title: The gamma distribution model for pulsed-field gradient NMR studies of molecular-weight distributions of polymers.
abstract: Self-diffusion in polymer solutions studied with pulsed-field gradient nuclear magnetic resonance (PFG NMR) is typically based either on a single self-diffusion coefficient, or a log-normal distribution of self-diffusion coefficients, or in some cases mixtures of these. Experimental data on polyethylene glycol (PEG) solutions and simulations were used to compare a model based on a gamma distribution of self-diffusion coefficients to more established models such as the single exponential, the stretched exponential, and the log-normal distribution model with regard to performance and consistency. Even though the gamma distribution is very similar to the log-normal distribution, its NMR signal attenuation can be written in a closed form and therefore opens up for increased computational speed. Estimates of the mean self-diffusion coefficient, the spread, and the polydispersity index that were obtained using the gamma model were in excellent agreement with estimates obtained using the log-normal model. Furthermore, we demonstrate that the gamma distribution is by far superior to the log-normal, and comparable to the two other models, in terms of computational speed. This effect is particularly striking for multi-component signal attenuation. Additionally, the gamma distribution as well as the log-normal distribution incorporates explicitly a physically plausible model for polydispersity and spread, in contrast to the single exponential and the stretched exponential. Therefore, the gamma distribution model should be preferred in many experimental situations.
authors.affiliation: Department of Mathematical Statistics, Chalmers University of Technology and Gothenburg University, Gothenburg, Sweden. roding@chalmers.se
authors.forename: Magnus
authors.initials: M
authors.lastname: Röding
authors.forename: Diana
authors.initials: D
authors.lastname: Bernin
authors.forename: Jenny
authors.initials: J
authors.lastname: Jonasson
authors.forename: Aila
authors.initials: A
authors.lastname: Särkkä
authors.forename: Daniel
authors.initials: D
authors.lastname: Topgaard
authors.forename: Mats
authors.initials: M
authors.lastname: Rudemo
authors.forename: Magnus
authors.initials: M
authors.lastname: Nydén