An analytical treatment of electron spectral saturation for dynamic nuclear polarization NMR of rotating solids

Abstract

Saturation of electron magnetization by microwave irradiation under magic-angle spinning (MAS) is studied theoretically. The saturation is essential for dynamic nuclear polarization (DNP) enhancement of nuclear magnetic resonance signals. For a spin with a large g-anisotropy and a long T1 relative to the rotor period, the sample rotation distributes saturation to the whole powder sample spectrum. Analytical expressions for the saturation and frequency profiles are obtained. For a pair of coupled electrons such as those in bis-nitroxides, which are commonly used for MAS DNP, an el– er model (where el and er stand for electrons on the left and the right, respectively, in their spectral positions) is introduced to simplify the analysis of a coupled two-spin system under MAS. For such a system, strong electron couplings exchange magnetization during dipolar/ J rotor events when the two electron frequencies cross each other. The exchange is equivalent to a swap of the el and er electrons. This allows for the treatment of a coupled spin pair as two independent spins such that an analytical solution can be obtained for the steady-state magnetization and the difference between the two electrons. The theoretical study with its analytical result provides a simple physical picture of electron saturation under MAS and of how radical properties and experimental parameters affect cross-effect DNP. The effects of depolarization and the extension to more coupled electron spins are also discussed using this approach.