A theory was developed for self-diffusion in single-file Langmuir zeolites of finite extent, and was confirmed by performing open-system kinetic Monte Carlo simulations. The theory was based upon a two-stage Fickian diffusion mechanism in which a vacancy had to traverse the entire file length in order to produce a particle displacement of one lattice spacing. For times shorter than the vacancy diffusion time, particle transport proceeded via non-Fickian single-file diffusion, with the mean-square displacement increasing with the square-root of time. For times longer than the vacancy diffusion time, it was found that self-diffusion in single-file systems was completely described by Fick's laws. It was noted that the fraction of time in the single-file diffusion mode scaled inversely with file length for long files; 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 file length for long files.

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