(49b) Breathing Transitions Upon Fluid Adsorption in MOFs Materials: A Thermodynamic Approach

Porous metal-organic frameworks (MOFs) are a topical class of materials that display an extremely large range of crystal structures and host-guest properties, potentially giving them a major impact in adsorption, separation, and storage of strategic gases (H2, CO2, CH4,...). A growing number of these materials show exceptional guest-responsive behaviors upon gas adsorption, due to the flexibility of their organic-inorganic frameworks. This includes examples of progressive swelling or contraction (also called breathing), pore deformation, and amorphous-to-crystal and crystal-to-crystal structural transitions. The MIL-53 materials family, a particularly eye-catching case of the last category, has attracted a lot of attention due to its large flexibility and the occurrence of a double structural transition upon adsorption of some gases (CO2, H2O, C2H6,...) but not others (H2, CH4).

The studies performed so far, both experimentally and by molecular simulation, mainly focused on structural characterization and energetics (by calorimetry, forcefield-based calculations and DFT). However, the current depiction of these guest-induced structural transitions is lacking a general thermodynamic interpretation of all the results obtained so far.

We developed a generic thermodynamic framework for the understanding of guest-induced structural transitions in flexible nanoporous materials such as MOFs, by use of the osmotic pseudoensemble. For a material that has two possible framework structures and where gas adsorption follows type I isotherms, we propose a full taxonomy of possible guest-induced structural transitions. This classification relies only on a few key parameters, such as the free energy difference between the (empty) host structures, their pore volumes, Vp(i), and the adsorption affinities for the guest, Ki. This method also allows us to calculate one of these parameters when the pressures of structural transitions are known. We demonstrate the robustness of the method on systems exhibiting such contrasting behaviors as ?breathing? and ?gate opening?. In the case of MIL-53 (Al), in particular, we use the available CO2 adsorption isotherm to calculate a free energy difference between the empty large pore and narrow pore forms of about 2.5 kJ/mol. This value is then used to successfully predict the position of the low-pressure transition, confirmed by calorimetry.This rather small value of 2.5 kJ/mol is of the order of kT at room temperature, explaining the bistability of MIL-53 (Al). Indeed, all guest-responsive hybrid materials we studied so far exhibit free energy differences between host structures in the range 2-5 kJ/mol.

This Osmotic Adsorption Solution Theory (OAST) is then extended to study mixtures adsorption in MOFs materials, in order to predict the possible adsorption selectivities in these flexible materials for strategic mixtures such as methane-carbon dioxide.