title: Gamma convolution models for self-diffusion coefficient distributions in PGSE NMR.
abstract: 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.
authors.affiliation: Ian Wark Research Institute, University of South Australia, Mawson Lakes Campus, Adelaide, SA 5095, Australia. Electronic address: magnus.roding@sp.se.
authors.forename: Magnus
authors.initials: M
authors.lastname: Röding
authors.affiliation: Ian Wark Research Institute, University of South Australia, Mawson Lakes Campus, Adelaide, SA 5095, Australia. Electronic address: nathan.williamson@mymail.unisa.edu.au.
authors.forename: Nathan H
authors.initials: NH
authors.lastname: Williamson
authors.affiliation: Ian Wark Research Institute, University of South Australia, Mawson Lakes Campus, Adelaide, SA 5095, Australia; Department of Energy and Resource Systems Engineering, University College London, 220 Victoria Square, Adelaide, SA 5000, Australia. Electronic address: m.nyden@ucl.ac.uk.
authors.forename: Magnus
authors.initials: M
authors.lastname: Nydén
keywords: Gamma convolution; Gamma distribution; Lognormal distribution; Pulsed-field gradient spin echo NMR; Self-diffusion