Gamma convolution models for self-diffusion coefficient distributions in PGSE NMR

We introduce a closed-form signal attenuation model for pulsed-field gradient spin echo (PGSE) NMR based on self-diffusion coefficient distributions that are convolutions of n gamma distributions, n≥1. Gamma convolutions provide a general class of uni-modal distributions that includes the gamma distribution as a special case for n=1 and the lognormal distribution among others as limit cases when n approaches infinity. We demonstrate the usefulness of the gamma convolution model by simulations and experimental data from samples of poly(vinyl alcohol) and polystyrene, showing that this model provides goodness of fit superior to both the gamma and lognormal distributions and comparable to the common inverse Laplace transform.