Molecular theory of elastic constants of liquid crystals. II. Application to the biaxial nematic phase

Abstract

The expression of distortion free energy derived in our earlier paper [Phys. Rev. A 45, 974 (1992)] is used to derive expressions for the 12 elastic constants of a biaxial nematic phase. These expressions are written in terms of order parameters characterizing the nature and amount of ordering in the phase and the structural parameters which involve the generalized spherical-harmonic coefficients of the direct pair correlation function of an effective isotropic liquid, the density of which is determined using a criterion of the weighted density-functional formalism. Using a reasonable guess for the values of the order and structural parameters we estimate the relative magnitudes of these constants. The values of three constants, which are associated with the deformations confined to a plane perpendicular to the principal director N^Λ, are (three or four) orders of magnitude smaller than the other constants. Two of the three mixed modes which arise because of biaxial ordering and vanish in the uniaxial phase are also about one order of magnitude smaller than other constants. In going from the uniaxial to the biaxial phase each constant associated with splay, twist, and bend splits into two and a mixed mode which in the uniaxial phase is just equal to the difference of splay and twist becomes a new constant. It is shown that the contributions to elastic constants arising from biaxial ordering and the departure from the axial molecular symmetry are small.