Theory of Birefringence of Nematic Liquid Crystals

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Abstract
A theory of the birefringence of nematic liquid crystals is developed taking into account the intermolecular potential energy arising from dipole-dipole, anisotropic dispersion, induction and repulsion interactions. The potential energy exhibits a dependence on molecular orientation and is expressible as - (u 0 + u 1 cosθ + u 2 cos2θ + u 4 cos4θ + u 4 cos4θ + …) where θ 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 molecules. The theory explains the experimentally observed result that the temperature coefficient of the extraordinary 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 temperature variation of the birefringence. Assuming that the molecular librations in the liquid crystal can be represented by a system of harmonic oscillators, the rms librational amplitude is evaluated for p-azoxyanisole from recent measurements of the ultrasonic velocity. The increase in the rms amplitude with temperature in the nematic range is found to be in good agreement with that obtained directly from the experimental data on birefringence.

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