(369c) Knudsen Diffusion in One-Dimensional Zeolite Channels

Diffusion of small molecules in zeolite channels proceeds by navigation around transport structures in four levels: windows, channels, cavities, and networks. Knudsen diffusion is encountered when the channel diameters are much larger than molecular diameters, and the only obstacles are molecule-wall collisions; its analysis depends on the statistics of molecular rays between adsorption sites on walls.  The distribution of ray length varies over an enormous range, and the length of an occasional outlier ray has no upper bound; this distribution is not Gaussian, and has a very high kurtosis.  The diffusivities from many Monte Carlo simulations follow a log-normal distribution, where many conventional concepts and methods of normal distributions do not apply.   

            The principal types of one-dimensional channels are: straight channels, zig-zag or sinusoidal channels, and connected cavities.  Knudsen diffusivity is very sensitive to the geometry of the channels. The zig-zag channels and the connected cavities can have diffusivities that are much lower than the straight channels, due to two effects of: lower vista which reduces the lengths of the rays and outliers, and negative correlation which increases the probability that consecutive steps are in opposite directions.