Quadrupole linewidths

General Principles Quadrupole Moment, Relaxation, Linewidth... 

These nuclei (and they form by far the majority of the NMR-active nuclei ) are subject to relaxation mechanisms which involve interactions with the quadrupole moment. The relaxation times Tj and T2 (T2 is a second relaxation variable called the spin-spin relaxation time) of such nuclei are very short, so that very broad NMR lines are normally observed. The relaxation times, and the linewidths, depend on the symmetry of the electronic environment. If the charge distribution is spherically symmetrical the lines are sharp, but if it is ellipsoidal they are broad. 

It is worth mentioning that >NH protons may often appear somewhat broader than their -OH counterparts, for another reason >NH protons have another relaxation mechanism available to them (quadrupole relaxation) because the 14N nucleus has an electric quadrupole moment. This extra relaxation capability can lead to a shorter relaxation time for >NH protons, and since the natural linewidth of a peak is inversely proportional to the relaxation time of the proton(s) giving rise to it, a shorter relaxation time will give rise to a broader peak. 

Table 5.4 A comparison of specific surface area ratio calculated from quadrupole splitting (Aq), spin-lattice relaxation rate (Rf, half-height linewidth (Avj/2) and isotherm data for an unbleached linerboard pulp beaten to various degrees.

The scatter plot in Figure 1 gives correlation of the quadrupole splitting and the chemical shift (at 78°K.) for several tin compounds (5, 9, 16) using white tin (beta) for a chemical shift reference. The various sources and their linewidths are also shown. 

Hence, application of the MAS technique for the investigation of quadrupole nuclei leads to a decrease of the linewidth of the CT by a factor of about 3.6. A further improvement of the resolution of the NMR spectra of quadrupole nuclei requires the application of more sophisticated techniques, such as the DOR (27) or the more recently developed MQMAS NMR spectroscopy (26,28). Until now, however, neither of these techniques has been applied for investigations of working solid catalysts, and they are therefore not considered in this review. 

The 7Li resonance in zeolites is also difficult to interpret, even though the quadrupole moment is much lower. Lechert et al. (227) believe that the 7Li linewidth is controlled by the dipole-dipole interaction with 27A1 nuclei in the aluminosilicate framework. According to Herden et al. (232) the increase of 7Li frequency from 9 to 21 MHz does not affect the second moment of the spectra in zeolites Li-X and Li-Y, which means that the quadrupolar interaction is small. The second moment was also independent of the Si/Al ratio. The mean Li-Al distance calculated from the van Vleck formula was 2.35 A. Small amounts of divalent cations reduce the movement of Li + considerably, with the activation energy for this process increasing from 30 to 60 kJ/mol. 

The expressions for the linewidths in a spectrum with quadrupole splittings for nuclei with I = 3/2 has been derived (13). Thus the central peak has the same linewidth as the narrow component in Equation lib. In Ref. 13 the linewidths of the two satellites have also been calculated to be ... 

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