Theoretical aspects of Dynamic Nuclear Polarization in the solid state - the cross effect.

In recent years Dynamic Nuclear Polarization (DNP) signal enhancement techniques have become an important and integral part of modern NMR and MRI spectroscopy. The DNP mechanisms transferring polarization from unpaired electrons to the nuclei in the sample is accomplished by microwave (MW) irradiation. For solid samples a distinction is made between three main enhancement processes: Solid Effect (SE), Cross Effect (CE) and Thermal Mixing (TM) DNP. In a recent study we revisited the solid state SE-DNP mechanism at high magnetic fields, using a spin density operator description involving spin relaxation, for the case of an isolated electron spin interacting with neighboring nuclei. In this publication we extend this study by considering the hyper-polarization of nuclei in systems containing two interacting electrons. In these spin systems both processes SE-DNP and CE-DNP are simultaneously active. As previously, a quantum description taking into account spin relaxation is used to calculate the dynamics of spin systems consisting of interacting electron pairs coupled to (core) nuclei. Numerical simulations are used to demonstrate the dependence of the SE- and CE-DNP enhancements on the MW irradiation power and frequency, on electron, nuclear and cross relaxation mechanisms and on the spin interactions. The influence of the presence of many nuclei on the hyper-polarization of an individual core nucleus is examined, showing the similarities between the two DNP processes. These studies also indicate the advantages of the CE- over the SE-DNP processes, both driving the polarization of the bulk nuclei, via the nuclear dipole-dipole interactions.