Theoretical aspects of dynamic nuclear polarization in the solid state--spin temperature and thermal mixing

Dynamic nuclear polarization is a method which allows for a dramatic increase of the NMR signals due to polarization transfer between electrons and their neighboring nuclei, via microwave irradiation. These experiments have become popular in recent years due to the ability to create hyper-polarized chemically and biologically relevant molecules, in frozen glass forming mixtures containing free radicals. Three mechanisms have been proposed for the polarization transfer between electrons and their surrounding nuclei in such non-conducting samples: the solid effect and cross effect mechanisms, which are based on quantum mechanics and relaxation on small spin systems, and thermal mixing, which originates from the thermodynamic macroscopic notion of spin temperature. We have recently introduced a spin model, which is based on the density matrix formalism and includes relaxation, and applied it to study the solid effect and cross effect mechanisms on small spin systems. In this publication we use the same model to describe the thermal mixing mechanism, and the creation of spin temperature. This is obtained without relying on the spin temperature formalism. Simulations of small model systems are used on systems with homogeneously and inhomogeneously broadened EPR lines. For the case of a homogeneously broadened line we show that the nuclear enhancement results from the thermal mixing and solid effect mechanisms, and that spin temperatures are created in the system. In the inhomogeneous case the enhancements are attributed to the solid effect and cross effect mechanisms, but not thermal mixing.