Hard spherocylinders in an anisotropic mean field: A simple model for a nematic liquid crystal

Abstract

A simple model for a nematic liquid crystal is presented, in which the short‐range intermolecular repulsions are represented by repulsions between hard spherocylinders, and the (anisotropic) intermolecular attractions are treated self‐consistently in the mean field approximation. Using scaled particle theory, an expression for the total configurational free energy is derived and from it the equation of state and other thermodynamic properties of the system in the nematic and isotropic phases are obtained. Extensive numerical results for a model system with a molecular length‐to‐breadth ratio of three are compared with available experimental data for the common nematogen p‐azoxyanisole. Excellent qualitative agreement between theory and experiment is obtained: using reasonable values of the two mean field energy parameters, one can predict the nematic→isotropic transition temperature and the ratio γ= (−ρ/T) [(∂ η/∂ ρ)_T/(∂ η/∂ T)_ρ] quantitatively (η and ρ are the nematic order parameter and the number density, respectively) while explaining other aspects of the experimentally observed behavior qualitatively. The central question of the relative importance of intermolecular attractions and repulsions in stabilizing nematic order is discussed in the light of these results and of related work by several other authors.