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Updated: Apr 17, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Systematic bias in NMR diffusion measurements on polydisperse systems
Xiaoyue Zhou1, Kaipin Xu1, Shanmin Zhang1
1Physics Department and Shanghai Key Laboratory of Magnetic Resonance, East China Normal University, Shanghai, China.
Abstract:
Least-squares fitting of the Stejskal-Tanner equation is a routine process in the measurement of molecular diffusion coefficient (MDC) using Nuclear Magnetic Resonance (NMR) Spectroscopy. It is simple and elegant. However, a bias of the MDC is noticed when the system is polydispersed. This is due to improper accounts of the diffusion coefficient distribution. Eventually, it leads to a discrepancy between the observed MDC and the statistical mean value of the distribution. To reveal the discrepancy, an analytical solution is derived when the diffusion data is taken a logarithmic linearization. Computer simulation is also applied to obtain a non-linear regression result. For a Gaussian distribution of the MDCs, the bias is proportional to the square of the distribution width (linear regression), but it is also inversely proportional to the statistical mean value of the distribution (non-linear regression). This indicates that the MDC derived from Stejskal-Tanner equation only holds well for narrow distribution of MDCs. Otherwise, molecular radius derived from the Stokes-Einstein equation needs to be reconsidered due to the incorrect estimation of the MDC.
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