Magnetic field effects in radical pair recombination. II. Spin exchange relaxation and CIDN(E)P in bulk recombination

Abstract

The method of analytical solution of the stochastic Liouville equation developed in the previous paper is applied to derive the Bloch equations describing spin exchange relaxation (SER) and magnetic field effects such as CIDNP and CIDEP in bulk recombination of radicals. Simple analytical expressions for transversal and longitudinal SER rates are obtained which are applicable in the limit |Q|/ Dα 2 ⪡ 1, where Q is the characteristic intraradical magnetic interaction (hfi etc.), D is the relative diffusion coefficient and α −1 is the characteristic size of the exchange interaction potential. These expressions show that in the low viscosity limit | Q| d 2/ D ⪡ 1, where d is the distance of closest approach, the transversal SER rate is equal to the longitudinal one. However in the opposite limit of high viscosity transversal SER rate becomes two times larger than the longitudinal one. These formulae also predict the appearance of significant phase shifts of hfs lines (comparable with the SER line widths) due to SER in the high viscosity limit. The rigorous relation between polarization enhancement in bulk radical recombination and the value of chemically induced dynamic polarization arising in geminate recombination of radical pairs is found. Some experimental investigations of SER and CIDEP in bulk recombination are analyzed by the theory developed. It is shown that such an analysis gives valuable information on the interaction and relative motion of radicals in liquids.