Single-file diffusion Subject

It should be noted that in the literature the term single-file diffusion has sometimes been used to indicate only the mutual steric hindrance of the molecules in zeolite channels and not the additional constraint of an absolute exclusion of their mutual passage. Such terminology is clearly misleading since in this case molecular propagation would also be subjected to Pick s laws. 

Water inside a carbon nanotube (CNT) shows another set of unusual features which have been the subjects ofgreat interest in recent years and are currently being studied extensively by experiments and simulations. A remarkable aspect unearthed is the ability of a CNT to act as water transporter and filter. The properties of water inside a CNT depend on the diameter d of the CNT, which is analogous to the parameter Wq of reverse micelles discussed in the preceding chapter. However, water within a single-wall CNT shows unusual features, such as single-file diffusion, the theory of which was developed in the past but a proper model system was lacking. The orientational motion of individual water molecules exhibits slow dynamics, quite different from those in the bulk. 

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. 

Our understanding of diffusion and reaction in single-file systems is impaired by the lack of a comprehensive analytical theory. The traditional way of analytically treating the evolution of particle distributions by differential equations is prevented by the correlation of the movement of distant particles. One may respond to this restriction by considering joint probabilities covering the occupancy and further suitable quantities with respect to each individual site. These joint probabilities may be shown to be subject to master equations. 

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