DOSY experiments can resolve signals from the individual components of a mixture of compounds without physically separating the compounds. This is achieved by using the different rates that molecules diffuse through solution to separate the signals. DOSY data are typically presented as a multi-dimensional NMR spectrum where one of the dimensions corresponds to the diffusion rate. Unlike the frequency dimensions, the diffusion data is not processed with a fourier transform. Instead, non-linear curve fitting is used to extract rates from which a pseudo spectrum is created.
In a DOSY experiment a series of spectra are collected using either a series of different diffusion delays or a series of different diffusion gradient strengths. This produces a series of spectra with differing intensities. The spectra can be 1D or 2D spectra. The figure below shows an expansion of the series of 1D 1H spectra collected for a 2D DOSY experiment. The spectra have been fourier transformed in the frequency dimension, but no processing of the diffusion dimension has been done. This data was collected on a mixture of erthyromycin (MW 733.94), 3-(t-butoxycarbonyl)-2-phenylthiazolidine-4-carboxylic acid (MW 309.38), and geraniol (MW 154.25) in DMSO-d6. Note how the intensity of the peaks from different compounds decreases at different rates.
To process the diffusion dimension, the intensity at the same chemical shift in each of the series of spectra is extracted and plotted against the diffusion variable (either the delay or the gradient strength). This produces a gaussian shaped curve. The figure below shows the intensities from the first figure plotted against the strength of the diffusion gradient. The intensities have been normalised by dividing them by the intensity in the first spectrum. This allows the different rates of the signal decay to be more easily seen. Note that the larger the molecule the slower the decay.
The decay curves can be fitted to the equation
I = Io e -D γ2 g2 δ2 (Δ -δ/3)
where I is the measured intensity, Io the initial signal intensity, D the diffusion rate, γ the gyromagnetic ratio of the observed nucleus, g the gradient strength, δ the gradient duration, and Δ the diffusion time. Notice how the exponential term of the equation contains terms for the gradient strength g, the gradient duration δ, and the diffusion time Δ. This means that diffusion rates could be measured by collecting a series of spectra in which any one of these three variables are changed. Typically, the gradient strength is changed because this does not affect the time taken to complete the pulse sequence. Changing the other two parameters, and thus changing the length of the pulse sequence, would complicate the data analysis.
This equation is for the basic DOSY experiment. Experiments that use bipolar gradients or stimulated echoes require modifications to the equation but the form remains the same.
The equation can be fitted to all data points in the spectra, or peak picking can be performed first and only regions containing peaks can be fitted. Once the fitting is done, a list of chemical shifts and their associated diffusion rates is obtained. Chemical shifts that have similar diffusion rates must come from the same compound. Grouping the chemical shifts by their diffusion rates allows signals from different compounds to be separated.
The user can work with the list of chemical shifts and diffusion rates or a simulated spectrum can be constructed with one more dimension than the original spectra that corresponds to the diffusion rates. Peaks are placed in the diffusion dimension according to the value of the diffusion rates. The width of the peak in this dimension is typically determined by the quality of the fitting and by a user defined scaling factor.
Acknowledgements
Thanks to Kelsey Alexander in the Gerwick Lab for preparing the samples and allowing me to use them to record the data.
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