Inhomogeneous dipolar interactions

Here /, is the 13C nuclear spin, S is the unpaired electronic spin, and A j- is the Fermi contact hyperfine coupling tensor. This coupling is identical for all 13C nuclei as long as the C60 ion is spherical, but becomes different for different nuclei after the Jahn-Teller distortion leading to an inhomogeneous frequency distribution. The homogeneous width of the 13C NMR lines is, on the other hand, mainly determined by the electron-nuclear dipolar interaction... 

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. 

As a second example, we look at echoes. We saw in Chapter 9 that a 180° pulse refocuses not only chemical shifts and the effects of magnetic field inhomogeneity but also spin coupling provided that the pulse does not also disturb the spin state of the coupled nucleus (see Fig. 9.2) However, in a homonuclear spin system a nonselective pulse does effect spin states. We found in Chapter 7 that dipolar interactions have the same mathematical from as indirect spin coupling, and it is known that a 180° pulse does not produce an echo in a solid because spin states are disturbed. However, it is possible to obtain a solid echo or dipolar echo by applying the pulse sequence 90, T, 90r It is very difficult to rationalize an echo from... 

It has been established that the mobility of protons can be estimated by the detaUed analysis of NMR lineshape. Fen e et al. theoretically treated the influence of isotropic thermal motion upon MAS NMR for spin I = 1/2. When the broadening results from an inhomogeneous magnetic dipolar interaction, the Uneshape is expressed by Lorentzian line with Une width given by the following equation. 

Slichter s spin echo approach is a variation on the spin echo double resonance (SEDOR) experiment originally proposed by Hahn I03. To see how this experiment works, consider the spin echo sequences shown in Fig 53. The first case, Fig 53a, describes Hahn s original echo experiment 103. In a hetero-nuclear case (always observing the rare spin) any heteronuclear dipolar interactions (along with the chemical shift and inhomogeneous line broadening processes) will be refocused as a result of this sequence. The second example. Fig 53b, is Hahn s SEDOR experiment (74). Here, the heteronuclear dipole-dipole interaction is not refocused because of the application of the second tt pulse to... 

SPI-i accordingly provides recoupling of the heteronuclear dipolar interaction, without recoupling of the S2 chemical shielding terms to this order of AHT approximation. A similar cancellation of terms can be shown to yield compensation of RF inhomogeneity (wj and isotropic... 

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