Molecular Simulation of the Impact of Defects on Electrolyte Intrusion in Zeolites.

We have investigated through molecular simulation the intrusion of electrolytes in two representative pure-silica zeolites, silicalite-1 and chabazite, in which point defects were introduced in varying amounts. We distinguish between two types of defects, considering either "weak" or "strong" silanol nest defects, resulting in different hydration behaviors. In the presence of weak defects, the hydration process occurs through a homogeneous nucleation process, while with strong defects, we observe an initial adsorption followed by a filling of the nanoporous volume at a higher pressure. However, we show that electrolytes do not penetrate the zeolites, and these defects appear to have only marginal influence on the thermodynamics of electrolyte intrusion. While replacing pure water by the electrolyte solution shifts the intrusion pressure toward higher values because of the drop of water saturation vapor pressure, an increase in hydrophilicity of the framework due to point defects has the opposite effect, showing that controlling the amount of defects in zeolites is crucial for storage energy applications.

Forced intrusion of water and aqueous solutions in microporous materials: from fundamental thermodynamics to energy storage devices.

We review the high pressure forced intrusion studies of water in hydrophobic microporous materials such as zeolites and MOFs, a field of research that has emerged some 15 years ago and is now very active. Many of these studies are aimed at investigating the possibility of using these systems as energy storage devices. A series of all-silica zeolites (zeosil) frameworks were found suitable for reversible energy storage because of their stability with respect to hydrolysis after several water intrusion-extrusion cycles. Several microporous hydrophobic zeolite imidazolate frameworks (ZIFs) also happen to be quite stable and resistant towards hydrolysis and thus seem very promising for energy storage applications. Replacing pure water by electrolyte aqueous solutions enables to increase the stored energy by a factor close to 3, on account of the high pressure shift of the intrusion transition. In addition to the fact that aqueous solutions and microporous silica materials are environmental friendly, these systems are thus becoming increasingly interesting for the design of new energy storage devices. This review also addresses the theoretical approaches and molecular simulations performed in order to better understand the experimental behavior of nano-confined water. Molecular simulation studies showed that water condensation takes place through a genuine first-order phase transition, provided that the interconnected pores structure is 3-dimensional and sufficiently open. In an extreme confinement situations such as in ferrierite zeosil, condensation seem to take place through a continuous supercritical crossing from a diluted to a dense fluid, on account of the fact that the first-order transition line is shifted to higher pressure, and the confined water critical point is correlatively shifted to lower temperature. These molecular simulation studies suggest that the most important features of the intrusion/extrusion process can be understood in terms of equilibrium thermodynamics considerations.

What makes zeolitic imidazolate frameworks hydrophobic or hydrophilic? The impact of geometry and functionalization on water adsorption.

We demonstrate, by means of Grand Canonical Monte Carlo simulation on different members of the ZIF family, how topology, geometry, and linker functionalization drastically affect the water adsorption properties of these materials, tweaking the ZIF materials from hydrophobic to hydrophilic. We show that adequate functionalization of the linkers allows one to tune the host-guest interactions, even featuring dual amphiphilic materials whose pore space features both hydrophobic and hydrophilic regions. Starting from an initially hydrophobic material (ZIF-8), various degrees of hydrophilicity could be obtained, with a gradual evolution from a type V adsorption isotherm in the liquid phase to a type I isotherm in the gas phase. This behavior is similar to what was described earlier in families of hydrophobic all-silica zeolites, with hydrophilic "defects" of various strength, such as silanol nests or the presence of extra-framework cations.

Metal-organic frameworks with wine-rack motif: what determines their flexibility and elastic properties?

We present here a framework for the analysis of the full tensors of second-order elastic constants of metal-organic frameworks, which can be obtained by ab initio calculations. We describe the various mechanical properties one can derive from such tensors: directional Young's modulus, shear modulus, Poisson ratio, and linear compressibility. We then apply this methodology to four different metal-organic frameworks displaying a wine-rack structure: MIL-53(Al), MIL-47, MIL-122(In), and MIL-140A. From these results, we shed some light into the link between mechanical properties, geometric shape, and compliance of the framework of these porous solids. We conclude by proposing a simple criterion to assess the framework compliance, based on the lowest eigenvalue of its second-order elastic tensor.

Adsorption induced transitions in soft porous crystals: an osmotic potential approach to multistability and intermediate structures.

