Molecular Statistical Theory of the Nematic Phase
The counterpart of the phenomenological theory of liquid crystals is the molecular-statistical description. In this chapter we discuss the molecularstatistical theory of nematic and chiral nematic liquid crystals. For reasons of clarity we reformulate the existing theories in such a way that they become accessible to simple analytical treatment. Thus we hope to ensure that the reader may gain clear insight into the status of the present theories with a minimum of effort. Because of the qualitative character of all these theories we do not feel that we jeopardize the real meaning of them by this simplified treatment. First of all we deal briefly with the theory of simple liquids. Then we generalize this theory to the case of anisotropic fluids and we derive an equation of state for nematics. The assumptions involved in this derivation are emphasized in order to avoid the danger that they are obscured by the mathematics. Starting from this equation of state for nematics two well-known approaches are discussed. The first approach is due to Onsager and ascribes the origin of nematic ordering to the anisotropic shape of the molecules, i.e. to repulsive interactions. The second approach, which was formulated by Maier and Saupe, states that the nematic ordering essentially originates from the anisotropic attractive interactions. Next a theory of the chiral nematic phase is presented starting from a model consisting of a Maier-Saupe type interaction and a twist interaction. Finally we give a brief discussion of the relevance of molecular models.
KeywordsPartition Function Hard Sphere Axial Ratio Helmholtz Free Energy Nematic Phase
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