A Unified Description of the Spin−Spin and Spin−Lattice Relaxation Rates Applied to Nitroxide Spin Labels in Viscous Liquids

Abstract

For nitroxide spin labels the application of electron and nuclear spin relaxation theory has caused a seeming paradox to develop, even in the fast motion limit. Two well-resolved EPR lines are seen when using 15N nitroxide spin labels (or three lines with 14N nitroxide spin labels) due to the interaction of the electron with the nitrogen nucleus. The observed line widths are related to the spin−spin relaxation rates. The different widths indicate that the spin−spin relaxation rates for the two (or three) lines depend on the nuclear manifold, or nuclear spin state z quantum number. The theory (developed by Kivelson and Freed) treated each line independently and gave a quantitative accounting of the differences seen in the relaxation rates of the lines. When the same treatment is applied to the spin−lattice relaxation rates, a strong dependence of the spin−lattice relaxation rate on the particular line (nuclear manifold) chosen is predicted. However, the experimental spin−lattice relaxation rates show no dependence on the nuclear manifold (nuclear quantum number). The treatment presented here shows that by following the operator method of Abragam one can develop a consistent picture for both spin−lattice relaxation and spin−spin relaxation that leads to theoretical predictions that agree with the experimental results.