A numerical investigation of nematic ordering based on a simple hard-rod model

Abstract

On the basis of a simple functional scaling, we have constructed the direct generalization of the Carnahan–Starling equation for the free energy of a hard sphere fluid to a nematic liquid crystal. The orientational degrees of freedom are completely decoupled from translational ones under that scaling, which is equivalent to the well-known decoupling approximation for the pair correlation function of hard-core fluids. For long rods the generalized free energy reduces exactly to Onsager’s in the low density limit. Numerical calculations have been performed for a variety of the length-to-diameter ratios of hard spherocylinders, with the aid of an accurate iterative solution to the nonlinear integral equation for the orientational distribution function. The predictions made by our calculations are in fairly good agreement with the results of Monte Carlo simulations on a system of rather short rods. We present the calculations of the jump in the order parameter, critical packing fraciton, and the other thermodynamic properties at the isotropic–nematic transition.