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.

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.

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.

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.

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).

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.

Stress-Based Model for the Breathing of Metal-Organic Frameworks

Gas adsorption in pores of flexible metal-organic frameworks (MOF) induces elastic deformation and structural transitions associated with stepwise expansion and contraction of the material, known as breathing transitions between large pore (lp) and narrow pore (np) phases. We present here a simple yet instructive model for the physical mechanism of this enigmatic phenomenon considering the adsorption-induced stress exerted on the material as a stimulus that triggers breathing transitions. The proposed model implies that the structural transitions in MOFs occur when the stress reaches a certain critical threshold. We showcase this model by drawing on the example of Xe adsorption in MIL-53 (Al) at 220 K, which exhibits two consecutive hysteretic breathing transitions between lp and np phases. We also propose an explanation for the experimentally observed coexistence of np and lp phases in MIL-53 materials.