MOLECULAR THEORY OF ELASTIC-CONSTANTS OF LIQUID-CRYSTALS .2. APPLICATION TO THE BIAXIAL NEMATIC PHASE

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 w ritten in terms of order parameters characterizing the nature and amou nt of ordering in the phase and the structural parameters which involv e the generalized spherical-harmonic coefficients of the direct pair c orrelation function of an effective isotropic liquid, the density of w hich is determined using a criterion of the weighted density-functiona l formalism. Using a reasonable guess for the values of the order and structural parameters we estimate the relative magnitudes of these con stants. The values of three constants, which are associated with the d eformations confined to a plane perpendicular to the principal directo r (N) over cap, are (three or four) orders of magnitude smaller than t he other constants. Two of the three mixed modes which arise because o f biaxial ordering and vanish in the uniaxial phase are also about one order of magnitude smaller than other constants. In going from the un iaxial to the biaxial phase each constant associated with splay, twist , and bend splits into two and a mixed mode which in the uniaxial phas e is just equal to the difference of splay and twist becomes a new con stant. It is shown that the contributions to elastic constants arising from biaxial ordering and the departure from the axial molecular symm etry are small.