PGSE sequence

Fig. 3. The phase spectrum for PGSE sequence and the diffusion spectrum (dotted) for the Uhlenbeck time-dependent self-diffusion.

Suppose that we evaluate the case of a usual PGSE sequence comprising finite pulses of width 8 and gradient amplitude G. The phase spectrum follows from Eqs. (59) and (64) as... 

This relationship holds quite generally for the narrow pulse PGSE sequence provided that the phase distribution is Gaussian. This may be seen by considering the relationship between the particle displacement and the velocity correlation ... 

Since it is also true that ySG sin[(wA/2)/( w/2)] is the spectrum of the PGSE sequence [Eq. (73)] with short pulses separated by A, Eq. (78) follows directly. Note, however, that Eq. (78) gives the first term in the cumulant expansion and will only yield the correct echo attenuation if the phase distribution is Gaussian. 

Fig. 9. (A) Selective excitation and destruction of magnetization using a magnetic field gradient pulse. PGSE sequences used for diffusional attenuation of the solvent signal, based on the Hahn spin-echo sequence (B) and the stimulated-echo sequence (C). In the Hahn spin-echo sequence the magnetization is always subject to spin-spin relaxation. However, in the stimulated-echo sequence the delays can be set such that A is mainly contained in t2 where the relaxation is longitudinal and thus this sequence is preferable for large solute molecules since the condition T2 < usually holds.

Providing the echo interval in WATERGATE is kept short to minimize /-modulation, T2 relaxation and molecular diffusion effects (i.e. note the similarity with the Hahn spin-echo-based PGSE sequence in Fig. 9B), the desired resonances are retained in the spectrum with near-full intensity while the water peak should be suppressed by a factor of at least 1(1. Scalar coupling evolution can be refocused if the ir pulse in the WATERGATE sequence excites only some of the solute resonances but not the scalar coupled partners (for example amide resonances). ... 

Fig. 4.5.5 Pulsed field gradient sequences to obtain velocity and diffusion data (a) spin-echo (PGSE) and (b) stimulated-echo (PGSTE). The application of imaging gradients C Gy and Gz allows the measurement of velcocity maps and spatially-resolved diffusion coefficients and size distribution in emulsions.

Several NMR pulse sequences have been developed for measuring the diffusion coefficient. The most successful and currently used experiment is the modified spin-echo experiment (PGSE) proposed by Stejskal in 1967.62 As the echo signal is due to the transversal components of magnetic moments, the echo attenuation normalized for the attenuation due to relaxation can be written as63 ... 

Cosgrove and Warren 33) used the PGSE method of Packer, et al. 9). with the Meiboom-Gill rf pulse sequence 7> to investigate concentrated polystyrene solutions. 

Fig. 18. Pulsed-gradient spin-echo (PGSE) pulse sequence...

Figure 27 Pulse sequence for stimulated echo PGSE diffusion spectroscopy...

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