Improving the accuracy of pulsed field gradient NMR diffusion experiments: Correction for gradient non-uniformity

Pulsed field gradient NMR is a well-established technique for the determination of self-diffusion coefficients. However, a significant source of systematic error exists in the spatial variation of the applied pulsed field gradient. Non-uniform pulsed field gradients cause the decay of peak amplitudes to deviate from the expected exponential dependence on gradient squared. This has two undesirable effects: the apparent diffusion coefficient will deviate from the true value to an extent determined by the choice of experimental parameters, and the error estimated by the nonlinear least squares fitting will contain a significant systematic contribution. In particular, the apparent diffusion coefficient determined by exponential fitting of the diffusional attenuation of NMR signals will depend both on the exact pulse widths used and on the range of gradient amplitudes chosen. These problems can be partially compensated for if experimental attenuation data are fitted to a function corrected for the measured spatial dependence of the gradient and signal strength. This study describes a general alternative to existing methods for the calibration of NMR diffusion measurements. The dominant longitudinal variation of the pulsed field gradient amplitude and the signal strength are mapped by measuring pulsed field gradient echoes in the presence of a weak read gradient. These data are then used to construct a predicted signal decay function for the whole sample, which is parameterised as the exponential of a power series. Results are presented which compare diffusion coefficients obtained using the new calibration method with previous literature values.