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Measurement of diffusion-weighted NMR spectra as a function of time allows the time-dependence of concentration and the isolated spectrum to be found for each component in a reaction, without prior assumptions about spectra, kinetics or diffusion behaviour, by data decomposition using the PARAFAC algorithm.

Nuclear magnetic resonance (NMR) spectroscopy is frequently used in the monitoring of reaction kinetics, due to its nondestructive nature and to the wealth of chemical information that can be obtained. However, when spectra of different mixture components overlap, as is common, the information available is greatly reduced, sometimes to the point where the identification of individual chemical species is not possible. In such cases, the resolution of component spectra and their concentration timecourses can be greatly improved by recording DOSY (diffusion-ordered spectroscopy) data for each time point during the reaction. Adding this additional degree of freedom to the experimental data, allowing the signals of different species to be distinguished through their different rates of diffusion, makes the data trilinear and, therefore, susceptible to analysis by powerful multiway (here, more specifically multilinear) model-free decomposition methods such as PARAFAC (parallel factor analysis). This approach is shown to produce high quality data even for species with near-degenerate spectra. Another important limitation of NMR is its inherently low sensitivity. Here, we show that the combination of DOSY and PARAFAC is surprisingly robust with respect to input data with low signal-to-noise ratio. High quality component spectra and kinetic profiles are obtained from a data set in which the signal-to-noise ratios of the reaction components in the spectra for individual time points are below the detection level.