Basic Principles of NMR Self-Diffusion Studies

Self-Diffusion Measurement by Pulsed-Field Gradient NMR 

In a magnetic field of strength B, the resonating nuclear spins precess with the Larmor frequency 

Because each spin contributes to the total transverse magnetization via the cosine of the phase difference A f the quantity observed in PFG NMR is given by the relation 

According to Eqs. (4)-(6), the molecular mean square displacements and thus the self-diffusion coefficients may be determined from the slope of a semilogarithmic plot of the PFG NMR signal F versus (Sg) The observation time of self-diffusion is the separation between the two field gradient pulses, t. Owing to their relatively large gyromagnetic ratio and to their natural abundance of 1, protons provide very suitable conditions for NMR self-diffusion studies, but C 44), F 45), and Xe 46-48) resonances have also been used successfully in recent PFG NMR studies of zeolites. 

For a diffusion tensor of axial symmetry with Dj D., Fig. 1 shows the influence of a diffusion anisotropy on the PFG NMR spin-echo attenuation as simulated in numerical calculations 49). The quantitative analysis shows, however, that for principal tensor elements not too different from each other (i.e., for tensor elements within one order of magnitude), the ini- 

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