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Metal-organic frameworks (MOFs), which possess a high degree of crystallinity and a large surface area with tunable inorganic nodes and organic linkers, often exhibit soft mechanics upon molecular adsorption[1]. When guest molecules are adsorbed heterogeneously, heterogeneity in the lattice structure and stiffness of host frameworks––elastic heterogeneity––emerges due to the interaction between guest molecules and host matrices. However, the role of elastic heterogeneity in soft MOFs remains elusive.
We first show the asymmetric role of elastic heterogeneity in the adsorption-desorption transition[2]. We construct a minimal model incorporating adsorption-induced lattice expansion/contraction and an increase/decrease in the elastic moduli. By using Monte Carlo simulations, we find that the transition is hindered by the entropic and energetic effects, which become asymmetric in the adsorption and desorption processes, leading to the strong hysteretic nature of the transition. Furthermore, we find that elastic heterogeneity can stabilize a superlattice of the guest molecules[3]. Our results provide a theoretical guideline for designing MOFs with tunable adsorption hysteresis and patterns of adsorbates using elastic heterogeneity.
Elastic heterogeneity also plays an essential role in non-equilibrium dynamics in MOFs. In the adsorption process, the adsorption domain growth occurs from the boundary in contact with the guest particle bath. A rough surface of the adsorption domain emerges due to elastic heterogeneity. The roughness shows a dynamic scaling behavior called Family-Vicsek scaling.

[1]S. Horike, S. Shimomura and S. Kitagawa, Nat. Chem. 1, 695 (2009).
[2] KM and K. Takae, Proc. Natl. Acad. Sci. 6, e2302561120 (2023).
[3] KM and K. Takae, Phys. Rev. Res. 6, L012029 (2024).

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