The possibility for performing self-diffusion measurements by Carr-Purcell-Meiboom-Gill (CPMG) experiments using the inherent magnetic field inhomogeneities as a gradient field were tested for six sample molecules, using a Maran Ultra NMR instrument with a 0.5 T permanent magnet. The method tested assumed that the magnetic field inhomogeneities could be approximated by a linear gradient, and the estimated parameter representing the magnetic field inhomogeneities in this model have been estimated to 25 μT2 m−2. The estimated diffusion coefficients were within 10-20 % of literature values, except for some samples, where convection was a problem The estimated field gradient have also been estimated from a Hahn echo experiment, and found to be consistent with the estimate from CPMG. The data obtained have also been used to probe the form of the magnetic field inhomogeneities, and have been found to be well described by a parabolic approximation. Some generalizations of the CPMG-signal was done to account for the parabolic form, which allows the CPMG-signal to be modified by introducing a correction function K, revealing the dependency of the sample height L, vertical displacement of the sample, l, and the form of the NMR tube used.
Sensitivity analysis for the diffusion coefficient have been included, indicating that the diffusion coefficient may be detected as low as 10−11 m2 s−1 at the instrument used. The sensitivity of the K-function for the various parameters have also been included, revealing the sample height as the most influential parameter.
The suitability for the free induction decay (FID) as an experiment for determining the transverse relaxation time have also been tested, and have been indicated to be unsuited for instruments with magnetic field inhomogeneities.