Molecular theory of elastic constants of liquid crystals: application to uniaxial phases

Abstract

We use density-functional theory to derive an expression for the distortion free energy of molecular ordered phases and expand it in terms of the order parameters characterizing the structure of the phase and the molecular correlation function of an effective isotropic liquid. We derive expressions for the elastic constants of the uniaxial nematic and smectic-A phases of the liquid crystals and express the results in terms of the spherical-harmonic coefficients of the direct pair-correlation function of the effective isotropic liquid. These harmonic coefficients are obtained by solving the Ornstein-Zernike equation using the Percus-Yevick closure relation for a hard-core system and using a perturbation method for a model system interacting via a pair potential that has angle-dependent attractive parts in addition to hard-core repulsion. It is shown that the repulsive part of the pair interaction makes a dominant contribution to the elastic constants of the liquid crystals.