Jeener relaxation

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

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. 

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]. 

The requirements on the phases of the pulses is somewhat less stringent than implied by the sequence above. The second pulse must be in quadrature with the first but the third pulse can have any arbitrary phase because the dipolar order is not referenced by any external directions. To observe the Jeener echo, the reference phase of the receiver must be 90° out of phase with the third pulse. When the detector reference phase is identical with that of the third pulse, a Zeeman signal can be observed which is simply the FID resulting from the magnetization which has relaxed back to the z direction in the time since the first pulse. 

The most obvious application of the Jeener echo is to measure T by plotting echo amplitude vs. time spent in a state of dipolar order. If the system under study is homogeneously broadened, then the location on the echo where the amplitude is measured, provided it is chosen consistently, is immaterial for the measurement of T - In an inhomogeneously broadened system, such as a poly crystalline material, the Jeener echo may be a superposition of Jeener echoes with different shapes and different T- s. If so, it may matter where the echo amplitude is sampled. The most obvious test is to plot relaxation curves from different parts of the echo to determine whether the echo is relaxing uniformly. For a crystalline material, one expects that the dipolar relaxation time T p will be independent of the crystal orientation in the external field because the state of dipolar order is independent of this external field. 

It differs from the Jeener echo in that the dipolar state is prepared by an off-resonance saturation radiation rather than the first two pulses in the Jeener sequence. The application of the saturation method to short relaxation times comparable to the Jeener echo is discussed by Emid, et al. (1980). 

Jeener and Broekaert introduced, in 1%7, a three-pulse B,(r) sequence to measure the relaxation time Tm of the dipolar order of / = 1 spin systems in the presence of a conventional high Zeeman field, Bq, which is based on the decay time of the so-called Jeener echo . It was later extended by Spiess and Kemp-Harper and Wimperis to study in a similar way the quadrupolar order in / a 1 systems. The appearance of a Jeener echo depends upon the existence of interactions that are not averaged out by molecular motions on the considered time scale. The method has become of great importance in recent relaxation studies, in particular of liquid crystals because, in standard spin relaxation theories, it provides a power l means to separate and analyse the spectral densities / v) and /2) j. i4,is,2025 ggg... 

In order to measure of equation (11b) frequency or field dependent for frequencies greater than 5 MHz, where the standard technique no longer works, Bq must be varied over the relaxation period the generation and detection of the local spin order can be achieved under any suitable high-field condition. We realized this possibility with two of our FC spectrometers by a Bq cycle with a fast field switch Bpi from the polarization to the relaxation field at the beginning of the relaxation period (t2 interval), and the inverse switch Bp from the relaxation to the detection field Bp = Bp at the end of the T2 interval. The extended Jeener sequence... 

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.

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. 

In another work the MAS NMR technique is compared to the static powder quadrupole echo (QE) and Jeener-Brockaert (JB) pulse sequences for a quantitative investigation of molecular dynamics in solids. The line width of individual spinning sidebands of the ID MAS spectra were found to be characteristic of the correlation time from 10 to s so that the dynamic range is increased by approximately three orders of magnitude when compared to the QE experiment. As a consequence, MAS NMR is found to be more sensitive to the presence of an inhomogeneous distribution of correlation times than the QE and JB experiments which rely upon line shape distortions due to anisotropic T2 and Tiq relaxation, respectively. All these results have been demonstrated experimentally and numerically using the two-site flip motion of dimethyl sulfone and of the nitrobenzene guest in the a-p-tert-butylcalix[4]arene-nitrobenzene inclusion compound. 

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... 

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. ... 

Another relaxation technique that is likely to see much utilization for structural studies in the future is the two-dimensional (2D) NOE experiment. The basic experiment has been largely developed in Ernst s lab with applications to proteins illustrated in Wutti ch s k. The pulse sequence [ n/2) -ti- n/2 -ZM ( /2)%-h-] generates a 2D spectrum following the two Fourier transforms. The intenrity of a peak in fte 2D-NOE spectrum arising from interaction of nucleus k with nucleus 1 is (Jeener et al., 1979 Macura and Ernst, 1980)... 

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