Generated By The Interaction Of Molecules In Nematic Liquid Crystals By Phase Transition

In nematic liquid crystal, the anisotropy of the molecular shape leads to phase transitions from isotropic phase to nematic, from unixial nematic to biaxial nematic. In order to investigate the influence of molecular shape to the phase transitions, a simple model of a rigid biaxial liquid crystal molecule is proposed. Here the molecule is considered as three perpendicular long rods. Using interaction energy of singl(?)-rod-like molecule, the interaction energy of rigid biaxial molecule is obtained by the superposition of all rod-to-rod interactions. Using mean field theory, orientation distribution function, partition function and free energy are obtained. Finding the minimum value of the free energy, the non-linear equations of order parameters in equilibrium states are obtained. The numerical solutions of order parameters show that when temperature decreases the system consisted by uniaxial molecules will have a first-order phase transition from isotropic to positive nematics. When the degree of biaxiality increases, the system will have a second-order phase transition from positive nematic to biaxial nematics, then from biaxial to negative nematics. The phase diagram in the plane of reduced temperature and structure parameter is given. In order to discuss the possible measurement of order parameters, NMR quadrupole splitting in liquid crystal is considered. A general relationship between spectrum frequency splitting and biaxial order parameters is derived.