Modeling Liquid Crystal Director Configuration

In order to model the liquid crystal director configuration, we must first know how Uquid crystals interact with externally applied electric fields. Many liquid crystal devices make use of uniaxial nematic liquid crystals which are dielectrics. We consider the electric energy of nematic liquid crystals in externally applied electric fields through dielectric interaction. A typical liquid crystal device cell is shown in Figure 7.1, where the liquid crystal is sandwiched between two parallel substrates with transparent electrodes. The electric energy of the liquid crystal is given by [11-13]. 

Before outlining the effect of fields on the orientation of the director, it must be emphasized that surface interactions and boundary conditions are usually of importance. The models applied here assume that there is a well-defined director distribution in the absence of any external field, and in practice this can only be provided by suitable treatment of boundary surfaces. The strength of surface interactions must also be considered as this will influence the equilibrium director configuration in the presence of a field. For the simplest description of field effects in liquid crystals it is usual to assume an infinite anchoring energy for... 

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