## Theoretical Aspects of Magic Angle Spinning – Dynamic Nuclear Polarization

Mentink-Vigier, F., et al., Theoretical Aspects of Magic Angle Spinning – Dynamic Nuclear Polarization. J. Magn. Reson., 2015.

http://www.sciencedirect.com/science/article/pii/S1090780715001500

Magic Angle Spinning combined with Dynamic Nuclear Polarization has been proven in recent years to be a very powerful method for increasing solid state NMR signals. Since the advent of biradicals such as TOTAPOL to increase the nuclear polarization new classes of radicals, with larger molecular weight and/or different spin properties have been developed. These have led to unprecedented signal gain, with varying results for different experimental parameters, in particular the microwave irradiation strength, the static field, and the spinning frequency. Recently it has been shown that spinning of the sample imposes DNP enhancement processes that differ from the DNP processes enhancing the nuclear polarizations in static samples. During the sample spinning the DNP enhancements are the results of energy level anticrossings occurring periodically during each rotor cycle. In this work we present experimental results of the MAS spinning frequency DNP enhancement profiles of four nitroxide based radicals at two different sets of temperature 110 and 160 K. These results emphasize the reduction of these enhancements for increasing spinning frequencies. The simulation code calculating MAS-DNP powder enhancements of small model spin systems has been improved to extend our studies of the influence of variations in the interaction and relaxation parameters on powder enhancements. These studies provide a better understanding of the impact of changes in these parameters on the MAS-DNP mechanism. To accomplish this we simulated the spin dynamics of a single three-spin system { e a – e b – n } during its steady state rotor periods and used the Landau-Zener formula to characterize the influence of the different anti-crossings on the polarizations of the system and their necessary action for reaching steady state conditions together with spin relaxation processes. Based on these model calculations we demonstrate that the maximal steady state nuclear polarization cannot become larger than the maximal polarization difference between the two electrons during the steady state rotor cycle. This study also shows the complexity of the MAS-DNP process and therefore the necessity to rely on numerical simulations for understanding parametric dependences of the enhancements. Finally an extension of the three-spin system allowed us to probe the first steps of the transfer of polarization from the nuclei coupled to the electrons to further away nuclei, demonstrating a decrease in the spin-diffusion barrier under MAS conditions.