The gamma distribution model for pulsed-field gradient NMR studies of molecular-weight distributions of polymers

Magnus Röding*, Diana Bernin, Jenny Jonasson, Aila Särkkä, Daniel Topgaard, Mats Rudemo, Magnus Nydén

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

74 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)105-111
Number of pages7
JournalJournal of Magnetic Resonance
Publication statusPublished - Sept 2012
Externally publishedYes


  • Pulsed-field gradient NMR
  • Self-diffusion
  • PEG
  • Polymer
  • Gamma distribution
  • Log-normal distribution
  • Molecular-weight distribution


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