Quadrupolar relaxation examples

Table 14 summarizes the magnitudes and absolute signs of a variety of couplings involving nitrogen in oximes. The entries include examples of spin coupling between other nuclei and and N. Spin coupling between and H nuclei is not usually observable because of the rapid quadrupolar relaxation of the nucleus. 

Often it is possible, for the experimentalists, to exclude one or several of these contributions by using common knowledge concerning which mechanisms are most likely not important. So for example, the quadrupolar relaxation (Q) can be dropped, simply because is not a quadrupolar (/ > ) nucleus. Of the four mechanisms left the DD and SR could be separated from each other due to their opposite temperature dependencies while the CSA and SC mechanisms could be separated according to their field dependencies. 

In some cases, signals may be broadened and this can affect the measurement of the relative integrals of signals. For example, signals arising from protons attached to N are broadened due to quadrupolar relaxation by N (7 = 1). Exchange with solvent protons also causes broadening, e.g. ... 

Ligand nuclei have been the subject of many studies, for example, CINMR has been used as a probe of chelated zinc(n) environments. Molar relaxivity is suitable for characterizing the zinc environment in terms of the quadrupolar relaxation of nuclei that it can produce in... 

Solute resonances provide less equivocal results about solute-solvent interactions, and also give information about solute-solute interactions as well. Where the observed nucleus has spin / > the symmetry of the solvation sphere is expected to influence the quadrupolar relaxation asymmetric fields leading to broader lines,e.g. " Al line widths (/ = f) in A1 (DMF) (octahedral) and KAl(OH)4 (tetrahedral) are 39 Hz and 200 Hz respectively. It must be pointed out that this is not always the case the above example refers to a situation with slow exchange, but in one case of fast exchange the variation in T2 for Cs" (/ = i) in H2O-D2O mixtures is ascribed to changes in solvent viscosity. ... 

Before discussing quadrupolar relaxation, it could be useful to say a few words about quadrupoles and give some illustrative examples taken from molecular physics. A quadrupole can be visualized as an ensemble of four charges or, what is better, as two opposite dipoles. A pair of two dipoles oriented as in Figure 5 is a good example of a quadrupole. 1,4-dioxane and trans-1,2-dichloroethylene are quadrupolar molecules but also benzene and all the horaonuclear diatomic molecules like H2 or N2. 

Because of the dependence on the efg, high-resolution spectroscopy is possible for fairly weakly quadrupolar nuclei if the electronic environment is sufficiently symmetric. Examples are H, Li, Be, N, or Cs. Indeed, quadrupolar relaxation for aqueous Li" is so inefficient that relaxation times of 1000 s have been observed. Asymmetry of the efg is marked for atoms carrying lone pair electrons with s character. Thus N lines are sharp for NH/ but quite broad ca. 200 Hz) for pyridine. The lines for monocovalent bromine or iodine are usually broadened out of existence, but can be observed for aqueous 1 and lO, for example, because of the high local symmetry (Chapter 17). 

While the terminology scalar relaxation of the first kind concerns J modulation (J spin spin or scalar or indirect coupling constant) by exchange phenomena, the usual example of the second kind is a spin 1/2 nucleus (7), J coupled to a fast relaxing quadrupolar nucleus (S) with relaxation times Tj and Tf (and spin number /s)- The relevant interaction is of the form... 

The procedures for recording spectra of heteronuclei often differ considerably from those for H and (which would today be considered routine ) since it is necessary, even for routine measurements, to adjust the experimental conditions to suit the special properties of the nuclei to be observed. For example, the spin-lattice relaxation times for some nuclides, such as N, are very long, whereas for others (especially those with an electric quadrupole moment, such as N) they are very short. Also, the spectra observed for some nuclides contain interfering signals caused by other materials present, for example the glass of the sample tube ("B, Si), the spectrometer probe unit ( Al) or the transmitter/receiver coil. For many nuclides the sample temperature and its constancy are important factors for example, quadrupolar nuclides such as O give narrower signals when the temperature is increased. 

Another important nuclear characteristic is the nuclear quadrupole moment which, possessed by nuclei for which 7 1, has given rise to the important field of nuclear quadrupole resonance spectroscopy. A major importance of the quadrupole moment with respect to NMR absorption resides in the effects of quadrupole coupling constants on nuclear relaxation times and, therefore, on the line widths and saturation characteristics of NMR absorption (9). In addition, in favorable situations, quadrupole coupling constants can be derived from the characteristics of nuclear resonance of quadrupolar nuclei 127). Some examples of these effects will be described in Sections III, IV and VI of this chapter. 

Because of the 100% isotopoic abundance of 27A1 and its very short spin-lattice relaxation time, even traces of aluminum are often detectable by MAS NMR. For example, Thomas et al. (156) were able to show that aluminum present as an impurity in soda glass is four-coordinated. However, quantitative determination of Al concentration in the sample is only possible when the quadrupolar effects are not so large as to affect significantly the apparent intensity of the 27A1 signal. 

The faithful representation of the shape of lines broadened greatly by dipolar and, especially, quadrupolar interactions often requires special experimental techniques. Because the FID lasts for only a very short time, a significant portion may be distorted as the spectrometer recovers from the short, powerful rf pulse. We saw in Section 2.9 that in liquids a 90°, t, 180° pulse sequence essentially recreates the FID in a spin echo, which is removed by 2r from the pulse. As we saw, such a pulse sequence refocuses the dephasing that results from magnetic field inhomogeneity but it does not refocus dephasing from natural relaxation processes such as dipolar interactions. However, a somewhat different pulse sequence can be used to create an echo in a solid—a dipolar echo or a quadrupolar echo—and this method is widely employed in obtaining solid state line shapes (for example, that in Fig. 7.10).The formation of these echoes cannot readily be explained in terms of the vector picture, but we use the formation of a dipolar echo as an example of the use of the product operator formalism in Section 11.6. 

Because quadrupolar nuclides have I > /2, there are more energy levels to consider, and the probability of a relaxation transition between one pair of levels in a single nucleus may not be equal to that between another pair of levels. For example, nuclides with I = 3/2 (such as 23Na) have distinctly different relaxation rates for the m — % — V2 transition and the V2 — 3/2 transitions. In an even slightly anisotropic environment, such as a liquid crystal solvent or a biological cell, the spectrum of a free 23Na ion has two components, as indicated in Fig. 8.5, with quite different values of both T, and T2. 

Relaxation rate R,s 2nJ and R,s R/. This situation occurs, for example, where I = 1/2 and is coupled with a moderately large value of J to a quadrupolar nucleus S that relaxes rapidly. (Because of the rapid relaxation of S, the expected splitting of the resonance lines of I does not occur, as we have seen in previous chapters.) Equations for this type of scalar relaxation have been derived ... 

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