Calculations Of The Distribution Of The Director In The Nematic Liquid Crystal Cell Using Finite Elements Method

Calculations of the distribution of the director in the liquid crystal cell and change with electromagnetic field are thought as the basis for studying display characters of liquid crystal devices. Solving differential equation definite conditions problem is the standard method to calculate the distribution of the director in the liquid crystal cell. But to a lot of questions, there are seldom analytic solutions. The finite elements method is a numerical calculation method to solve maths and physics problems which based on variation principle. In the elasticity theory of nematic liquid crystals(NLC), physics principles are described by variation problem initially. So in this paper we use finite elements method to solve this variation problem directly. To calculate the distribution of the director in the strong and weak anchor planar alignment NLC cell which is in magnetic field respectively. The results are same to those got by solving differential equation definite conditions problem.It is another hot point to study the surface elastic free energy of liquid crystal. It is known in NLC that the Nehring-Saupe free energy is not bounded from below due to the presence of the kn surfacelike elastic term which taking into account the second order derivative of the director. Thus, a minimizing director field cannot be found in the class of continuous functions. According to [4], the k surfacelike elastic term favors the occurrence of a surface discontinuity of the director field at the interfaces of the NLC cell. There is a paradox between discontinuity of director field and suppose of continue theory of NLC. This is termed "the Oldano-Barbero Parodox" and has been the object of some debate in many literatures.In recent years, different theoretical approaches have been proposed in the literature to bypass this problem. But every approaches all cann't solve this problem perfectly. And it is the focus of this problem that whether there is the kn surfacelike elastic term or not. In this paper, we study this problem by means of finite elements method. The main results as follow :(1) There is a discontinuity of the director field at the plate interfaces of the tile angle antisymmetric strong anchor NLC cell due to the presence of the kn surfacelike elastic term. The distribution of the director change regularly with different k^. Thedirection of change is according to the sign of These numerical results are same to those got by Ritz method[13].(2) In the weak anchor planar alignment NLC cell which is in the magnetic field, the distribution of the director change regularly with different kn when we use two-node interpolation. When kn/kn is positive, the tile angle of the director became small. And when kn/kn is negtive, the direction of change of the director tile angle is contrary. Surged curves with fixed period appear when by three-node interpolation, this result need much more debate and further research.