Fast passage dynamic nuclear polarization on rotating solids.

Magic Angle Spinning (MAS) Dynamic Nuclear Polarization (DNP) has proven to be a very powerful way to improve the signal to noise ratio of NMR experiments on solids. The experiments have in general been interpreted considering the Solid-Effect (SE) and Cross-Effect (CE) DNP mechanisms while ignoring the influence of sample spinning. In this paper, we show experimental data of MAS-DNP enhancements of (1)H and (13)C in proline and SH3 protein in glass forming water/glycerol solvent containing TOTAPOL. We also introduce a theoretical model that aims at explaining how the nuclear polarization is built in MAS-DNP experiments. By using Liouville space based simulations to include relaxation on two simple spin models, {electron-nucleus} and {electron-electron-nucleus}, we explain how the basic MAS-SE-DNP and MAS-CE-DNP processes work. The importance of fast energy passages and short level anti-crossing is emphasized and the differences between static DNP and MAS-DNP is explained. During a single rotor cycle the enhancement in the {electron-electron-nucleus} system arises from MAS-CE-DNP involving at least three kinds of two-level fast passages: an electron-electron dipolar anti-crossing, a single quantum electron MW encounter and an anti-crossing at the CE condition inducing nuclear polarization in- or decrements. Numerical, powder-averaged, simulations were performed in order to check the influence of the experimental parameters on the enhancement efficiencies. In particular we show that the spinning frequency dependence of the theoretical MAS-CE-DNP enhancement compares favorably with the experimental (1)H and (13)C MAS-DNP enhancements of proline and SH3.