Density-functional theory of curvature elasticity in nematic liquids. III. Numerical results for the Berne-Pechukas pair-potential model

Abstract

The theory for curvature elasticity in nematics described in an earlier paper [Phys. Rev. A 34, 548 (1986)] is applied to a simple model of Berne and Pechukas [J. Chem. Phys. 56, 4213 (1972)] in which the strength parameter ω(r^₁₂,Ω₁,Ω₂) and the range parameter ε(r^₁₂,Ω₁,Ω₂) depend upon the ratio of major to minor ellipsoidal axis and the relative position and orientation of the two molecules. The softness in the repulsion core is found to have a large effect on the value of the Frank elastic constants. The attractive part of the interaction which has the same angle dependence as the repulsive interaction is found to have a small effect on the value of all three constants associated with splay, twist, and bend deformations. Contrary to what has been reported for a single-center, r⁻⁶ attractive potential, the attractive part (more accurately the perturbation potential) of this model makes negative contributions to all three elastic constants. The magnitude of this contribution increases with the length-to-width ratio x₀ of the molecules. However, the value remains very small compared with that of the reference potential, which is also found to increase with x₀ and is always positive. Numerical results for the elastic constants are reported for a range of x₀, temperature, and density. It is shown that with better knowledge of the order parameters P⁻₂ and P⁻₄ and their temperature and density dependence and the potential parameters appearing in the model, one can calculate accurate values of all the Frank constants of any given system. The need to extend the theory to include the flexibility of the alkyl chain and the deviation from the cylindrical molecular symmetry is emphasized.