Quadrupole induced relaxation

Because of rapid, quadrupole-induced relaxation, NMR signals frequently are 200 or 300 Hz wide or more. This is not as severe a problem as it may at first appear because vanadium-51 has a large chemical shift range of about 3000 ppm. As illustrated in Figure 2.2, the line widths shown vary from about 130 to 1000 Hz (1.3 to 10.0 ppm with a 400 MHz spectrometer), yet the spectrum is well resolved. The fast relaxation does mean that spectra can be accumulated very rapidly. Only in atypical situations will 20 or 30 accumulations per second lead to problems of... 

Similar to the situation for quadrupole-induced relaxation, the quadrupole splitting in liquid crystals is zero if the molecular symmetry is tetrahedral or higher. Electric field gradients are zero for such symmetries so there can be no quadrupolar interaction. However, one expects to see small splittings from tetrahedral or octahedral derivatives because of structural distortions. These predominately arise from specific interactions with extraneous materials such as lipophilic headgroups in surfactant systems, as seen, for instance, in both cationic and anionic octahedral cobalt(III) species [23], Much larger splittings will be expected from other structure... 

FIGURE 13. Calculated 13C NMR line shapes 7Li bound 13C, /(13C,7 Li) = 43.3 Hz as a function of the 7Li quadrupole induced relaxation rate jq. Reprinted with permission from Reference 14. Copyright (1995) American Chemical Society... 

Resonance line broadening due to chemical exchange and quadrupole-induced relaxation in the H and nB n.m.r. spectra of some boron-nitrogen adducts ArNMe2,BY3 (Y = halogen) has been observed and used to determine the mechanism of amine scrambling in these adducts.165 This is thought to occur via a unimolecular ionization rather than a B—N bond-rupture process. 

The proton magnetic resonance spectrum of pyrrole shows a very broad line at low field due to the proton of the imino group, and a spectrum of 8 lines due to the other protons. Temperature effects show the broad peak to arise from quadrupole-induced relaxation of N. In pyrrole, the spin couplings of the imino proton with the protons at C(2> and C(3) are nearly equal. 

When platinum is bound by ligands with donor atoms having quadrupolar nuclei (e.g. N, As), NMR peaks are frequently broad, because the rate of quadrupole-induced relaxation is such that Pt is only partially decoupled from the quadrupolar nucleus. 

It is interesting to note that in the quadrupole relaxation process discussed in Section 3.4 (Fig. 12) the core hole can be regarded as fluctuating between the different degenerate orbital magnetic sublevels. In this way, the core hole can form a static quadrupole moment and induce a quadrupole screening charge distribution. 

We saw in Chapter 7 that the resonance frequency of a quadrupolar nucleus is dependent on the orientation of the molecule in which it resides. Molecular tumbling now causes fluctuating electric fields, which induce transitions among the nuclear quadrupole energy levels. The resulting nuclear relaxation is observed in the NMR just as though the relaxation had occurred by a magnetic mechanism. 

Spin relaxation in a nucleus is induced by random fluctuations of local magnetic fields. These result from time-dependent modulation of the coupling energy of the resonating nuclear spin with nearby nuclear spins, electron spins, quadrupole moments, etc. Any time-dependent phenomenon able to modulate these couplings can contribute to nuclear relaxation. The distribution of the frequencies contained in these time-dependent phenomena is described by a correlation function, characterized by a parameter Tc, the correlation time. Its reciprocal can be considered as the maximum frequency produced by the fluctuations in the vicinity of the nuclear spin. If more than one process modulates the coupling between the nuclear spin and its surroundings, the reciprocal of the effective correlation time is the sum of the reciprocals of the various contributions... 

In general the Cooper pairs in conventional superconductors induced by phonons have. -symmetry where the gap opens uniformly on the Fermi surface and the temperature dependence of physical quantities below Tc is exponential. On the other hand, when the attractive force originates from spin or electron charge fluctuations, the Cooper pair has p- or d-wavc symmetry where the gap disappears on lines or points on the Fermi surface and the physical quantities have power-law temperature dependences. The quantities that are measured by NMR and nuclear quadrupole resonance (NQR) are the nuclear spin-lattice relaxation rate, 1 / T, the Knight shift, K, the spin echo decay rate, 1/T2 and the NQR frequency, vq. The most important quantities, K and 1/77 for the determination of the symmetry of the Cooper pairs are reviewed in the following sections. 

If the NH exchange rate is low, the NH peak is still broad because the electrical quadrupole moment of the nitrogen nucleus induces a moderately efficient spin relaxation and, thus, an intermediate lifetime for the spin states of the nitrogen nucleus. The proton thus sees three spin states of the nitrogen nucleus (spin number = 1), which are changing at a moderate rate, and the proton responds by giving a broad peak. In this case, coupling of the NH proton to the adjacent protons is observed. Such is the case for pyrroles, indoles, secondary and primary amides, and carbamates (Fig. 4.34). 

A nuclear electric quadrupole moment arises from a non-spherical distribution of electrical charges in the nucleus. Because the energy of an electric quadrupole moment depends on its orientation with respect to an EFG, a randomly varying electric field gradient associated, for example, with molecular rotation having a finite amplitude of its spectral density at the Larmor speed can induce effective relaxation of the quad-rupolar nucleus. In liquids, it is possible to write down... 

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