The Micrtoscopic Theory For BPⅠ And BPⅡ Of The Blue Phase

During recent 30 years, The blue phase of liquid crystal has attracted much attention. The physical nature of BPI (the first subphase of blue phase) and BPII(the second subphase of blue phase)have the symmetry of space group. As a liquid, the blue phase shows the 3D-space group symmetry, just like crystals, which arouses people's interest.As to the theory of the blue phase, up to now, the common works were carried out within the framework of the Ginzberg-Landau's theory (we call these theories the Ginzberg-Landau's phenomenology theory). In these theories the form of order-parameter tensor of BPI, BPII were given according to the space symmetries of the blue phase determined by experimental results. And the free energies were proposed. Based on the free energy, the phase diagram of the chiral liquid crystal among BPI, BPII, BPIII, cholesteric phase and isotropic phase can be obtained. Then the order parameter tensors of BPI, BPII are determined by comparison with the experimental results, therefore, the structure of BPI and BPII can be get to know. However, the phenomenology theory is unrelated to the microscopic mechanism of blue phase's forming, i.e., what kind of molecular and their interaction may respond to the blue phase. In this paper, a statistical theory of the blue phase of chiral liquid crystal is proposed. The form of the interaction potential between molecules is assumed to be the same with which is used in the theory of cholesteric phase. Using the method of the cell-model of the liquid statistical theory, we deduce the distribution function of molecule. The derived free energy of the system obtained, has the same form with the Ginzberg-Landau's phenomenology theory.The differential equation of the tensor order parameter is obtained by the variation of free energy. The coefficients corresponding to those of Landau free energy are associated with some kinds of statistical average, so they are related to temperature. Using the molecular interaction potential, with proper potential parameters, we also calculate the order-parameter tensors' phases which are depended on the reduced temperature. The theoretical calculated results can be compared with experiment's.