Elastic heterogeneity governs anomalous scaling in a soft porous crystal

Nanoscale molecular transport plays a crucial role in regulating mass diffusion and responsiveness in condensed matter systems. In soft porous crystals, in particular, adsorption of guest molecules induces host framework deformation and changes in rigidity, underpinning their characteristic stimuli-responsive behaviour. Surface-mediated adsorption leads to inhomogeneous adsorbate distribution, which, through local framework deformation, induces spatial variations in rigidity -- elastic heterogeneity. Although this heterogeneity is expected to affect adsorption kinetics and mechanical behaviour, its role remains poorly understood. Here we show that elastic heterogeneity governs adsorption kinetics, leading to emergent phenomena including size-dependent uptake, surface creasing, and anomalous dynamic scaling that is distinct from established scaling. Stress relaxation near corners facilitates adsorption, resulting in a size-dependent deviation from diffusive kinetics. Away from corners, flexible unadsorbed regions between rigid adsorbed domains relieve stress through crease formation. The resulting lateral correlations exhibit anomalous dynamic scaling, characterized by a breakdown of scale invariance between global and local interfacial fluctuations. These findings provide a mechanistic foundation for controlling adsorption and deformation kinetics in soft porous materials via elastic heterogeneity. Our work opens a route to engineering responsive materials, where mechanical feedback is harnessed to control cooperative molecular transport and drive macroscopic shape changes under external perturbations.