Stochastic Theory of Dynamic Spin Polarization in Viscous Liquids with Anisotropic ElectronSpin Relaxation
Abstract
A previously developed theory of dynamic nuclear polarization (DNP) in liquids is extended and applied to viscous liquids with anisotropic electronspin relaxation (T_{1e}>>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 timedependent field acting on the spin S and a random time dependence of the dipole interaction between S and I. The quantummechanical equations of motion in an applied rotating field near Sspin 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 twospin relaxation in our model is derived. Using these, the only restrictions on the application of our theory would be that the SS as well as the II interactions must be small and that the amplitude of the rotating field must be substantially smaller than the constant external field.
 Publication:

Physical Review A
 Pub Date:
 October 1971
 DOI:
 10.1103/PhysRevA.4.1539
 Bibcode:
 1971PhRvA...4.1539L