Diffusion in Channels and Channel Networks

Abstract

A large variety of nanoporous materials host channel networks with pore diameters on the order of typical molecular dimensions. Molecular diffusion and reaction in such systems exhibits a number of peculiarities, which are exemplified in more detail in this chapter.

As a main feature of diffusion in channels with diameters small enough so that the individual diffusants cannot pass each other, their mean square displacement is found to increase with the square root of time rather than with the time itself, as to be required for normal diffusion. In channels of finite extension this peculiarity of “single-file” diffusion is soon masked by a second mechanism, stipulated by the fast particle exchange at the boundary, which leads to molecular displacements following the time dependence of normal diffusion. The interplay of these two processes is discussed in Sect. 2. In mutually intersecting arrays of channels, molecular diffusion in different directions may be correlated between each other. Section 3 in particular considers the question, up to which extent the “memory” of the diffusants may affect this correlation. If the different arrays have different affinities to the constituents of multicomponent systems, the rate of molecular reactions in such systems may be enhanced in comparison with systems, where all parts of the pore system are equally accessible by the involved components. The potentials and limits of reactivity enhancement by this effect of “molecular transport control” are discussed in Sect. 4. In addition to the examples of experimental reference, which are appropriately included in each of the individual sections, Sect. 5 is exclusively devoted to the question, how closely the textbook structure of nanoporous materials with channel arrays is approached by reality.