Molecular model of biaxial ordering in nematic liquid crystals composed of flat molecules with four mesogenic groups

Relative stability of uniaxial and biaxial nematic phases is analyzed in a model nematic liquid crystal composed of flat molecules of C2h symmetry with four mesogenic groups rigidly linked to the same center. The generalized effective quadrupole mean-field potential is proposed and its constants are evaluated numerically for the pair intermolecular potential based on Gay-Berne interaction between mesogenic groups. The dependencies of the constants on molecular shape parameters are systematically analyzed. Order parameters of the uniaxial and biaxial nematic phases are evaluated by direct minimization of the free energy at different temperatures. The corresponding phase diagrams are obtained enabling one to study the effects of molecular model parameters on the stability regions of uniaxial and biaxial phases. The results are used to clarify the nature of experimentally observed biaxial ordering in nematic liquid crystals composed of tetrapode molecules with the same symmetry.