Diffusional Attenuation During Soft Pulses: a Zangger-Sterk Pure Shift iDOSY Experiment

Diffusion-ordered spectroscopy experiments in which existing delays in a parent pulse sequence are used for diffusion encoding – iDOSY experiments – are potentially attractive because of their simplicity and sensitivity. However the calculation of diffusional attenuation in Zangger-Sterk pure shift iDOSY experiments is a very difficult problem to attack analytically, and is more easily approached numerically. Numerical simulations show that for typical experimental conditions, the dependence of diffusional attenuation on diffusion-encoding gradient amplitude is well represented by a shifted Gaussian function. The shift in gradient can be calculated analytically for the limiting case where the selective pulse is replaced by a hard 180° pulse at its midpoint; numerical simulations show that the effect of using different shapes of selective pulse is to scale down this limiting gradient shift by a constant factor that depends on the pulse shape used. The practical consequence is that under the experimental conditions appropriate for small molecules, the pure shift iDOSY method should allow good diffusion coefficient measurements to be made if appropriate allowance is made for the change in effective diffusion-encoding gradient. Parallel sets of numerical simulations and experiments are presented, and a practical application of a Zangger-Sterk pure shift iDOSY experiment to a simple test mixture is illustrated.

Files provided:

Data
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Figs. 2 to 4 and S1 to S4
Figure 6a Oneshot-45
Figure 6b ZS-iDOSY

Code
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Mathematica code
MGC analysis and figures.nb
Process simulated / experimental data for figs. 2 to 5 and S1 to S4
Matlab code
gradient_shift_analysis.m
gradient_shift_test.m
idosyzs.m
Simulate data for figs. 2 to 4 and S1 to S4

Sequence code
gmmgc
Fig. 1c, for figs. 2 to 4 and S1 to S4
kp_ifZS-iDOSY_03
Fig. 1a, for fig. 6b ZS-iDOSY
kp_oneshot45_02
Fig. 1d, for fig. 6a Oneshot-45

N.B. The definition of d20 has been corrected to match the diffusion delay
in these sequences, correcting errors in the sequences used for acquisition
of, and found in, the data directories “Figs. 2 to 4 and S1 to S4” and “Figure
6b ZS-iDOSY”

VnmrJ macros
GMgshift
Calculate and apply gradient value shift
GMPKBrukerNUG
Calculate and apply amplitude and diffusion coefficient correction
for gradient non-uniformity
GMprocPK22
Produce Fig. 6a
GMprocPK1002
Produce Fig. 6b