Elastic Coefficient Of Biaxial Nematic Liquid Crystal Mixture System

A binary mixture system of nematic liquid crystal system is considered, and general shape molecules are abstracted into three perpendicular rods. Firstly, under the assumption of ideal phase order, using superposition of rod-to-rod interaction energy, the total interaction energy of liquid crystal system and the elastic energy density of the system in Saupe’s form are derived. Simple analytical relationships between the elastic constants and interaction strength, molecular structure, order parameters, component ratio are obtained. Then the relationships between elastic constants and molecular structures are discussed. Secondly, considering the fact that the molecular rods will deviate from the local biaxial directors due to thermal motion, it is necessary to average the molecular rods’ orientation in the director coordinates. Under the non-ideal phase order assumption, the elastic constants as functions of molecular structure, interaction strength, component ratio, order parameters are obtained. This method can be generalized to triple (or above) mixture system of biaxial nematic liquid crystal with other types of molecular structure.A binary mixture system composed by two types of V-shaped liquid crystal molecules is considered. Assuming a simple interaction energy between rods, and using superposition of rod-to-rod interaction energy, simple analytic relationships between the elastic constants and interaction strength, molecular structures, order parameters, component ratio are obtained. When the angle of one type of V-shaped molecule is 180°, the system is simplified as a mixture of rod-like and V-shaped molecules. Because of the coupling between the bent shapes of molecules with bend distortion, a biaxial nematic phase may be induced in the binary system. Consider the fact that the splay deformation has little influence on molecular short axis orientation, system may still be in an uniaxial nematic phase. Therefore, for each case, i.e., biaxial and uniaxial nematic phases, two ideal phase orders are assumed respectively. The relationship between the ratio of bent, splay elastic constants and the molecular shape, component ratio of rod-like to V-shape molecules, Y, is obtained from the analytic expression of elastic constants. The results show that the structure of V-shaped molecule has a significant contribution to the decreasing of γ.