Soft porous crystals are flexible metal-organic frameworks that respond to physical stimuli (temperature, pressure, and gas adsorption) by large changes in their structure and unit cell volume. We propose here a thermodynamic treatment, based on the osmotic ensemble, of the interplay between guest adsorption and host deformation, where the bare host material can undergo elastic deformation, as well as structural transitions between metastable phases in the case of a multistable material. We show that in addition to structural transitions between metastable phases of bistable or multistable host frameworks, a new guest-stabilized host phase can be created when the size of the adsorbate is larger than the empty material's pore size. We then confront the findings of our approach with experimental data for systems exhibiting phenomena such as gate opening and breathing.

Alchemical Osmostat for Monte Carlo Simulation: Sampling Aqueous Electrolyte Solution in Open Systems.

Molecular simulations involving electrolytes are usually performed at a fixed amount of salt ions in the simulation box, reproducing macroscopic concentration. Although this statement is valid in the bulk, the concentration of an electrolyte confined in nanoporous materials such as MOFs or zeolites is greatly affected and remains a priori unknown. The nanoporous material in equilibrium with the bulk electrolyte exchange water and ions at a given chemical potential Δµ in the semi-grand-canonical ensemble, that must be calibrated in order to determine the concentration in the nanoporous material. In this work, we propose an algorithm based on nonequilibrium candidate Monte Carlo (NCMC) moves to ultimately perform MC simulations in contact with a saline reservoir. First, we adapt the Widom insertion technique to calibrate the chemical potential by alchemically transmuting water molecules into ions by using NCMC moves. The chemical potential defines a Monte Carlo osmostat in the semi-grand-constant volume and temperature ensemble (Δµ, N, V, T) to be added in a Monte Carlo simulation where the number of ions fluctuates. In order to validate the method, we adapted the NCMC move to determine the free energy of water solvation and subsequently explore thermodynamics of electrolyte solvation at infinite dilution in water. Finally, we implemented the osmostat in MC simulations initialized with bulk water that are driven toward electrolyte solutions of similar concentration as the saline reservoir. Our results demonstrate that alchemical osmostat for MC simulation is a promising tool for use to sample electrolyte insertion in nanoporous materials.

Anisotropic elastic properties of flexible metal-organic frameworks: how soft are soft porous crystals?

We performed ab initio calculations of the elastic constants of five flexible metal-organic frameworks (MOFs): MIL-53(Al), MIL-53(Ga), MIL-47, and the square and lozenge structures of DMOF-1. Tensorial analysis of the elastic constants reveals a highly anisotropic elastic behavior, some deformation directions exhibiting very low Young's modulus and shear modulus. This anisotropy can reach a 400:1 ratio between the most rigid and weakest directions, in stark contrast to the case of nonflexible MOFs such as MOF-5 and ZIF-8. In addition, we show that flexible MOFs can display extremely large negative linear compressibility. These results uncover the microscopic roots of stimuli-induced structural transitions in flexible MOFs, by linking the local elastic behavior of the material and its multistability.

How can a hydrophobic MOF be water-unstable? Insight into the hydration mechanism of IRMOFs.

We report an ab initio molecular dynamics study of the hydration process in a model IRMOF material. At low water content (one molecule per unit cell), water physisorption is observed on the zinc cation but the free⇄bound equilibrium strongly favors the free state. This is consistent with the hydrophobic nature of the host matrix and its type-V isotherm observed in a classical Monte Carlo simulation. At higher loading, a water cluster can be formed at the Zn(4)O site and this is shown to stabilize the water-bound state. This structure rapidly transforms into a linker-displaced state, where water has fully displaced one arm of a linker and which corresponds to the loss of the material's fully ordered structure. Thus an overall hydrophobic MOF material can also become water unstable, a feature that has not been fully understood until now.

Predicting mixture coadsorption in soft porous crystals: experimental and theoretical Study of CO2/CH4 in MIL-53(Al).

We present a synergistic experimental and theoretical study of CO(2)/CH(4) mixture coadsorption in breathing metal-organic framework MIL-53(Al). Mixture adsorption experiments were performed and their results were analyzed by comparing them to predictions made from pure-component adsorption data using the Osmotic Framework Adsorption Solution Theory (OFAST). This analytical model, fully validated for the first time, was then used to predict coadsorption properties as a function of temperature, pressure, and mixture composition. The phase diagrams obtained show a surprising non-monotonic behavior.

Experiment and theory of low-pressure nitrogen adsorption in organic layers supported or grafted on inorganic adsorbents: toward a tool to characterize surfaces of hybrid organic/inorganic systems.

