Phase Transition Study Of Biaxial Columnar Liquid Crystal Mixtures

The study of small particle thermotropic biaxial nematic phase transition is the basis of the liquid crystal physics. Since a biaxial smectic-A(SmAb) has been observed in mixtures of rodlike and platelike molecules, the phase transition and the possibility of stabilizing a biaxial nematic phase caused people’s new attention in mixtures of liquid crystal field. In this paper, two mixture systems of two different component biaxial mesogens are considered:(1) a binary mixture of two different cross-like molecules. Supposing a simple interaction model between molecules, and using mean field approximation, the free energy of the system as a nonlinear function of order parameters is obtained by mean-field theory approximation. By numerical calculations, phase diagrams in the plane of molecular structure parameter rA (the length ratio of short and long rods of A type molecule) and reduced temperature t are obtained. The results show there exists a Landau point, through which the binary mixture can enter directly from isotropic phase to biaxial nematic phase. The optimal molecular structure at this point depends on the structures, the number ratio of A and B type molecules. Mixing rod-like and plate-like molecules with equal numbers will lead to this optimal structure. When rB, the length ratio of short and long rods of B type molecules increases, the rA value at Landau point decreases.(2) a binary mixture of two different V-shaped liquid crystal molecules. In this paper, we abstract a V-shaped biaxial liquid crystal molecule into two linked rod-like arms with the interarm angle a. The interaction energy of the molecule is obtained by the superposition of all rod-to-rod interactions. Using mean field theory, nonlinear equations satisfied by order parameters are derived and the numerical solutions are found. By numerical calculations, the phase diagrams in the plane of reduced temperature and molecular structure parameter are obtained. Relationship between A and B type molecules.at the Landau point is discussed. In order to discuss the stability of a biaxial nematic phase in the mixture system, we assume the interaction between the two different shaped liquid crystal molecules is independent. Comparing the free energy curves corresponding to completely mixed system and phase separated system, we find that by increasing the interaction strength between different types of molecules, increasing temperature, decreasing the structural difference between different molecules, the chance of phase separation will be reduced.