Landau Theory And The Application Of It In Liquid Crystal

The impact of magnetic field, electric field on the liquid crystal molecules has been studied in this paper with the Landau theory,and the relations of the free energy expansion coefficients of Landau theory and Frank theory are also studied.On the basis of Landau theory and the continuum theory of elastic deformation of liquid crystal, using finite-difference iterative method, under the magnetic field and electric field, the spatial distribution of nematic liquid crystals molecules and order parameter in the second Freedericksz transition has been derived, most of the parameters are used in references, the results obtained is consistent with the theory and the results of the literature.The boundary graphics of the sequence parameters and the liquid crystal molecules have a mutation. In order to explain and explore the reasons for this change, we consider the influence of the order-electricity energy for the liquid crystal molecules, and computer simulation and numerical results are discussed.Frank theory and Landau theory have been put on the liquid crystal and used as two basic theories, but the expressions of the free energy density of the two theories are different. We derive the relationship of the two expansion coefficients on the base of the first (or third) Freedericksz transition of nematic liquid crystal, and also deduced the relation between the coefficient of elasticity and the outfield when the sequence parameter is a determined value, according to the pre-changing magnetic field and pre-changing electric field of the second Freedericksz for nematic liquid crystal box, we get the relations for order expansion of Frank elastic constants of the free energy.