Diffusion in Porous Media

Porous media are of considerable interest in a very diverse range of activities. They comprise a wide variety of substances—plastics, ceramics, cements, clays, rocks, porous glasses, carbons, silica gels, zeolites, the recently emerging metal–organic frameworks and coordination polymers, and many more. Even biological tissues may share many features of porous media. Depending on the given nature, the pore diameters in these substances may range from the subnanometer region up to macroscopic dimensions. The efficiency of their technical use is intimately connected with their transport properties. Diffusion measurements in porous systems are therefore of direct practical relevance. Moreover, systematic diffusion studies in such systems may contribute to a better understanding of such fundamental questions as the interaction between molecules and solid surfaces,1 and the behavior of molecular systems of reduced dimensionality.2 For emphasizing the wide relevance of diffusion in general and of diffusion in porous media in particular, we may refer to the two focus issues on “Brownian Motion and Diffusion in the 21st Century” and “Physics of Magnetic Resonance on Porous Media”, published by the New Journal of Physics. Among the methods of studying molecular diffusion in porous media, NMR spectroscopy is of particular relevance. As a noninvasive method, it allows the observation of molecular transportation without interfering with the internal processes. The technique may be applied under both equilibrium and nonequilibrium conditions. Using different NMR techniques, various aspects of molecular transport may be investigated, including the elementary processes of diffusion and the rate of molecular propagation over microscopic and macroscopic distances. A review of the principles of these techniques and examples of their application is given in the section “Pieces of Information”. Probably the most powerful NMR method for studying molecular propagation is the pulsed field gradient nuclear magnetic resonance (PFG-NMR) method, and this is described in more detail in the section “Principles of PFG-NMR”. The capability of PFG-NMR to trace indications of anomalous diffusion in porous media is discussed in the section “Ordinary versus Anomalous Diffusion”. The section “Restricted Diffusion” deals with very general relationships between diffusion occurring in pore spaces and their structural properties. Finally, as an illustration of the versatility of PFG-NMR, the sections “Diffusion in Microporous Crystallites” and “Diffusion in Mesoporous Materials” summarize the information provided by this method about molecular diffusion in beds of microporous crystallites (zeolites) and mesoporous materials, respectively.