Cooperative Adsorption by Porous Frameworks: Diffraction Experiment and Phenomenological Theory

Materials science of metal open frameworks is a state-of-the-art field for numerous applications, such as gas storage, sensors, and medicine. Two nanoporous frameworks, γ-Mg(BH₄ )₂ and MIL-91(Ti), with different levels of structural flexibility, were examined with in situ X-ray diffraction guest adsorption-desorption experiments. Both frameworks exhibit a cooperative guest adsorption correlated with a lattice deformation. This cooperativity originates from the long-range interactions between guest molecules, mediated by elastic response of the host porous structure. The observed experimental scenarios are rationalized with a mean field Gorsky-Bragg-Williams (GBW) approach for the lattice-gas Ising model. The adjusted GBW model, in combination with in situ synchrotron powder diffraction, demonstrates an efficient experimental and phenomenological approach to characterize thermodynamics of the adsorption in MOFs not only for the total uptake but also for every specific guest site.