Blue Phase Iii To Isotropic Phase Transition Of Self-consistent Model

The blue phase III is one product of blue phase in the liquid crystals. Compared with BPI and BPII, BPIII has no exact structure. We can obtain the physical message of BPIII by the phase transition theory between BPIII and Isotropic.At present, there are two methods of the phase transition theory of BPIII. One is phenomenological theory of Landau-Ginzburg-de Germs, the other is statistical field theory describing BPIII -ISO transition. Within the statistical field theory, we calculate the free energy of BPIII-ISO transition by using self-consistent model and cumulant expansion. By this method we obtain self-consistent equation, which not only account for the phase transition between Isotropic and BPIII but also demonstrate the importance of the cubic invariant.According to the method of Englert, we introduce perturbation to calculate the system Hamiltonian. In other words, we define a trial quadratic Hamiltonian .When helicity mode m = 2, the effect of perturbation is obvious. According to the theory of Engiert, we simple the system free energy and only take m - 2 . This predigestion is reasonable. The calculation becomes easy when we eliminate the coupling among different helicity modes. We can discuss the relation between temperature r and inverse correlation length parameter A during the phase transition between BPIII and Isotropic, then explain the phase transition of BPIII -Isotropic.Self-energy function which we select is the same to that of Lech Longa. Using the theories of Bogolyubov-Hellman-Feynman (BHF) and mean-spherical approximation, we get the system free energy within the four-order self-consistent cumulant expansion. According to the conditions of equilibrium state and self-consistent equation, we can obtain the relation between temperature r and inverse correlation length A . Although Lech Longa et al have calculated the system Hamiltonian within third-order self-consistent cumulant expansion, they did not analyse the variety of the line of phase transition. We calculate the system Hamiltonian within four-order self-consistent cumulant expansion and make up their deficiency. When the temperature is near to zero, there are two points of intersection in the line of phase transition of Lech Longa and that of us, which Lech Longa do not obtain. These show that our dates are close to the idealresult and our phase diagrams are perfect.In this paper, we discuss the free parameter of energy scale of the fluctuations a and cutoff radius A with the simple calculation of phase transition between Isotropic and BPIII. Using the phase translation theory, we analyse the relation between the specific heat and temperature.blue phase III;order parameter tensors;phase transition...