DOSY Experiments - Emory University

Chapter 3 Gradient Calibration and Correction for
Gradient Non-Uniformity
3.1 Introduction
As described in section 2.1, the measurement of good quality DOSY data is highly dependent on
the careful optimization of experimental parameters and the reduction, or complete elimination,
where possible, of sources of systematic errors in the data. However, even when all possible
steps have been taken to maximize spectral data quality, some systematic sources of error will
remain that can degrade the quality of the final DOSY spectrum and reduce the accuracy of the
diffusion measurements. Among these remaining sources of systematic error, one of the most
significant is spatial non-uniformity of the field gradient pulses produced by the probe.
As described in section 2.1, diffusion measurements by NMR involve the fitting of the signal
amplitude as a function of the square of the gradient pulse area to the Stejskal-Tanner equation:
2
S( G)
=
S(
0)
exp( −Diγ
δ G
[1]
where S(G) and S(0) are the signal intensities obtained with gradients strengths of G and 0,
respectively, D is the diffusion coefficient, γ is the gyromagnetic ratio, δ is the gradient pulse
duration and Δ is the effective diffusion delay.
Unfortunately, largely due to necessary compromises made in all probe designs, the field
gradients produced are not perfectly uniform over the active volume of the sample. In diffusion
experiments this leads to problems with gradient calibration and to signal decays whose form
deviates slightly from that of the Stejskal-Tanner (S-T) equation. Fitting such data to the S-T
equation without correcting for non-uniform gradients has some undesirable consequences: first,
with increasing diffusion weighting, the deviation of the signal decay from the S-T equation also
increases. This means that the apparent diffusion coefficient calculated from the fit depends on
the level of diffusion weighting used. Second, the standard deviation of D estimated in the fitting
process is increased because the experimental and theoretical decays do not match, a problem
that gets worse as the diffusion weighting increases. Since the standard error is used to define
the width of a peak in the diffusion domain of a DOSY spectrum, (see section 4.5) any increase in
the standard error leads to a loss of diffusion resolution.
Fortunately, it is straightforward to correct for almost all of these effects of gradient non-uniformity
by fitting the experimental data to a modified Stejskal-Tanner equation that takes into account the
actual gradient shape produced by the probe. A single experiment is used to determine the
necessary correction to the S-T equation, which can then be used in the processing of all DOSY
data. The steps involved in correcting for gradient non-uniformity can be summarized as follows:
Mapping of the gradient shape
Calculation of the actual signal decay under this gradient shape
Parameterization of the experimental signal decay
Each of these steps is described in the sections below.
12
2 2Δ
)