DOSY

Importing a DOSY spectrum

The DOSY sequence includes a delay (for diffusion) and a pulse (the gradient pulse). Their values must be known, otherwise the raw data can only be processed as an array of 1-D spectra. The exponential decay (due to diffusion) of the signals can be expressed in the general form:

signal(z) = max(signal) exp(-zD)

D is the diffusion constant and z is a function of the diffusion delay and the gradient pulse. A script does the job of extracting the values from the original files and calculating the list of z values. iNMR itself only reads the calculated values of z from a text file called “zeta”, already written by the script. Examples of scripts can be found on the website. You need to run the script only once (to create the file “zeta”), with the DOSY experiment already open and in the foreground. You are free to edit this file or generate it with your own program or script, using the language of your choice.
Note that the quantity of zD is dimensionless. You are free to choose, and responsible for choosing, any unit for z. The diffusion coefficients will be expressed in the inverse of that unit. iNMR does not interpret or validate those units.

Pre-Processing

A DOSY spectrum must first be processed like an arrayed spectrum (for example, like an experiment of inversion recovery). In other words, you process it as a 2-D spectrum, but applying the FT along the rows only. Then it is necessary to correct the phase accurately. A baseline correction might be useful or deleterious. Try with and without and judge for yourself. iNMR assumes that the chemical shifts are constant during the experiment. If this is not the case, apply binning along the rows only: the spectrum will be less resolved, but the peaks will not wander from row to row.

Recognition

It is important that iNMR recognizes a DOSY experiment as an arrayed experiment. In practice, this means that iNMR should recognize that one of the indirect dimensions (normally f-1) is not suitable for FT processing. This recognition is normally automatic and happens the first time you open the spectrum with iNMR. The program then stores the information using a simple trick, namely by defining a dummy atomic species, whose symbol is a dot. If iNMR fails to recognize a DOSY experiment as an arrayed experiment, open the dialog Edit > Metadata and modify the atomic symbol manually, substituting a dot for the H (for example). Avoid using the “fake FT” option: it solves the problem only partially, because iNMR cannot tell which dimension to apply the DOSY processing along.

Processing a DOSY spectrum

The command “Process > DOSY > Mono-Exponential” can effectively process spectra where each column contains a single signal, or where all the signals at any given chemical shift belong to a single component of a mixture. In this case it is enough to fit the experiment with a simple mono-exponential decay. Here is the meaning of the parameters:

Max. log D: You can restrict the range of the diffusion scale. Quite likely, however, iNMR will further restrict your limits to fit the results. iNMR cannot, instead, expand your limits. The diffusion coefficients have negative logarithms, therefore higher values mean smaller (in absolute value) negative logarithms. In general, larger diffusion coefficients correspond to smaller molecules.
Min. log D: The diffusion scale follows the convention of the Cartesian plane and increases from bottom to top. At the bottom there are the slowest (and largest) molecules.
Restrict the Spectral Width...: You can optionally process just the part of the spectrum that contains the peaks of interest.
Final Number of Rows: While iNMR is free to restrict the vertical scale to match the diffusion coefficients, the number of rows will be exactly the value you require. Any integer value between 16 and 1024 is acceptable, it doesn't have to be a power of 2.
X-Smoothing: This OPTIONAL filter is a cosmetic manipulation with which the different results of adjacent columns are averaged. This operation improves the alignment of the peaks and makes them more realistic. Set the parameter to zero to skip this treatment. Set it to higher values to get broader and more regular peaks. Use 0 or very small values if you have already “binned” your spectra.
Max Width in the diffusion dimension: The DOSY plot is an artificial representation in which the position of each synthetic peak corresponds to the calculated value of a diffusion constant and the width (along the diffusion dimension) is proportional to the root-mean-square error. The area is proportional to the natural height of the peak. Like with normal NMR spectra, the user can change the width of the peaks. Unlike normal NMR spectra, the only possibility that is given in our module is to put an upper limit to the RMSE, therefore to the width of the peaks. If a peak is broader than the user-defined limit, it will be narrowed. This limit is expressed in units of points. If you keep this value constant and, at the same time, increase the number of rows, the peaks will actually become narrower (along the diffusion scale). In other words, what really matters is the ratio (Max Width) / (Final Number of Rows). When there are many deviations from a pure exponential decay, this correction greatly improves the readability of the plot. The apparent variance may, however, underestimate the true uncertainty.
Acceptable Signal / Noise: This is a preliminary filter to eliminate not only the weakest peaks but, most importantly, the tails of the strongest peaks. The diffusion coefficients are indeed less accurate if measured from the tails.

Undoing the mono-exponential analysis

If you select the command Process > DOSY > Mono-Exponential again and then close the dialog with the button “Cancel” you'll return to the frequency-domain spectrum before the DOSY-like transformation.

Reading and Storing the Values of the Diffusion Coefficients

The diffusion scale (vertical scale) is either logarithmic (more precisely, it corresponds to the negative of the logarithm) or linear. In the latter case, all the diffusion coefficients are multiplied by 10¹⁰. They are more readable in this way. A convenient way to determine the diffusion coefficient is to put a horizontal mark on the peak of interest (or up to 5 such marks on different peaks) and choose the command Process > DOSY > Diffusion Coefficients...
A dialog appears. The calculated coefficients will be reported on the right, in their true dimension. You can store them in the document, by clicking the button at the bottom.

Extracting the components: Multi-exponential Fitting

Once you have created a list of diffusion coefficients with the command above, you can extract the single components with the command “Extract Components”. You still get the same kind of DOSY plot but, this time, if a column contains more than one signal, you will get two different peaks. The plot generated by this command contains far fewer rows than the mono-exponential DOSY plot; actually you cannot specify the number of rows. There are so few rows that it is necessary to use a stacked plot to display the result.

The dialog shows a few options, at the top, that are identical to the ones seen for the mono-exponential case. The completely new parameter is called “Ignore components under...%”. The percentage is calculated relative to the highest component of the column. If you discover that the separation is not good, increase this value and repeat the processing. The risk is that a true minor component can disappear. If you already know, however, that the signals of the components of the mixture fall at different frequencies, then it is OK to ignore even components under 99%.

If the list of the diffusion coefficients contains more than 2 values, you can select a subset. This strategy can be useful when only a portion of the spectrum is processed.