DENSITY-FUNCTIONAL APPROACH TO STUDY THE ELASTIC-CONSTANTS OF BIAXIALNEMATIC LIQUID-CRYSTALS

A density functional theory for bulk and surface elastic constants of biaxial nematic liquid crystals is developed. It is based on a functio nal Taylor expansion of the free energy of a distorted biaxial nematic with respect to the one-particle distribution function. Detailed micr oscopic expressions for the biaxial elastic constants of bulk and surf ace deformations are derived by expanding further the distribution fun ctions into symmetry-adapted Wigner matrices. The final expressions de pend on generalized orientational order parameters characterizing the biaxial nematic and on expansion coefficients of the direct pair corre lation function. The case where the expansions are truncated at the lo west nontrivial order with respect to the momentum index of the Wigner matrices is analyzed in detail. It gives only six-distinct, nonzero b ulk elastic constants. The mixed elastic constants, which measure dist ortions of more than one director, vanish within this approximation. A s in the uniaxial case, a splay-bend degeneracy for all directors is a pparent. The theory is next applied to the biaxial nematic phase recen tly studied by Biscarini et al. [Phys. Rev. Lett. 75, 1803 (1995)] pro viding numerical estimates of biaxial elastic constants for the case o f thermodynamically stable biaxial ordering. It is shown that the valu es of the elastic constants connected with secondary directors are muc h lower than those associated with the primary one. (C) 1998 American Institute of Physics.