Spin Relaxation in Free Radical Solutions Exhibiting Hyperfine Structure

Abstract

Experimental studies of spin-lattice relaxation in aqueous solutions of the free radical peroxylamine disulfonate ion, ON(${\mathrm{S}{\mathrm{O}}_3)}_2^{--}$, have been made in fields near 30 oersteds. The continuous wave saturation technique was used to study the transition $F=\frac{3}{2}$, $m_F=-\frac{3}{2}\to F=\frac{3}{2}$, $m_F=-\frac{1}{2}$, for which the frequency was 60 Mc ${\sec }^{-1\mathrm{}}$. Because the hyperfine interaction of the unpaired electron with the ${\mathrm{N}}^{14}$ nucleus leads to six unequally spaced energy levels, a unique relaxation time cannot be defined. A general treatment of the saturation method leads to definition of the relaxation probability, which reduces for a system with two energy levels to the reciprocal of twice the relaxation time. The experimentally measured relaxation probability is found to be concentration independent below 0.005 molar in ON(${\mathrm{S}{\mathrm{O}}_3)}_2^{--}$, approaching an asymptotic value of 2×${10}^6$ ${\sec }^{-1\mathrm{}}$. Experiment and theory both rule out as the source for this relaxation probability the interaction of the electron moment with the nuclear moments of the ${\mathrm{H}}_2$O solvent molecules, and theory also rules out the effect of the ${\mathrm{N}}^{14}$ electric quadrupole coupling to solvent motions; the latter can, in principle, effect electron relaxation because of the hyperfine coupling between the ${\mathrm{N}}^{14}$ nuclear spin and the electron spin. Estimates are made of the role played by spin-orbit coupling, and it appears probable that the observed relaxation involves this interaction. An interesting by-product of the analysis of the relaxation probability is the result that second order statistical processes, by which an electron spin is first carried with energy conservation to an excited Stark level before reaching the ground Stark level of opposite spin, may account for the observed relaxation. This process is somewhat similar to the Raman processes invoked by Van Vleck to explain relaxation in the alums, except that in Van Vleck's theory the intermediate excited Stark level is only virtually occupied, without energy conservation.