Relations Between Rotational Diffusion nd Frequency Sepctra of Nematic Liquid Crystals

Abstract

A critical analysis of the frequency regime which contributes to rotational diffusion in nematic liquid cryatals is made utilizing a rigorous molecular description and a requencey dependent friction constant. The equation of motion of a molecule is written in tensor form, since nematic liquids are anisotropic, and is t hat of a damped harmonic librator assuming a delta function external torque. A set of relaxation times is assumed and the role of different frequency regimes is analysed critically. The analysis shows that a high frequency cutoff in the hydrodynamic regime is inconsistent with experimental diffusion times. This result shows that high or intermediate frequencies are more significant than low frequency hydrodynamic modes in diffusion in nematics. The zero sound regime of frequencies, modified by molecular collisions, is found to be closer than the hydrodynamic regime to the predominant frequencies in rotational diffusion in nematics, which are in the range of 10¹¹ to 10¹² Hz-a frequency regime closer to that known to predominate in translational and rotational diffusion in isotropic liquids. The possibility that the molecular mass dependence of the rotatioinal diffusivity of cybotactic groups is m ^−3/2 rather than m ^−½, which is typical of monoatomic diffusion, is discussed.