Résumé
Low frequency lattice vibrations (phonons) can be used as indicators of a variety of structural transformations. In particular, conformational changes in flexible metal-organic frameworks (MOFs) can be successfully explained by analyzing materials phonon spectrum in frequency range below 200 cm-1 [1,2]. It has been shown that such lattice vibrations are responsible for pressure- and adsorption-induced gate-opening in zeolitic imidazolate frameworks (ZIFs), and pore breathing in materials from MIL-53 family. In this work we present a phonon-based methodology to analyze MOFs deformations that can be detected in adsorption experiments but cannot be explained at the microscopic level without theoretical support based on numerical simulations.As a case study we have chosen to analyze adsorption-induced transformations in ZIF-8. The step-like adsorption isotherm observed in this material was interpreted in the literature as a signature of gate-opening (enlargement of the pore free volume) induced by the increasing number of guest molecules entering the pore. To analyze this phenomenon at the microscopic level, we first calculated and visualized normal modes of the lattice vibrations. For that, density functional theory (DFT) with PBE functional and empirical dispersion correction D3(BJ) was used. Only the modes which fulfill two criteria: (i) their frequency is below 200 cm-1, and (ii) the related lattice deformation leads to increase of the pore free volume, have been further analyzed. These deformed structures, (including one related to gate-opening, pore breathing and one which combines both deformations) were selected to serve as the adsorbent model. Grand Canonical Monte Carlo (GCMC) simulations have been performed to calculate the isotherms of adsorption in selected structures. Surprisingly, in the structure related to gate-opening, the mode, located at ~40 cm-1, and considered in the literature as the one responsible for step-like form of the isotherm did not provided an uptake larger than the undistorted structure. On the other hand, in the structure resulting from simultaneous pore breathing and gate-opening deformation the adsorption is significantly increased. Therefore, we consider that this deformation, induced by pore breathing and gate-opening phonons explains better the experimental observations..1. F. Formalik, et al., Microporous and Mesoporous Materials, (2018),2. M. R. Ryder, et al., Physical Review Letters, 113 (2014), 215502-21550