Magic angle spinning rotation frequencies

Figure 1 Schematic representation of the 13C (or 15N) spin-lattice relaxation times (7"i), spin-spin relaxation (T2), and H spin-lattice relaxation time in the rotating frame (Tlp) for the liquid-like and solid-like domains, as a function of the correlation times of local motions. 13C (or 15N) NMR signals from the solid-like domains undergoing incoherent fluctuation motions with the correlation times of 10 4-10 5 s (indicated by the grey colour) could be lost due to failure of attempted peak-narrowing due to interference of frequency with proton decoupling or magic angle spinning.

Application of magic-angle-spinning (MAS), a physical rotation of the sample about a fixed axis, removes the frequency distribution of Equation 1 from the NMR spectrum by averaging the frequency for each nucleus over the rotation path. The angular dependent term in Equation (1) can then be replaced by its value averaged over the rotation ... 

The amplitudes of ring- and main-chain motions of a variety of polystyrenes have been established from the 13C NMR magic-angle spinning sideband patterns of dipolar and chemical shift tensors. The frequencies of the same motions have been determined by TiCC) and TjpCC) experiments. The most prevalent motion in these polymers is restricted phenyl rotation with an average total displacement of about 40°. Both the amplitude and frequency of this motion vary from one substituted polystyrene to another, and from site to site within the same polystyrene. A simple theory correlates the observed ring dipolar patterns with s. 

Rotation of powdered samples involves another difficulty [27,41,42] magic-angle spinning makes the orientation of each crystallite time-dependent. In the presence of substantial chemical shift anisotropy, this modulation leads, after Tr/2 pulses, to unwanted rotor lines [41], which appear in both dimensions and form cross-peaks of their own. The situation becomes even more complicated when or pulses or a train of different pulses is involved, especially if the magic angle is set incorrectly [42]. In addition, the rotational sidebands can be enhanced and the observed peaks correspondingly broadened for certain MAS frequencies [27]. 

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