced Structural Transitions Research Articles

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.

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.

Adsorption on Ligand-Tethered Nanoparticles.

We use coarse-grained molecular dynamics simulations to study adsorption on ligand-tethered particles. Nanoparticles with attached flexible and stiff ligands are considered. We discuss how the excess adsorption isotherm, the thickness of the polymer corona, and its morphology depend on the number of ligands, their length, the size of the core, and the interaction parameters. We investigate the adsorption-induced structural transitions of polymer coatings. The behavior of systems involving curved and flat “brushes” is compared.

Simulation study on the critical adsorption and diffusion of polymer chains on heterogeneous surfaces with random adsorption sites.

The critical adsorption and diffusion of a linear polymer chain on a heterogeneous surface with randomly distributed adsorption sites are studied using dynamic Monte Carlo simulations. Results show that the critical fraction of the adsorption sites at which critical adsorption takes place decreases exponentially with the increasing polymer-surface attraction strength and, at the same time, decreases with the increasing intra-polymer attraction strength. For adsorbed polymers with large intra-polymer attraction strength, we also find an adsorption-induced structural transition from a three-dimensional compact globule to a two-dimensional compacted pancake with an increasing fraction of adsorption sites. Anomalous sub-diffusion is observed for the adsorbed polymer diffusion on heterogeneous surfaces, in contrast to the normal diffusion on a homogeneous surface. The polymer on heterogeneous surfaces shows larger fluctuation in the total surface attraction energy and a longer waiting time.

Nanosheet Synthesis of Metal Organic Frameworks in a Sandwich-like Reaction Field for Enhanced Gate-Opening Pressures

Elastic layer-structured metal–organic frameworks (ELMs) are a family of flexible nanoporous metal organic frameworks (MOFs) showing gate-opening gas adsorption. The gate-opening pressure shifts to a higher value by crystal downsizing. However, the MOF nanoparticles and nanorods showing the gate-opening gas adsorption grow more than 50 nm even for their shortest sides. Here, we describe the synthesis and unique gas adsorption behavior of the first example of nanosheets of ELMs (ELM-NSs). The thickness and horizontal width of the ELM-NSs obtained from a new synthetic method using the inside the bilayers in hyperswollen lyotropic lamellar (HL) phases as sandwich-like reaction fields (SRFs) are a few nanometers and several hundreds of nanometers, respectively. The previously reported rationalization of the temperature dependence of the gate-opening pressures for ELMs enables us to discuss the size effects in terms of the adsorption-induced structural transitions and the Helmholtz free energy change of the host.

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

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

Free Energy Analysis for Adsorption-Induced Structural Transition of Colloidal Zeolitic Imidazolate Framework-8 Particles

Particle size and shape of flexible metal–organic frameworks have been reported to change the gate adsorption phenomenon which is characterized by an abrupt increase in the adsorbed amount induced by structural transitions of a host framework, although a detailed mechanism has not yet been clarified. Here, we focus on zeolitic imidazolate framework-8 (ZIF-8) whose structural flexibility stems from the rotation of 2-methylimidazole linkers. We perform free energy analyses with the aid of adsorption simulations to understand the dependence of the gate adsorption phenomenon on the particle size and shape of ZIF-8. For the adsorption simulations, we construct a simulation cell referred to as the nanoparticle model, which has a ZIF-8 slab structure and gas phase regions. Our simulations demonstrate that a decrease in the slab width results in a reduction of the average adsorbed amount. This can be explained by the smaller amount adsorbed in the region close to the surface of the ZIF-8 structure, which reaches ...