We report experimental nitrogen adsorption isotherms of organics-coated silicas, which exhibit a low-pressure desorption branch that does not meet the adsorption branch upon emptying of the pores. To address the physical origin of such a hysteresis loop, we propose an equilibrium thermodynamic model that enables one to explain this phenomenon. The present model assumes that, upon adsorption, a small amount of nitrogen molecules penetrate within the organic layer and reach adsorption sites that are located on the inorganic surface, between the grafted or adsorbed organic molecules. The number of accessible adsorption sites thus varies with the increasing gas pressure, and then we assume that it stays constant upon desorption. Comparison with experimental data shows that our model captures the features of nitrogen adsorption on such hybrid organic/inorganic materials. In particular, in addition to predicting the shape of the adsorption isotherm, the model is able to estimate, with a reasonable number of adjustable parameters, the height of the low-pressure hysteresis loop and to assess in a qualitative fashion the local density of the organic chains at the surface of the material.

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.

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.

Structural transitions in MIL-53 (Cr): view from outside and inside.

We present a unified thermodynamic description of the breathing transitions between large pore (lp) and narrow pore (np) phases of MIL-53 (Cr) observed during the adsorption of guest molecules and the mechanical compression in the process of mercury porosimetry. By revisiting recent experimental data on mercury intrusion and in situ XRD during CO(2) adsorption, we demonstrate that the magnitude of the adsorption stress exerted inside the pores by guest molecules, which is required for inducing the breathing transition, corresponds to the magnitude of the external pressure applied from the outside that causes the respective transformation between lp and np phases. We show that, when a stimulus is applied to breathing MOFs of MIL-53 type, these materials exhibit small reversible elastic deformations of lp and np phases of the order of 2-4%, while the breathing transition is associated with irreversible plastic deformation that leads to up to ∼40% change of the sample volume and a pronounced hysteresis. These results shed light on the specifics of the structural transformations in MIL-53 (Cr) and other soft porous crystals (SPC).

Water adsorption in hydrophobic MOF channels.

We report an investigation of water adsorption in the hydrophobic metal-organic framework Al(OH)(1,4-naphthalenedicarboxylate) by means of molecular simulation. We show how simple molecular models allow us to reproduce the experimental isotherm, and how grand canonical Monte Carlo simulations can help elucidate the question of the thermodynamic nature of the adsorption transition, which turns out to be a continuous transition, though the experimental isotherm is quite steep. Moreover, we study the influence of functionalisation of the MOF organic linkers on the hydrophobicity of the material and the nature of the adsorption transition, and explain it in terms of the liquid-vapour phase diagram of water in this family of materials.

Double structural transition in hybrid material MIL-53 upon hydrocarbon adsorption: the thermodynamics behind the scenes.

We rationalize the thermodynamics behind the guest-induced structural transitions of hybrid material MIL-53, showing that the existence of a double transition depends on the relative guest affinities for the two phases, rather than absolute adsorption enthalpies. Based on a simple model, we interpret recent experimental data on alkane adsorption and predict transition pressures.

Prediction of breathing and gate-opening transitions upon binary mixture adsorption in metal-organic frameworks.

Among the numerous applications of metal-organic frameworks (MOFs), a topical class of nanoporous materials, adsorptive separation is gaining considerable attention. Some of the most exciting candidates for gas separation processes exhibit structural transitions, such as breathing and gate opening. While predictive analytical methods are crucial in separation science and have been widely used for rigid nanoporous solids, a lack exists for materials that exhibit flexibility. We propose here a general method predicting, for the first time, the evolution of structural transitions and selectivity upon adsorption of gas mixtures in flexible nanoporous solids.

Thermodynamics of guest-induced structural transitions in hybrid organic-inorganic frameworks.

We provide a general thermodynamic framework for the understanding of guest-induced structural transitions in hybrid organic-inorganic materials. The method is based on the analysis of experimental adsorption isotherms. It allows the determination of the free energy differences between host structures involved in guest-induced transitions, especially hard to obtain experimentally. We discuss the general case of adsorption in flexible materials and show how a few key quantities, such as pore volumes and adsorption affinities, entirely determine the phenomenology of adsorption, including the occurrence of structural transitions. On the basis of adsorption thermodynamics, we then propose a taxonomy of guest-induced structural phase transitions and the corresponding isotherms. In particular, we derive generic conditions for observing a double structural transition upon adsorption, often resulting in a two-step isotherm. Finally, we show the wide applicability and the robustness of the model through three case studies of topical hybrid organic-inorganic frameworks: the hysteretic hydrogen adsorption in Co(1,4-benzenedipyrazolate), the guest-dependent gate-opening in Cu(4,4'-bipyridine)(2,5-dihydroxybenzoate)2 and the CO2-induced "breathing" of hybrid material MIL-53.

Structural changes in nanoporous solids due to fluid adsorption: thermodynamic analysis and Monte Carlo simulations.

A thermodynamic analysis based on the osmotic ensemble scheme enables the prediction of structural changes occurring in silicalite-1 zeolite upon halocarbon molecule adsorption.

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.