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.

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.

We provide the first molecular dynamics study of the mechanical instability that is the cause of pressure-induced amorphization of zeolitic imidazolate framework ZIF-8. By measuring the elastic constants of ZIF-8 up to the amorphization pressure, we show that the crystal-to-amorphous transition is triggered by the mechanical instability of ZIF-8 under compression, due to shear mode softening of the material. No similar softening was observed under temperature increase, explaining the absence of temperature-induced amorphization in ZIF-8. We also demonstrate the large impact of the presence of adsorbate in the pores on the mechanical stability and compressibility of the framework, increasing its shear stability. This first molecular dynamics study of ZIF mechanical properties under variations of pressure, temperature, and pore filling opens the way to a more comprehensive understanding of their mechanical stability, structural transitions, and amorphization.

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.

Theoretical studies on the experimental feasibility of hypothetical Zeolitic Imidazolate Frameworks (ZIFs) have focused so far on relative energy of various polymorphs, by energy minimization at the quantum chemical level. We present here a systematic study of stability of 18 ZIFs as a function of temperature and pressure, by molecular dynamics simulations. This approach allows us to better understand the limited stability of some experimental structures upon solvent or guest removal. We also find that many of the hypothetical ZIFs proposed in the literature are not stable at room temperature. Mechanical and thermal stability criteria thus need to be considered for the prediction of new MOF structures. Finally, we predict a variety of thermal expansion behavior for ZIFs as a function of framework topology, with some materials showing large negative volume thermal expansion.

We report a structural and thermodynamic investigation of the phase behavior of Ga(OH,F)-MIL53, a gallium-based MOF having the MIL-53 topology containing 0.7 wt% fluorine bonded to the metal. Despite some small structural differences, especially for the hydrated form, the overall physical chemistry behavior of Ga(OH,F)-MIL-53 is very similar to standard fluorine free Ga-MIL-53 material. A combination of in situ X-ray diffraction, in situ Fourier transform infrared spectroscopy, differential scanning calorimetry and heat capacity measurements allowed to establish that Ga(OH,F)-MIL53 under vacuum (i.e. in the empty material) exhibits two stable phases: a nonporous narrow-pore (np) phase favored at low temperature and a large-pore (lp) phase favored at high temperature, accompanied by a huge hysteresis effect. Structure determination of the hydrated material Ga(OH,F)-MIL-53_np_H 2 O obtained after synthesis, activation and rehydration, was also performed. Density functional theory calculations show that it is not a stable structure of Ga(OH,F)-MIL53 in absence of adsorbed water molecules. Instead, this hydrated structure is a swollen variant of the np phase, where the flexible framework has expanded to accommodate water molecules.

Understanding the adsorption of water in metal-organic frameworks (MOF), and particularly in soft porous crystals, is a crucial prerequisite before considering MOFs for industrial applications. We report here a joint experimental and theoretical study on the behavior of a gallium-based breathing MOF, Ga-MIL-53, upon water adsorption. By looking at the energetics and thermodynamics of Ga-MIL-53, we demonstrate why it behaves differently from its sibling Al-MIL-53, showing a different phase at room temperature (a non-porous phase) and the presence of a hydrated narrow-pore structure at gas saturation pressure. Moreover, we present a complete water vapor pressure vs. temperature phase diagram of Ga-MIL-53 upon water adsorption.

Metal-organic frameworks demonstrate a wide variety of behavior in their response to pressure, which can be classified in a rather limited list of categories, including anomalous elastic behavior (e.g., negative linear compressibility, NLC), transitions between crystalline phases, and amorphization. Very few of these mechanisms involve bond rearrangement. Here, we report two novel piezo-mechanical responses of metal-organic frameworks, observed under moderate pressure in two materials of the zinc alkyl gate (ZAG) family. Both materials exhibit NLC at high pressure, due to a structural transition involving a reversible proton transfer between an included water molecule and the linker's phosphonate group. In addition, the 6-carbon alkyl chain of ZAG-6 exhibits a coiling transition under pressure. These phenomena are revealed by combining high-pressure single-crystal X-ray crystallography and quantum mechanical calculations. They represent novel pressure responses for metal-organic frameworks, and pressure-induced proton transfer is a very rare phenomenon in materials in general.