Crossover between Fickian and non-Fickian diffusion in a system with hierarchy

A hierarchical porous material was prepared by embedding microporous ZSM-5 zeolite into the mesoporous alumina matrix. The presence of the micropores with the size relevant to zeolite ZSM-5 and the mesopores of 4 nm in diameter were justified from the low-temperature N2 adsorption and desorption isotherm data. Transport of various diffusants with significantly different molecule size, e.g. methanol, isopropanol, n-hexane, benzene, cyclohexane, and cyclohexanol, through the as-prepared material was studied. The diffusants molecule sizes (d) are chosen to be smaller or larger compared to the ZSM-5 zeolite micropore size (dm). For the diffusants with d > dm, the mass transfer was found to follow the second Fick's law of diffusion. In contrast, the diffusants with d