Typically, single-file behavior is observed in one-dimensional pore structures with channel diameters comparable with those of diffusing molecules. Under these circumstances, the motion of diffusing molecules is highly excluded, since molecules cannot pass one another in the narrow channels. Consequently, displacements of a given molecule will necessitate shift of many other molecules in the same direction giving rise to the mean-square displacement, which rather than being proportional to observed time, is proportional to its square root, in the long time domain. So far, only a few experimental studies have been reported to validate this important phenomenon and are mostly limited to microscopic diffusion measurements techniques such as, PFG-NMR and QENS.
The present work is a systematic study of toluene diffusion in one-dimensional (1-D) ZSM-12 and three-dimensional (3-D) β-zeolite by means of tracer Zero length Column (TZLC) technique. It is shown that, in contrast to the well established theory for normal Fickian diffusion mechanism, which is linear in the longtime limit, single-file systems exhibit non-linear behavior, since effective self diffusivity decreases with time. Experimental tracer exchange desorption profiles obtained for toluene/ZMS-12 qualitatively reveal this characteristic feature of the single-file diffusion, while the observed trend for toluene/β-zeolite is consistent with normal diffusion.
Also, unlike with toluene/β-zeolite, a stronger dependence of diffusivity on pore loading was observed with toluene/ZSM-12, as would be expected from increased steric restriction with loading, in systems undergoing single-file diffusion. Similarly, the pronounced deviation of tracer exchange data from normal diffusion model at lower temperatures for toluene/ZSM-12 further substantiates our conclusion that this system follows single-file mechanism. These results provide significant evidence that the relatively simple and rapid tracer ZLC technique could be employed to validate single-file diffusion.