Title: Elastic heterogeneity governs asymmetric adsorption-desorption in a soft porous crystal

Abstract: Metal--organic frameworks (MOFs), which possess a high degree of crystallinity and a large surface area with tunable inorganic nodes and organic linkers, exhibit high stimuli-responsiveness and molecular adsorption selectivity that enable various applications. The adsorption in MOFs changes the crystalline structure and elastic moduli. Thus, the coexistence of adsorbed/desorbed sites makes the host matrices elastically heterogeneous. However, the role of elastic heterogeneity in the adsorption--desorption transition has been overlooked. Here we show the asymmetric role of elastic heterogeneity in the adsorption--desorption transition. We construct a minimal model incorporating adsorption-induced lattice expansion/contraction and an increase/decrease in the elastic moduli. We discover that the transition is hindered by the entropic and energetic effects which become asymmetric in adsorption process and desorption process, leading to the strong hysteretic nature of the transition. Furthermore, the adsorbed/desorbed sites exhibit spatially heterogeneous domain formation, implying that the domain morphology and interfacial area between adsorbed/desorbed sites can be controlled by elastic heterogeneity. Our results provide a theoretical guideline for designing soft porous crystals with tunable adsorption hysteresis and the dispersion and domain morphology of adsorbates using elastic heterogeneity.