  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.
