Theory of Birefringence of Nematic Liquid Crystals

Abstract

A theory of the birefringence of nematic liquid crystals is de- veloped taking into account the intermolecular potential energy arising from dipole-dipole, anisotropic dispersion, induction and repulsion inter- actions. The potential energy exhibits a dependence on molecular orientation and is expressible ae - (uo + u1 cost9 + uz cosat9 + u4 cos48 + u6 cosee + ...) where t9 is the angle which the long axis of the molecule makes with the uniaxial direction of the liquid crystal. The birefringence of the medium is evaluated in terms of the Boltzmann distribution of the oriented mole- cules. The theory explains the experimentally observed result that the temperature coefficient of the extraordumy index is large and negative whereas that of the ordinary index is small and positive. Analysis of the data on p-azoxyanisole and p-azoxyphenetole shows that dispersion and repulsion forces play a predominant role in determining the temperahre variation of the birefringence. Assuming that the molecular librations in the liquid crystal can be represented by a system of harmonic oscillators, the rn librational mnpli- tude is evaluated for p-azoxyaniaole from recent measurements of the ultrasonic velocity. The increase in the rn amplitude With temperature in the nematic range is found to be in good agreement with that obtained directly from the experimental data on birefringence.