Stochastic Theory of Dynamic Spin Polarization in Viscous Liquids with Anisotropic Electron-Spin Relaxation

A previously developed theory of dynamic nuclear polarization (DNP) in liquids is extended and applied to viscous liquids with anisotropic electron-spin relaxation ($T_{1e}\gg T_{2e}$). It is based on a Schrödinger equation for two spins, $S$ and $I$, in which the influence of the "lattice" motion is incorporated by a randomly time-dependent field acting on the spin $S$ and a random time dependence of the dipole interaction between $S$ and $I$. The quantum-mechanical equations of motion in an applied rotating field near $S$-spin resonance are solved and the DNP of the $I$ spin is expressed in terms of the stochastic parameters which characterize the liquid motion. Using values of these parameters as obtained from EPR and NMR experiments on two dilute organic radical solutions, one finds excellent agreement with our DNP measurements on these systems as reported in the preceding paper. It is characteristic of these solutions that the NMR requires a distribution of relaxation times. The analysis of DNP measurements confirms this; it gives a somewhat different distribution and permits a more specific correlation between it and the structure of the liquid. The range of applicability of the theory is discussed, and in an appendix a completely general set of equations for the two-spin relaxation in our model is derived. Using these, the only restrictions on the application of our theory would be that the $S-S$ as well as the $I-I$ interactions must be small and that the amplitude of the rotating field must be substantially smaller than the constant external field.