Abstract
The investigation of the effects of diffusion in a magnetic field gradient on the spin-echo experiment in nuclear magnetic resonance (NMR) is extended to small samples in which the diffusion is bounded, or restricted. From the point of view of NMR, bounded diffusion means that the spin dephasing time , the average time for a molecule to diffuse once across a sample width . A more realistic criterion is that is small enough or that the diffusion coefficient is large enough that the quantity is about equal to or less than 1, where is a linear magnetic field gradient and is the nuclear gyromagnetic ration. An effective self-diffusion coefficient is defined from the Hahn spin-echo experiment, where is the time of the echo, and is the echo amplitude. For infinite samples, , the true self-diffusion coefficient. However, when , then and depends on . The measurement of is made by holding the times of an echo, , constant and varying . Experimental data are presented on for four values of and values of which range from being much greater than unity to less than unity. Results of the Carr-Purcell experiment are also presented and briefly discussed. A comparison of data from the spin-echo experiment is made with a theoretical calculation of which uses Torrey's modification of the Bloch equations and requires that boundary conditions be satisfied. Results are compared with the theory developed by Robertson. A universal curve for versus is plotted, illustrating that is independent of . It is shown that the reduced rate of decay of the echo envelope in the case of bounded diffusion is, in effect, a motional-narrowing phenomenon.
- Received 20 June 1966
DOI:https://doi.org/10.1103/PhysRev.151.264
©1966 American Physical Society