Molecular statistical theory of nematic liquid crystals

Abstract

Assuming a model based on permanent dipole-dipole, dispersion, induction and repulsion forces, the potential energy of a molecule in a nematic liquid crystal is derived as a function of its orientation. Analysis of the temperature variation of the degree of orientational order in p-azoxyanisole (PAA) and p-azoxyphenetole (PAP) indicates that the permanent dipole interactions are relatively unimportant. Making use of a mean field approximation, a statistical theory of long-range orientational order is developed and the thermodynamic properties of the ordered system are derived relative to those of the completely disordered one. Application of the theory to PAA and PAP shows conclusively that a certain degree of short-range orientational order is present in the liquid phase. Using just three parameters for each compound, viz. the two constants of the potential function and a numerical factor to allow for short range order, the following physical properties have been evaluated which are in quantitative agreement with the experimental data: the long-range orientational order parameter, specific heat and compressibility as functions of temperature in the liquid crystalline range, the latent heat and volume change at the nematic-isotropic transition point. The magnetic birefringence of the liquid phase affords an independent estimate of the short range order which supports the previous calculations.