Accurate measurement of translational diffusion coefficients: a practical method to account for nonlinear gradients

For NMR probes equipped with pulsed field gradient coils, which are not optimized for gradient linearity, the precision and accuracy of experimentally measured translational diffusion coefficients are limited by the linearity of the gradient pulses over the sample volume. This study shows that the accuracy and precision of measured diffusion coefficients by the Stejskal--Tanner spin-echo pulsed field gradient experiment can be significantly improved by mapping the gradient z-profile and by using the mapped calibration parameters in the data analysis. For practical applications the gradient distribution may be approximated by a truncated linear distribution defined by minimum and maximum values of the gradient. By including the truncated linear gradient distribution function in the Stejskal--Tanner equation, the systematic deviation between the fitted curve and the experimental attenuation curve decreases by an order of magnitude. The gradient distribution may be calibrated using an intense NMR signal from a sample with a known diffusion coefficient. The diffusion coefficient of an unknown sample may then be determined from a two-parameter fit, using the known gradient distribution function.