Theoretical Model and Numerical Simulation of Adsorption and Deformation in Flexible Metal-Organic Frameworks

Metal-organic frameworks (MOFs) have recently attracted considerable attention as new nanoporous materials with applications to separation of fluid mixtures, catalysis, gas capture and storage, and drug delivery. A subclass of MOFs, the MIL-53 (with Al or Cr) family, exhibits a complex structural phase transition, often referred to as the breathing transition, which occurs when gas molecules are adsorbed in its pore space. In this phenomenon, the material morphology oscillates between two distinct phases, usually referred to as the narrow-pore (np) and large-pore (lp) phases. We describe a statistical mechanical model based on the energetics of the system that couples the adsorbates with the host and the ensuing structural deformation of the materials. The Hamiltonian of the system consists of the elastic energy of the MOF, the fluid phase energy, and the interaction energy between the gas and MOFs. Minimizing the total energy with respect to both the gas density and the displacement field in the material yields the governing equations for both. The model is used to study the adsorption of CO2 and CH4 in MIL-53(Al). The results demonstrate that all reported experimental features of the phenomenon are produced by the model. In particular, consistent with experimental data, the model predicts that the material experiences contraction in the np phase, whereas it undergoes swelling in the lp phase, and that the two phases coexist in the transition zone. The model is, however, completely general and is applicable to any type of guest-responsive material that undergoes deformation as a result of its interaction with the guest molecules.