TY - JOUR

T1 - The gamma distribution model for pulsed-field gradient NMR studies of molecular-weight distributions of polymers

AU - Röding, Magnus

AU - Bernin, Diana

AU - Jonasson, Jenny

AU - Särkkä, Aila

AU - Topgaard, Daniel

AU - Rudemo, Mats

AU - Nydén, Magnus

PY - 2012/9

Y1 - 2012/9

N2 - 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.

AB - 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.

KW - Pulsed-field gradient NMR

KW - Self-diffusion

KW - PEG

KW - Polymer

KW - Gamma distribution

KW - Log-normal distribution

KW - Molecular-weight distribution

UR - http://www.scopus.com/inward/record.url?scp=84865144697&partnerID=8YFLogxK

U2 - 10.1016/j.jmr.2012.07.005

DO - 10.1016/j.jmr.2012.07.005

M3 - Article

C2 - 22864268

AN - SCOPUS:84865144697

SN - 1090-7807

VL - 222

SP - 105

EP - 111

JO - Journal of Magnetic Resonance

JF - Journal of Magnetic Resonance

ER -