Study On Nematic And Blue Phase In Liquid Crystals

Liquid crystal is an important kind of soft condensed matter as well as functional material. Liquid crystalline state has orientation order and it contains different phases. In macroscopic volume, if the director is uniform, this is nematic phase; if the director changes periodically at the space of one dimension, this is the cholesteric phase; if the director changes periodically at the space of three dimensions, this is the blue phase. The microscopic theory of liquid crystals is studied in this article in which two parts are divided:1. The microscopic theory of nematic phase.Liquid crystal is essentially a kind of classical fluid. Up to now, classical theories have been used widely. Considering that the liquid crystals are many-body system, so many-body effect or collective excitation can have an important effect on macroscopic properties. Because quantum theory methods have been developed very maturely, the spin wave theory is adopted to research the nematic liquid crystals in this article.Since the orientation of the molecular long axis and the angular momentum of the molecule rotating around its long axis have the same direction, operators can be introduced to express the orientation of the molecules. Using the cell model and the Holstein-Primakoff transformation, the Hamiltonian of the system can be obtained, which has the same form as that of the ferromagnetic substance. The relation between the order parameters and reduced temperature can be gotten. It is in good agreement with the experimental results at low temperature region, the accordance is better than that of the molecular field theory and the computer simulation. At high temperature region close to the transition point, by considering the higher-order effect, theoretical values are in accordance with the experimental ones, too. That indicates the many-body effect (collective excitation) is important.2. Microscopic theory of the blue phase.As far as the theoretical description of the blue phases of chiral liquid crystals is concerned, Ginzburg-Landau theory has been used. That is phenomenological theory and can not explain themicroscopic mechanism of the blue phases, so we proposed the microscopic theory of the blue phases.The space group symmetry of BP I and BP II are originated from that the orientations of the molecular long axis are different in each point and have the symmetry of the space group. The properties can be reflected by the order parameter tensor, which is the function of the space position vector. Beginning with the potential between two molecules, by using the cell model of liquid, the distribution function can be gotten. Then we can obtain: (1) The free energy of the system. It can be expressed as the function of the order parameter tensor, which is the same as the results of Ginzberg-Landau's phenomenological theory. (2) The differential equation that the order parameter tensor of the blue phase. The expressions of the order parameters of BPI and BPII can also be acquired by calculation, which respectively have the symmetry of a space group 0s and O2. The relevant parameter tensors are calculated numerically which is in accordancewith the experimental results.Quantum theory methods are adopted in the two parts work of this article. In the first part it is used is due to the physical reason, while in the second part is due to the mathematical method reason.