Synthesis of zeolitic imidazolate framework-8 particles of controlled sizes, shapes, and gate adsorption characteristics using a central collision-type microreactor

Controlling the particle size and shape of soft metal-organic framework compounds is crucial for understanding and regulating the adsorption-induced structural transitions that lead to the unique stepwise adsorption behavior of these materials. The present study demonstrates that the intensive mixing facilitated by a microreactor enables the synthesis of monodisperse zeolitic imidazolate framework-8 (ZIF-8) particles with high reproducibility. In the flow microreactor process used in this study, the particle size is predominantly determined by the reaction conditions during the initial mixing in the microreactor. On the other hand, the particle shape depends upon the temperature during the subsequent aging process. The technique proposed in this study is additive-free and allows control of both particle size from 50nm to 2μm and particle shape from cube to chamfered cube to rhombic dodecahedron, simply by adjusting the concentration of feed solutions and reaction temperature. Furthermore, we demonstrate that both particle size and particle shape are key physical parameters determining the adsorption characteristics of ZIF-8 particles.

Adsorption deformation of microporous composites.

We study here the behavior of flexible adsorbent materials, or soft porous crystals, when used in practical applications as nanostructured composites such as core-shell particles or mixed matrix membranes. Based on simple models and the well-established laws of elasticity, we demonstrate how the presence of a binder results in an attenuation of the adsorption-induced stress and deformation. In the case where the adsorbent undergoes adsorption-induced structural transitions, such as the gate opening phenomenon occurring in some metal-organic frameworks, we show that the presence of the binder will result in shifts of the adsorption-induced transition pressures.

Two-dimensional self-assembly of amphiphilic peptides; adsorption-induced secondary structural transition on hydrophilic substrate

Adsorption of sequential amphiphilic peptides on solid substrates triggered the spontaneous construction of nanoscaled architecture. An amphiphilic peptide designed with a cationic amino acid as a hydrophilic residue turned an anionic mica substrate into a water-repellent surface, simply by adsorbing it on the substrate surface. In contrast, an amphiphilic peptide designed with an anionic amino-acid residue formed a precisely controlled fiber array comprising a β-sheet fiber monolayer at the anionic substrate/water interface. This phenomenon was based on the secondary structural transition from random-coil to β-sheet, which occurred specifically when amphiphilic peptide adsorbed on the substrate surface. Such surface-specific nonorder/order transition was implemented by exploiting the strength of adsorption between the peptide and the substrate. A strategic design exploiting weak bonding such as hydrophobic interactions is essential for constructing precisely controlled nano-architectures in two dimensions.

Adsorption-Induced Structural Transition of ZIF-8: A Combined Experimental and Simulation Study

Zeolitic imidazolate framework-8 (ZIF-8) has a “gate-opening” framework with narrow pore apertures that swing open by reorientation of 2-methylimidazolate (MeIM) linkers enforced by guest adsorption. The present study aimed to employ free energy analysis to provide insight into the mechanism of the adsorption-induced structural transition that results from the reorientation of the MeIM linkers. We combined experimental Ar adsorption at cryogenic temperatures with grand canonical Monte Carlo simulations to determine the free energy profiles as functions of the rotational angle of the MeIM linker (θIM) and bulk gas pressure. We also estimated the energy fluctuation of the system, which is crucial to discussing the structural transition from a metastable state. The results from the free energy analysis, for example, at 91 K, suggest the following conclusions: A gradual reorientation of the MeIM linkers up to θIM = 10.5° occurs with increasing gas pressure that is followed by a spontaneous structural transition to θIM = 25.5° during the adsorption process (gate opening), and then, during the desorption process, an equilibrium structural transition occurs with the opposite reorientation of the MeIM linkers from θIM = 25.5° to θIM = 10.5° (gate closing).

A thermodynamic description of the adsorption-induced structural transitions in flexible MIL-53 metal-organic framework

We briefly review the concept of temperature-loading phase diagram that we derived from an osmotic statistical ensemble analysis of the adsorption-induced structural transitions observed in the MIL-53 family of metal-organic framework nanoporous materials. We highlight the generic nature of this diagram and comment on the occurrence of breathing transitions depending on the guest fluid, the framework functionalisation and the nature of the metal centre.

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.

