Density-functional theory of curvature elasticity in nematic liquids. I.

Abstract

A density-functional theory for the Frank elastic constants described in an earlier paper is reformulated and simplified. The excess free energy of aligned nematic liquids subjected to curvature (i.e., ``splay,'' ``twist,'' and ``bend'') deformations is written in terms of the direct correlation functions of the isotropic liquids. This leads to expansion of the elastic constants in successively higher-order direct correlation functions. The truncation of this series at an early stage is found to introduce large error. The number of terms explicitly considered and the use of a [1,0] Pad\'e approximant make our calculation reliable. The other expansion which our theory involves is one in powers (products) of order parameters. These order parameters are the coefficients of a spherical harmonic expansion of an orientational singlet distribution. The convergence of this series is also tested for a simple model of hard ellipsoids of revolution. Qualitative features exhibited by our calculation for both ordinary and discotic nematics are in agreement with the results of previous workers and experiments. While this paper focuses on the role of packing forces the theory can be generalized to include dispersion and other long-range interactions, noncylindrical geometry, and nonrigidity of molecules.