Semi-analytical mean-field model for predicting breathing in metal-organic frameworks

A new semi-analytical mean-field model is proposed to rationalise breathing of MIL-53 type materials. The model is applied on two case studies, the guest-induced breathing of MIL-53(Cr) with CO2 and CH4, and the phase transformations for MIL-53(Al) upon xenon adsorption. Experimentally, MIL-53(Cr) breathes upon CO2 adsorption, which was not observed for CH4. This result could be ascribed to the stronger interaction of carbon dioxide with the host matrix. For MIL-53(Al) a phase transition from the large pore phase could be enforced to an intermediate phase with volumes of about 1160-1300 angstrom(3), which corresponds well to the phase observed experimentally upon xenon adsorption. Our thermodynamic model correlates nicely with the adsorption pressuremodel proposed by Coudert et al. Furthermore the model can predict breathing behaviour of other flexible materials, if the user can determine the free energy of the empty host, the interaction energy between a guest molecule and the host matrix and the pore volume accessible to the guest molecules. This will allow to generate the osmotic potential from which the equilibria can be deduced and the anticipated experimentally observed phase may be predicted.