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Diffusion processes of particles or energy exhibit a characteristic scaling behavior with space and time. In this contribution, the background of this scaling behavior will be shortly described and its consequences in physics, chemistry, biology and various areas of technology shall be explored. Furthermore, some demonstration experiments for different aspects of diffusion and its scaling behavior will be discussed in the course of the article.

Real systems always contain some degree of polydispersity and yet the effects of this real and very important problem have not been studied in great detail in NMR diffusion experiments. The effects of polydispersity become even less clear when we are outside the short gradient pulse (SGP) limit (which we generally are). Here we investigate the effects of polydispersity, in the form of a Gaussian distribution of characteristic distances, on the coherence features of PGSE NMR experiments of a model system. Characteristic pore sizes were determined from the coherence features and compared to characteristic distances determined from Fourier transforms of the second derivative.

The time taken to complete an NMR diffusion experiment is typically ~10 minutes. For systems that rapidly evolve conventional pulsed field gradient spin-echo (PGSE) experiments cannot be used to obtain reliable estimates of molecular mobility. Modern ‘fast-diffusion’ experiments provide a means of obtaining this information and thus open up new vistas for the application of PGSE NMR. In this paper we review the various advantages and disadvantages of these methods.

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