Comment on “Volume shrinkage of a metal–organic framework host induced by the dispersive attraction of guest gas molecules”

In a recent paper, Joo et al. report from density functional theory calculations that H2 adsorption in MOF-5 lead to a contraction of metal-organic framework's unit cell. The authors contrast that finding with the intuition that gas adsorption in a confined system (e.g., pores in a material) increases internal pressures and then leads to volumetric expansion, and describe contraction as extraordinary. We would like to point out in this comment that adsorption-induced contraction of microporous materials is actually a very generic phenomenon, which has been demonstrated experimentally in a large range of microporous materials and explained theoretically. At same time, we would like to acknowledge that authors should be credited for demonstrating this effect on MOF-5 framework and characterizing its extent (of order of 1% in volume). This is not atypical, if somewhat large, for inorganic microporous materials like zeolites, but small compared to metal-organic frameworks that show adsorption-induced structural transitions, such as breathing MIL-53 (∆V/V ~ 40%).

Fluids in nanospaces: molecular simulation studies to find out key mechanisms for engineering

We have analyzed various phenomena that occur in nanopores, focusing on elucidating their key mechanisms, to advance the effective engineering use of nanoporous materials. As ideal experimental systems, molecular simulations can effectively provide information at the molecular level that leads to mechanistic insight. In this short review, several of our recent results are presented. The first topic is the critical point depression of Lennard-Jones fluid in silica slit pores due to finite size effects, studied by our original Monte Carlo (MC) technique. We demonstrate that the first layers of adsorbed molecules in contact with the pore walls act as a “fluid wall” and impose extra finite size effects on the fluid confined in the central portion of the pore. We next present a new kernel for pore size distribution (PSD) analysis, based entirely on molecular simulation, which consists of local isotherms for nitrogen adsorption in carbon slit pores at 77 K. The kernel is obtained by combining grand canonical Monte Carlo (GCMC) method and open pore cell MC method that was developed in the previous study. We show that overall trends of the PSDs of activated carbons calculated with our new kernel and with conventional kernel from non-local density functional theory are nearly the same; however, apparent difference can be seen between them. As the third topic, we apply a free energy analysis method with the aid of GCMC simulations to investigate the gating behavior observed in a porous coordination polymer, and propose a mechanism for the adsorption-induced structural transition based on both the theory of equilibrium and kinetics. Finally, we construct an atomistic silica pore model that mimics MCM-41, which has atomic-level surface roughness, and perform molecular simulations to understand the mechanism of capillary condensation with hysteresis. We calculate the work required for the gas–liquid transition from the simulation data, and show that the adsorption branch with hysteresis for MCM-41 arise from spontaneous capillary condensation from a metastable state.

Adsorption Deformation and Structural Transitions in Metal–Organic Frameworks: From the Unit Cell to the Crystal

Much attention has recently been focused on soft porous crystals, a fascinating subclass of metal–organic frameworks that behave in a remarkable stimuli-responsive fashion, presenting structural changes of large amplitude in response to guest adsorption, mechanical pressure, or variations in temperature. In this Perspective, we summarize the recently developed thermodynamic and mechanical theoretical models for the understanding of these materials, based on the concepts of adsorption stress and osmotic thermodynamic ensemble. We show how these models provide a coherent picture of adsorption-induced deformation and structural transitions in flexible metal–organic frameworks, all the way from the length scale of the unit cell to that of the full crystal. In particular, we highlight the new perspectives opened by these models, as well as some of the important open questions in the field.

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.

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.

Free energy landscapes for the thermodynamic understanding of adsorption-induced deformations and structural transitions in porous materials

Soft porous crystals are flexible metal-organic frameworks that respond to physical stimuli such as temperature, pressure, and gas adsorption by large changes in their structure and unit cell volume. While they have attracted a lot of interest, molecular simulation methods that directly couple adsorption and large structural deformations in an efficient manner are still lacking. We propose here a new Monte Carlo simulation method based on non-Boltzmann sampling in (guest loading, volume) space using the Wang-Landau algorithm, and show that it can be used to fully characterize the adsorption properties and the material's response to adsorption at thermodynamic equilibrium. We showcase this new method on a simple model of the MIL-53 family of breathing materials, demonstrating its potential and contrasting it with the pitfalls of direct, Boltzmann simulations. We furthermore propose an explanation for the hysteretic nature of adsorption in terms of free energy barriers between the two metastable host phases.

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.