Electric-Field Fluctuations and Spin Relaxation in Liquids

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Abstract
The intermolecular potentials in liquids are modulated by the motion of the molecules, and the electron spin in an s=½ molecule senses this variation in electric field through spin—orbit coupling. The three most important nonrotational mechanisms, the Van Vleck direct process, the Van Vleck—Raman process, and the Orbach process have been studied. The Raman process is negligible compared to the direct process unless ω02τc2≪1, where ω0 is the Zeeman frequency and τc is a mean correlation time for intermolecular fluctuations; under these conditions the direct process is proportional to the applied field squared and the Raman process is independent of field, but both processes appear to be of minor importance. If ω02τc2≫1, the Raman effect is negligible; the direct process is independent of applied field and probably not important. Even at ω02τc2≈1, the direct process is probably insignificant compared to other mechanisms such as spin—rotational relaxation. The Orbach process is significant if (δ0nℏ/kT) is not too large, i.e., less than six, where δ0nℏ is the excitation energy to the first excited state; this condition holds for symmetrical radicals in solution, i.e., for radicals that are orbitally degenerate in the gas phase. This mechanism may explain the anomalous ESR linewidths of Cu(H2O)6++, benzene− and coronene−. The Orbach process is independent of applied field and is proportional to τc−1; this correlation time can be related to the correlation time that enters into expressions for ir and Raman vibrational relaxation. In the absence of a low‐lying excited electronic state, the Orbach process vanishes and rotational relaxation mechanisms dominate.