The magnetic field dependence of cross-effect dynamic nuclear polarization under magic angle spinning.

We develop a theoretical description of Dynamic Nuclear Polarization (DNP) in solids under Magic Angle Spinning (MAS) to describe the magnetic field dependence of the DNP effect. The treatment is based on an efficient scheme for numerical solution of the Liouville-von Neumann equation, which explicitly takes into account the variation of magnetic interactions during the sample spinning. The dependence of the cross-effect MAS-DNP on various parameters, such as the hyperfine interaction, electron-electron dipolar interaction, microwave field strength, and electron spin relaxation rates, is analyzed. Electron spin relaxation rates are determined by electron paramagnetic resonance measurements, and calculations are compared to experimental data. Our results suggest that the observed nuclear magnetic resonance signal enhancements provided by MAS-DNP can be explained by discriminating between "bulk" and "core" nuclei and by taking into account the slow DNP build-up rate for the bulk nuclei.