Elucidating the particle size-dependent guest-induced structural transition of flexible metal–organic frameworks by exploring cooperative nature

Abstract

Flexible metal–organic frameworks (MOFs) exhibit a structural transition induced by adsorption of guest molecules. This guest-induced structural transition occurs at a certain gas pressure, resulting in an S-shaped adsorption isotherm. Consequently, these materials exhibit a high working capacity, making them highly competitive in energy-saving separation processes. However, the understanding of hysteresis loops between adsorption and desorption branches remains insufficient for industrial applications. Specifically, the particle size dependence of hysteresis behaviors is still actively being investigated. Generally, smaller particles of flexible MOFs show larger hysteresis loops. Herein, we constructed a simple multi-scale simulation model that couples molecular simulations for a unit cell with Ising lattice model-based simulations, in which solid–solid interactions for adjacent unit cells are considered, to address the cooperative nature within a flexible MOF particle. The solid–solid interactions strongly link unit cells in an identical state to form a domain, minimizing the heterointerface area. In transition states, the interfacial energy is independent of particle size, whereas the configurational entropy is significant for large particles, leading to a pronounced size dependence. This is applicable to real systems on the micron order, which is confirmed by the linear correlation between particle size and the free energy change of the unit cell over the hysteresis range. The correlation enables estimating particle size-dependent adsorption behavior, and consequently, tailoring the transition behaviors of flexible MOFs for target systems by controlling particle size. This study advances the understanding of hysteresis in guest-induced structural transitions and provides insights for designing adsorption-based separation processes.