Magic angle spinning dipolar interactions

Fig. 3. Magic angle spinning and its effect on anisotropic interactions. The dashed vector, denoting one particular dipolar interaction, or some other measure of molecular orientation, is shown on the right in terms of the geometry of sample spinning. By rotating the sample rapidly about an appropriate axis, the anisotropy or broadening experienced by the nucleus can be reduced to zero.

However, it is found that a combination of techniques, such as proton dipolar decoupling (removes the dipolar interactions), magic angle spinning (reduces the chemical shift tensor to the isotropic chemical shift value), and cross-polarization (increases the sensitivity of rare spins, like 13C) applied to a solid state material, results in sharp lines for 13C nuclei in the solid state10). Thus, the observation of narrow lines or high resolution NMR in the solid state is possible. 

In general, multiple pulse techniques sufficiently average the dipolar interactions, compress the chemical shift scale, but they do not affect heteronuclear dipolar interactions and the chemical shift anisotropy. A combination of both multiple pulse techniques and magic angle spinning, so-called CRAMPS (Combined Rotational And Multiple Pulse Spectroscopy) is found to yield satisfactory results in the solid state H NMR of solids 186). The limitations of all these techniques, from the analytical point of view, arises from the relatively small chemical shift range (about 10 ppm) as compared with some other frequently studied nuclei. However, high resolution H NMR of solids is useful in studies of molecular dynamics. 

Fig. 4. Quadrupolar powder patterns (a) Spin NMR powder pattern showing that the central -)<- ) transition is broadened only by dipolar coupling, chemical shift anisotropy, and the second-order quadrupolar interactions, (b) Spin 1 NMR powder pattern for a nucleus in an axially symmetric electric field gradient (see text). The central doublet corresponds to 6 = 90° in Eq. (10). The other features of low intensity correspond to 6 = 0° and 6 = 180°. (c) Theoretical line shape of the ) - -) transition of a quadrupolar nuclear spin in a powder with fast magic-angle spinning for different values of the asymmetry parameter t (IS) ...

Spectra of solids arc complicated, because of the multiplicity of parameters involved, especially by anisotropic interactions as dipolar coupling. Many techniques both experimental or computational have been developed for interpretation. A technique particularly useful for catalysis permits to selectively suppress anisotropic contributions by mechanical rotation of the sample (magic angle spinning, MASNMR) and by rotation of the nuclear magnetic dipoles with sequences of radiofrcqucncy pulses. 

Magic-Angle Spinning. One technique is to spin the sample at the so-called "magic angle" of 54.74°, which minimizes the spin-spin interaction effects In the dipolar expansion rewritten in terms of the dipole-dipole interaction between two dipoles fii and /i , with mutual angle of orientation (1 ... 

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