Magnetization partially relaxed

Figure 4-6. Representation of the magnetization components A/, A/., and A/,. (A) In presence of field without field H. (B) Immediately after absorption of energy from field Hi. (C) After partial relaxation back to the equilibrium position shown in A.

The signal intensities A correspond to the transverse magnetization after the 180°, t, 90° sequence. The transverse magnetization, in turn, arises from the partially relaxed longitudinal magnetization, given by integration of the Bloch equation (1.17 a) between AT, = — Mq at time t = 0 and Mz = Mz at t = v. 

Fig. 2.28. Motion of the magnetization vector during a saturation-recovery experiment the first 90J pulse rotates the magnetization vector M0 to the x y plane (a -> b). where the resultant transverse magnetization is dispersed by a field gradient pulse (homo-spoil) after r s (d), a second 90 pulse monitors the partially relaxed magnetization Mt (d - f), and the resultant FID signal is Fourier transformed to the NMR signal with amplitude Ax. (Reproduced by permission of the copyright owner from E. Breitmaier and G. Bauer ...

In Chapters 7 and 8, one-dimensional NOE experiments and a few two-dimensional experiments are presented. Strategies to minimize adverse paramagnetic effects are discussed, as well as ways to exploit such effects to extract structural and dynamic properties. Partial orientation and cross correlation between the Curie magnetic moment relaxation and nuclear dipolar relaxation are also discussed. Chapter 9 deals with the experimental strategies necessary to achieve the highest level of performance in NMR of paramagnetic compounds in solution. 

Gadolinium and dysprosium, both elements of the lanthanide family, differ in the electronic occupancy of their f-shells. As a result, they are very similar chemically but very different magnetically. The relaxivity 1/Tx of Dy-DTPA is as low as 0.1 1/mol s However, dysprosium has a pronounced ability to influence transiently the residual magnetic susceptibility of tissues as it passes through. This effect of Dy-DTPA seems to be ideal for cerebral perfusion imaging and may be useful for the quantitation of partial occlusions and reperfusion. 

In order to determine the content of this noncrystalline line further, we examined in more detail the behavior of the spin-lattice relaxation. Figure 5 shows the partially relaxed spectra in the course of the inversion recovery pulse sequence (180°-t-90°-FIDdd-10s)i2o with varying x values. The magnetization that was recovered for 10 s in the z direction was turned to negative z direction by 180° pulse and the magnetization recovered in z direction for varying x was measured in the xy plane under H DD. The spectra at different steps of the longitudinal relaxation were obtained by Fourier transform and are shown in Fig. 5. In these spectra the contribution from the crystalline components with Tic s of2,560 and 263 s are eliminated due to the lack of time for recovery at each pulse sequence. Therefore, we observed preferentially the relaxation process of the noncrys-... 

Figures 2.13, 9.1, and 9.2 demonstrate the formation of an echo following a tt pulse. Application of additional tt pulses can be used to form a train of echoes. It is clear that the dephasing of magnetizations following an echo is of the same form as the initial dephasing during the FID and that application of a second tt pulse at 3T causes a second echo at 4t, etc. The envelope formed by the echo peaks decays according to the real T2, rather than T2, and Fourier transform of each echo provides a set of partially relaxed spectra, from which T2 of each line may be determined. (Carr and Purcell first recognized the value of such a long sequence of TT pulses,104 and their names are usually used to depict the method, but the technique that we described for the spin echo in Chapter 2 and that discussed here include a refinement by Meiboom and Gill,105 as discussed later.)...

In applying suppression methods to multidimensional sequences, it is important to consider what preconditions the suppression scheme makes on the water magnetization. For example, multidimensional sequences are generally run with a recycle delay less than sufficient to allow the water magnetization to relax back to equilibrium before the start of the next scan. Thus the water is always at least partially saturated but the theory behind most suppression methods assumes that the water magnetization starts from thermal equilibrium in each instance. We note in particular that spin-lock, WATERGATE and diffusion filters can be used to suppress the water irrespective of whether the solvent magnetization is at equilibrium. 

Fig. 5.7 Illustration of the magnetization vectors M., My, and My for a system (a) in the presence of an external magnetic field Bo in the z-direction but no transverse field (b) after application of Bj in the (x, y)-plane and absorption of energy and (c) after partial relaxation back to the equilibrium configuration in (a).

Oldfield, E., and Allerhand, A. (1975)./. Amer. Chem. Soc. 97, 221. Identification of Tryptophan Resonances in Natural Abundance Carbon-13 Nuclear Magnetic Resonance Spectra of Proteins. Application of Partially Relaxed Fourier Transform Spectroscopy. 

They are easily separated by various relaxation experiments [10,96]. Figure 20 shows partially relaxed NMR spectra of polymer 4 (a-CDj) at four different pulse separations ti in a saturation recovery and a quadrupole echo sequence (see Fig. 6). The spectra refer to the same temperature and parallel orientation of alignment axis and magnetic field. Again two spectral components are observed. The central peaks refer to the mobile fraction of the polymer while the outer peaks correspond to the... 

Next, we examined the partially relaxed spectra in the transverse direction. As was explained in the theoretical sections, the relaxation of magnetization of macromolecules whose only nuclei possessing spin are and H is predominantly conducted by the time-fluctuation of the dipole-dipole interaction between and neighbouring H nuclei. However, the mechanism is somewhat different depending on the direction of the relaxation. The longitudinal relaxation is carried out by the o>c and ct>c cuh frequency components (see eqn (33)) of the fluctuation arising from random reorientation of chemically bonded internuclear vectors via... 

Figure B2.4.6. Results of an offset-saturation expermient for measuring the spin-spin relaxation time, T. In this experiment, the signal is irradiated at some offset from resonance until a steady state is achieved. The partially saturated z magnetization is then measured with a kH pulse. This figure shows a plot of the z magnetization as a fiinction of the offset of the saturating field from resonance. Circles represent measured data the line is a non-linear least-squares fit. The signal is nonnal when the saturation is far away, and dips to a minimum on resonance. The width of this dip gives T, independent of magnetic field inliomogeneity.

Even when they have a partial crystallinity, conducting polymers swell and shrink, changing their volume in a reverse way during redox processes a relaxation of the polymeric structure has to occur, decreasing the crystallinity to zero percent after a new cycle. In the literature, different relaxation theories (Table 7) have been developed that include structural aspects at the molecular level magnetic or mechanical properties of the constituent materials at the macroscopic level or the depolarization currents of the materials. 

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