Director Fluctuations and Spin Relaxation

Abstract

In the preceding chapter, it was found that the magnitudes of the motional frequency components at the Larmor frequency, at twice this frequency, and at zero frequency are important in NMR relaxation. Both spin-lattice and spin-spin relaxation rates are generally governed by random motion of spin-bearing molecules, Typically, a molecule remains in one state of motion for a short time (10-10-10-12 s). After this time, it suffers a collision with one of its neighbors, which changes its state of motion. When the molecule persists in some state of motion for a time of 10-10 s, its motion is expected to have frequency components ranging from zero to about 1010 Hz. Thus, these motional frequencies cover a wide range and contain the frequencies characteristic of NMR experiments. Several dynamic processes are recognized to cause spin relaxation in liquid crystals. The process known as director fluctuations is unique to liquid crystals and was first used to explain light scattering experiments in liquid crystals by Chatelain [6.1]. Other dynamic processes include molecular reorientation, translational motion, and internal rotations as in normal liquids. Director fluctuations involve collective motions of a large number of molecules. In examining the mode spectrum of director fluctuations, the question may be asked whether or not a high-frequency cutoff is needed. If so, should the wavelengths of these modes correspond to a molecular length or a somewhat larger length? The coupling between director fluctuations and individual motions of a single molecule further complicates the matter by introducing cross-terms in the contributions to spin relaxation.