François-Xavier Coudert

Necessary and Sufficient Elastic Stability Conditions in Various Crystal Systems

October, 2014)WhiletheBornelasticstabilitycriteriaarewell-knownforcubiccrystals,thereissomeconfusionintheliteratureabout the form it should take for lower symmetry crystal classes. We present here closed form necessary andsufficientconditionsforelasticstabilityinallcrystalclasses,asaconciseandpedagogicalreferencetostabilitycriteria in non-cubic materials.

Correlated defect nanoregions in a metal–organic framework

Throughout much of condensed matter science, correlated disorder is key to material function. While structural and compositional defects are known to exist within a variety of metal–organic frameworks, the prevailing understanding is that these defects are only ever included in a random manner. Here we show—using a combination of diffuse scattering, electron microscopy, anomalous X-ray scattering, and pair distribution function measurements—that correlations between defects can in fact be introduced and controlled within a hafnium terephthalate metal–organic framework. The nanoscale defect structures that emerge are an analogue of correlated Schottky vacancies in rocksalt-structured transition metal monoxides and have implications for storage, transport, optical and mechanical responses. Our results suggest how the diffraction behaviour of some metal–organic frameworks might be reinterpreted, and establish a strategy of exploiting correlated nanoscale disorder as a targetable and desirable motif in metal–organic framework design.

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.

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 Youngs 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.

Breathing Transitions in MIL‐53(Al) Metal–Organic Framework Upon Xenon Adsorption

MOFs come alive: The combination of gas‐adsorption experiments at various temperatures with an osmotic thermodynamic model produced a generic temperature–loading phase diagram that displays unexpected re‐entrant behavior. The breathing effect in the metal–organic framework MIL‐53(Al) is predicted to be general and should be observed over a limited temperature range regardless of the guest adsorbate.

Zeolitic imidazole frameworks: structural and energetics trends compared with their zeolite analogues

We use periodic DFT calculations to compute the total energy of known zeolitic imidazole frameworks (ZIFs) together with those of hypothetical porous ZIFs. We show that the total energy of ZIFs decreases with increasing density, in a similar fashion to the alumino-silicate zeolites, but with a more complex energy landscape. The computational evaluation of the stability of hypothetical ZIFs is useful in the search for viable synthesis targets. Our results suggest that a number of hitherto undiscovered nanoporous topologies should be amenable to synthesis (CAN, ATN) and that even the most open framework types might be obtained with appropriately substituted ligands.

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.

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 Youngs 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.

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 materials fully ordered structure. Thus an overall hydrophobic MOF material can also become water unstable, a feature that has not been fully understood until now.

Computational characterization and prediction of metal–organic framework properties

In this introductory review, we give an overview of the computational chemistry methods commonly used in the field of metal-organic frameworks (MOFs), to describe or predict the structures themselves and characterize their various properties, either at the quantum chemical level or through classical molecular simulation. We discuss the methods for the prediction of crystal structures, geometrical properties and large-scale screening of hypothetical MOFs, as well as their thermal and mechanical properties. A separate section deals with the simulation of adsorption of fluids and fluid mixtures in MOFs.