With The Molecular Field Theory To Calculate The Order Parameter Of The Liquid Crystal Blue Phase

As far as the theoretical description of the blue phases of chiral liquid crystals is concerned, Ginzburg -Landau theory has been using up to now. This theory is based on an assumed Landau free energy expanded in powers of the order parameter and its spatial derivatives. There has been a lot of work applied Landau theory to investigate the blue phases. To the best of our knowledge, there is no successful molecular theory of the blue phases to date.In this article, the molecular theory of the blue phases of chiral liquid crystals is proposed, that is, beginning with the potential between two molecules, by using cell model of liquid, applying statistical physical method, the distribution function and the free energy of the system are obtained. Following, by using the variational method, the differential equations that the order parameter tensors of the blue phases can satisfy are obtained. For simplifying the calculation, the order parameter tensor Q is replaced by the vector T of the 5X1 matrix. Besides, we sum up the question to be the eigenvalue problem in the quantum mechanics. Considering the symmetry of the blue phases, the orderparameter tensors of the blue phases BP I and BPII can be formed by using the eigenvectors. Their expressions are the same with Landau' s. Through calculating the coefficients of the order parameter tensors can be obtained in the located system, which is close to the predecessors' result.