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A. V. Barzykin, K. Hayamizu, W. S. Price, and M. Tachiya
[J. Magn. Reson, Series A 114, pp.39-46, 1995]
The theoretical basis of the pulsed-field-gradient spin-echo experiment and its applicability to the study of diffusive transport through a spherical interface into an external medium containing a relaxation agent are examined in the long-time diffusion limit. The theory is compared with previous experimental findings involving bicarbonate diffusion in and across human red blood cell membranes. To a first approximation, the addition of a relaxation agent to the external medium results in the interface becoming a "partially absorbing wall". However, the results of this study show that it is experimentally difficult to achieve the partially absorbing wall conditions, and, in any case, this one-site model is not very sensitive to permeability differences. The treatment is then extended to include the case where the transported spins do not relax instantly but instead have a small but finite lifetime. This model is shown to be more sensitive to permeability differences as well as being experimentally realizable.