The elastic constants of nematic and nematic discotic liquid crystals with perfect local orientational order

Abstract

Explicit expressions for the Frank elasticity coefficients of nematic liquid crystals are obtained using the model of perfect local orientational order. The use of the density functional approach enables one to express the results in terms of the direct correlation function for a liquid of perfectly aligned particles. Assuming an ellipsoidal shape for the equipotential surfaces, the direct correlation function can be related to that of the sphere fluid by means of the affine transformation. Both rod-like and plate-like molecules are considered. The dependence of the elasticity coefficients on the axial ratio of the molecule is discussed, and the results for the ratio of the coefficients K ₃/K ₁ are found to be in reasonable agreement with experimental data for nematics composed of rigid molecules.