Electron Paramagnetic Resonance Line Shifts and Line Shape Changes Due to Spin Exchange between Nitroxide Free Radicals in Liquids. 3. Extension to Five Hyperfine Lines. Additional Line Shifts Due to Re-encounters
The work in part 2 of this series (J. Phys. Chem. A 2002, 106, 4846) is extended experimentally and theoretically to include inhomogeneously broadened nitroxide spectra consisting of five hyperfine lines due to coupling to two equivalent 14N nuclei. The nitronyl-nitroxide 1-H-imidazol-1-yloxy-4,5-dihydro-4,4,5,5-tetramethyl-2-(o-nitrophenyl)-3-oxide, which is severely inhomogeneously broadened by unresolved hyperfine structure in the absence of spin exchange, is studied under conditions in which the spin-exchange frequency, ωe, varies from near zero to more than half of the hyperfine spacing. In common with part 2 of this series, as ωe increases we find the following: (a) each line is the sum of one absorption and one spin-exchange-induced “dispersion” line; no other terms are needed over the entire range; (b) intensity moves from the outer lines to the central line; (c) the outer lines are broadened slightly faster than predicted by perturbation theory; (d) the amplitudes of the “dispersion” components lead to a determination of ωe; (e) the experimental line shifts differ substantially from those predicted theoretically. Items a−e are unaffected theoretically by adding unresolved hyperfine structure which inhomogeneously broadens the lines. The discrepancy in item e is addressed by including spin precession during the spin-exchange act and re-encounters of the same spins during one collision. These additions to the theory yield an additional line shift that is proportional to ωe. From the additional shift, the time between re-encounters is estimated to be τD ∼ 10-10 s which is of the correct order of magnitude as estimated from a Stokes−Einstein diffusion model. Inclusion of the effect of re-encounters in the theory may permit a deeper understanding of the collision process as a function of liquid structure.