The gamma distribution model for pulsed-field gradient NMR studies of molecular-weight distributions of polymers
Journal article, 2012

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.

cellulose

spin-echo

self-diffusion

Log-normal distribution

Polymer

Pulsed-field gradient NMR

water

PEG

Gamma distribution

polydispersity

integral-equations

nuclear-magnetic-resonance

Self-diffusion

Author

Magnus Röding

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

SuMo Biomaterials

Diana Bernin

SuMo Biomaterials

Chalmers, Chemical and Biological Engineering, Applied Surface Chemistry

Jenny Jonasson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Aila Särkkä

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

D. Topgaard

Lund University

Mats Rudemo

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Magnus Nydén

Chalmers, Chemical and Biological Engineering, Applied Surface Chemistry

SuMo Biomaterials

Journal of Magnetic Resonance

1090-7807 (ISSN)

Vol. 222 105-111

Subject Categories

Biochemistry and Molecular Biology

DOI

10.1016/j.jmr.2012.07.005

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Latest update

3/2/2018 9