A theory was developed for self-diffusion in finite single-file Langmuir-type zeolites, and was checked by means of open-system kinetic Monte Carlo simulations. The theory was based upon a 2-stage Fickian diffusion mechanism in which a vacancy had to traverse the entire file length in order to produce a particle displacement of 1 lattice spacing. For times that were shorter than the vacancy diffusion time, the particle transport proceeded via a non-Fickian single-file diffusion mode, with mean-square displacements that increased with the square root of time. For times that were longer than the vacancy diffusion time, it was found that self-diffusion in single-file systems was completely described by Fick's laws. The fraction of time spent in the single-file diffusion mode scaled inversely with the file length for long files; thus suggesting that Fickian self-diffusion dominated transport in longer single-file zeolites. Due to correlations among the particle movements, the single-file self-diffusivity was sensitive to sorption limitations for short files, and scaled inversely with the file length for long files.

Self-Diffusion in Single-File Zeolite Membranes was Fickian at Long Times. P.H.Nelson, S.M.Auerbach: Journal of Chemical Physics, 1999, 110[18], 9235-43