Investigation of variable angle sample spinning (VASS) NMR of quadrupolar nuclei. I. Theory

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Abstract
Variable angle sample spinning NMR of quadrupolar nuclei in the solid state has been theoretically investigated in order to determine the optimal angles to achieve high-resolved and quantitative spectra. The earlier literature contributions have been included in a more general model. Complete analytical expressions were derived and are reported for all possible cases. It is concluded that magic angle spinning (at 54.7°) is to be used whenever the dipolar interactions and/or the chemical shift anisotropy dominate the spectra. For the other cases, θ=43.5° (which would allow an easy discrimination of the quadrupolar frequency and the asymmetry parameter), and θ=60°–70° (where the linewidth is half of that obtained for MAS conditions) are proposed as preferred spinning angles.