Single-file diffusion observation time

Another deviation from the pattern of ordinary diffusion must be expected if the reactant and product molecules are subjected to single-file conditions, i.e. if (i) the zeolite pore system consists of an array of parallel channels and if (ii) the molecules are too big to pass each other. In this case, the molecular mean-square displacement z t)) is found to be proportional to the square root of the observation time, rather than to the observation time itself. First PFG NMR studies of such systems are in agreement with this prediction [8]. By introducing a mobility factor F, in analogy to the Einstein relation for ordinary diffusion. 

Figure 15 Observation times / necessary for following various single-file mean diffusion paths - plotted against the site occupancy 0, as calculated on the basis of Eqs. (40) and (13) with D = 10 " m s and = 0.5 nm. The shaded area represents the region of maximum observation time accessible by PFG NMR. (From Ref. 162.)...

The single-file expressions Eq. 1 and Eq. 6 are only valid for sufficiently large observation times. In the limit of short observation times, i.e. in a time regime where the individual molecules have not yet become aware of their neighbors, molecular displacement may be described by a diffusion-like motion with a diffusivity... 

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