The lognormal and gamma distribution models for estimating molecular weight distributions of polymers using PGSE NMR.
We present comprehensive derivations for the statistical models and methods for the use of pulsed gradient spin echo (PGSE) NMR to characterize the molecular weight distribution of polymers via the well-known scaling law relating diffusion coefficients and molecular weights. We cover the lognormal and gamma distribution models and linear combinations of these distributions. Although the focus is on methodology, we illustrate the use experimentally with three polystyrene samples, comparing the NMR results to gel permeation chromatography (GPC) measurements, test the accuracy and noise-sensitivity on simulated data, and provide code for implementation.
Future Industries Institute, University of South Australia, Mawson Lakes Campus, Adelaide, SA 5095, Australia. Electronic address: nathan.williamson@mymail.unisa.edu.au.
Nathan H
NH
Williamson
Future Industries Institute, University of South Australia, Mawson Lakes Campus, Adelaide, SA 5095, Australia; School of Energy and Resources, UCL Australia, University College London, Torrens Building, 220 Victoria Square, Adelaide, SA 5000, Australia. Electronic address: m.nyden@ucl.ac.uk.
Magnus
M
Nydén
Future Industries Institute, University of South Australia, Mawson Lakes Campus, Adelaide, SA 5095, Australia; School of Energy and Resources, UCL Australia, University College London, Torrens Building, 220 Victoria Square, Adelaide, SA 5000, Australia; SP Food and Bioscience, Frans Perssons väg 6, 402 29 Göteborg, Sweden. Electronic address: magnus.roding@sp.se.
Magnus
M
Röding
Gamma distribution; Lognormal distribution; Molecular weight distribution; Polydispersity; Pulsed gradient spin echo NMR; Scaling law; Self-diffusion