Theory of Nuclear Magnetic Relaxation by Spin-Rotational Interactions in Liquids

The contribution of spin-rotational interactions to the nuclear magnetic relaxation of identical spin-½ nuclei at equivalent positions in spherical liquid molecules is calculated by use of the semiclassical form of the density-operator theory of relaxation, and the result is compared with the contributions of intra- and intermolecular dipole-dipole interactions. The angular velocity of a molecule is treated classically by assuming that it obeys an equation analogous to the Langevin equation that is postulated in treatments of translational Brownian motion. The change in orientation of a molecule is assumed to be due to isotropic rotational Brownian motion. By use of this model the correlation functions of components of the angular velocity of a molecule are calculated, and are found to have an exponentially decaying time dependence with a time constant (correlation time) ${\tau }_1$ that is quite different in its temperature dependence than the correlation time ${\tau }_2$ of the dipole-dipole interactions. In typical situations ${\tau }_1$ is much smaller than ${\tau }_2$. Use is made of this fact to evaluate the correlation functions of the functions of the orientation and angular velocity that occur in the tensor spin-rotational interactions. The result that ${\tau }_1\ll {\tau }_2$ explains the experimentally observed "quenching" of the relaxation effect of spin-rotational interactions in liquids, and the result that ${\tau }_{1}T$ increases as the temperature increases explains the experimentally observed temperature dependence of the relaxation effect of spin-rotational interactions in liquids.