Dynamic Theory of Cross Polarization in Solids under High-Speed Magic-Angle Spinning

Abstract

A general dynamic-theoretical analysis of cross polarization (CP) in solids under high-speed magic-angle spinning, based on more precise and consistent definitions of some dynamic and thermodynamic quantities, is presented. Two cases should be distinguished: slow correlation and fast correlation, corresponding to the two situations where τDc ≥ TIS and τDc ≤ TIS, respectively. The fast-correlation condition leads to the prediction that there will occur a monotonic change of magnetization for both rare and abundant nuclei, while in the slow-correlation case, the oscillation of the magnetization prevails in the sideband-matching case. The cross-polarization dynamics under the center-matching regime are quite different from the situation under the sideband-matching condition. The effect of molecular motion on CP dynamics is analyzed. The Hartmann-Hahn matching curve is also discussed and its asymmetric characteristics are explained. From the theoretical analysis, it emerges that CP at high spinning speeds is more effective under the sideband-matching condition.