Parameterization of NMR relaxation curves in terms of logarithmic moments of the relaxation time distribution

Oleg V. Petrov* (Corresponding Author), Siegfried Stapf

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
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This work addresses the problem of a compact and easily comparable representation of multi-exponential relaxation data. It is often convenient to describe such data in a few parameters, all being of physical significance and easy to interpret, and in such a way that enables a model-free comparison between different groups of samples. Logarithmic moments (LMs) of the relaxation time constitute a set of parameters which are related to the characteristic relaxation time on the log-scale, the width and the asymmetry of an underlying distribution of exponentials. On the other hand, the calculation of LMs does not require knowing the actual distribution function and is reduced to a numerical integration of original data. The performance of this method has been tested on both synthetic and experimental NMR relaxation data which differ in a signal-to-noise ratio, the sampling range and the sampling rate. The calculation of two lower-order LMs, the log-mean time and the log-variance, has proved robust against deficiencies of the experiment such as scattered data point and incomplete sampling. One may consider using them as such to monitor formation of a heterogeneous structure, e.g., in phase separation, vitrification, polymerization, hydration, aging, contrast agent propagation processes. It may also assist in interpreting frequency and temperature dependences of relaxation, revealing a crossover from slow to fast exchange between populations. The third LM was found to be a less reliable quantity due to its susceptibility to the noise and must be used with caution.

Original languageEnglish
Pages (from-to)29-38
Number of pages10
JournalJournal of Magnetic Resonance
Early online date13 Apr 2017
Publication statusPublished - Jun 2017

Bibliographical note

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 668119 (project “IDentiFY”). We thank Dr. Reiner Zorn for helpful comments on his article [7]; Dr. Oliver Neudert and Dr. Carlos Mattea for introduction to the field-cycling relaxometry and their suggestions about a test sample; and Prof. Dr. Michael Vogel for permission to use the 7Li stimulated-echo data.


  • Field-cycling relaxometry
  • Laplace inversion
  • Logarithmic moments
  • Non-exponential relaxation
  • Stretched exponential fit
  • T relaxometry


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