Jeener-Broekaert

Fig. 6. The generalized Jeener-Broekaert three pulse sequence. Note that FT of the solid echo and the alignment echo starts at times delayed by the pulse separation r, after the second and third pulse, respectively...

C. Jeener-Broekaert dipolar order relaxation sequence 464... 

In some sequences, such as the FFC variety of the Jeener-Broekaert sequence, the RF pulses applied during the preparatory sub-sequence need to be coordinated in phase with those applied during the detection subsequence. In such cases the preparatory and detection sub-sequence sections of the FFC sequence are no longer mutually independent. 

C. Jeener-Broekaert Dipolar Order Relaxation Sequence... 

The classical Jeener Broekaert sequence (133) is used to determine the dipolar-order relaxation time (in systems of spin 1/2 nuclides) and the Tiq relaxation time (in systems with spin 1 nuclides) of spin 1 nuclides with quadrupolar contributions to 7. Its FFC version is similar to the Inversion Recovery, except that the first 180° pulse is replaced by the sequence 90, — 5 — 45, the detection pulse becomes 45 and a special phase cycle is required. We shall not dwell on the details and purpose of the sequence since they go beyond the scope of this chapter. We wish to underline, however, the fact that sequences of this type require a close coordination of the preparatory sub-sequence with the signal-detection sub-sequence in order to isolate not just a particular magnetization component but a particular relaxation pathway. 

To bypass receiver deadtime effects, wideline spectra are derived by Fourier transformation of the decay of an echo. By use of the Hahn echo and the stimulated echo (Section 2.2.1), wideline spectra of and other spin-5 nuclei can be measured, for example, but not the spectra of dipolar coupled spins and of quadrupolar nuclei like H. The magnetization of nuclei with spin / = 1 can be refocused by the quadrupole echo or the solid echo, and by the Jeener-Broekaert echo or the alignment echo [Slil] (Fig. 3.2.6). 

Equation (3.2.14) is the starting point for numerical simulation of dynamic wideline NMR spectra. With the Jeener-Broekaert echo the imaginary part of the exponential depending on h is measured, and with the stimulated echo the real part is measured. The lineshapes of solid-echo spectra follow from (3.2.14) with t , = 0. 

These composite pulses can be used in liquid- and solid-state multi-pulse experiments such as the //V PT experiment (insensitive nuclei enhanced by polarization transfer) and the Jeener-Broekaert echo experiment [Wiml]. 

In the stimulated echo experiment, also shown in Fig. 6.2.3, the second pulse transfers the system into a mixture of Zeeman and double quantum order (alongandpg). Here, the relevant relaxation times are Ti (longitudinal Zeeman) and T q (double quantum), for which the 45 pulses of the Jeener-Broekaert sequence are replaced by 90v pulses. Again, two echos evolve at T] around the third pulse, and are refocussed by the fourth pulse. The two negative echo amplitudes vary as function of T2, with -[exp(-T2/Tiz) + exp(-T2/Ti3Q)], and both Ti and Tqq can be determined as separate values [14]. 

Fig. 5. Comparison of the frequency dependence of the total longitudinal proton relaxation time Ti and of the dipolar proton relaxation time Tto in the low-temperature nematic liquid crystal MBBA. r (v) was measured by the usual T] field-cycle with one B, r.f. pul%, shown by Rg. 1. Tto was measured by the usual Jeener-Broekaert sequence of three B r.f. pulses, in combination with a Bq field-cycle. which introduce an adjustable relaxation period between the second and third Bj pulse to give Tto(i )- The plots in the upper diagram show model fits according to equations (13a) 13d) with extensions described in the text. From the details at bottom about the experimental errors it can be clearly seen that the ratio T Tto significantly exceeds a value of 3 at medium frequencies, and in accordance with the model plot (frill line) approaches 1 in the low-frequency limit, where Bo is smaller than Bloc.

Rg.6. Schematic representation of various pidse sequences, employed in dynamic NMR of I = I spin systems Quadrupole echo sequence (QE), inversion recovery sequence (// ), saturation recovoy sequence (SR) and Jeener-Broekaert sequence (JB)... 

This is illustrated in Fig. 9. The 2D spectra refer to quadrupole echo sequences and characterize two possible reorientation mechanisms of a methyl group (three-site jumps vs continuous diffusion). Drastic spectral differences are observed. Ajqjarratly, these 2D relaxation spectra sensitively indicate the type of motion. The same is true for the corresponding normalized contour dots (see Fig. 9). We note that similar 2D spectra can be obtained from inversion recovery or Jeener-Broekaert sequences (see Fig. 6) [68]. Thus, by applying this 2D technique to different pulse sequoic, the various motions can be differentiated over an extremely wide dynamic range, extending from the fast-rotational to the ultraslow motional re me. Sin<% the different motions (see Fig. 4) modulate different kinds of molecular order (see Fig 3) these orders can be differentiated, likewise. 

Li and Be work has gained from the application of the stimulated-echo spectroscopy to study the ultra-slow dynamics of nuclear spin-3/2 probes. Apart from the dominant first-order quadrupolar interaction, the impact of the homonuclear dipolar interactions was also considered. Explicit analytical expressions describing various aspects of a coupled quadupolar pair subjected to a Jeener-Broekaert pulse sequence have been derived. Extensions to larger spin systems are also briefly discussed. These results are compared with experimental data on a single-crystalline Li ion conductor. 

In the rotating reference frame spin-lock rates Fj p(SL) were measured with locking fields of 10 and 40 G. Below 170 K, decay of quadrupolar order was observed with Jeener-Broekaert pulse sequences. 

The solid circles in Fig. 7 show the Jeener-Broekaert deuteron rates rip(JB) (Fig. 1) over the full data range down to 19 K. The smooth curve is drawn as a guide to the eye. At the bottom of Fig. 7 the open circles and straight line show again, for comparison, the laboratory frame F CD) and limiting low temperature Fie(D) fit from Fig. 3. The Fip(JB) rate cannot reflect dynamic relaxation because the low temperature Fxp(JB) rate is more than 25 times F. Fip(JB) rather represents an inhomogeneous... 

Figure 7. Jeener-Broekaert F pCD) rates (solid circles) down to 19 K. Laboratory frame rates Fx(D) from Fig. 3 also are shown (open circles).

The Jeener-Broekaert (J-B) pulse sequence [2.18] shown in Fig. 2.5 allows the creation of spin alignment and the observation of a stimulated echo [2.19] for a spin-1 system. The density matrix at the end of second pulse... 

Jeener-Broekaert pulse sequence, 128-29 Karplus equation, 57,224 3-Lactam, 138-39... 

Spin relaxation phenomena are usually described by the semiclassical theory developed by Wangsness, Bloch and Redfield and known as the WBR theory or Redfield theory. The semiclassical nature of the theory implies that the spin system is treated quantum mechanically, while the remaining degrees of freedom (such as molecular rotations) are treated classically. Few years ago, Segnorile and Zamar studied the issue of quantum decoherence (loss of system phase memory) in proton NMR of nematic liquid crystals. The spin dynamics - and the decay of the free induction decay - was found to be governed by several different processes, partly of purely quantum nature. During the period under the present review, the same group reported a related work concerned with the Jeener-Broekaert experiment on liquid crystals. ... 

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