Analytic theory of liquid crystalline phenomena

Abstract

This thesis is concerned with the application of analytic theory to the calculation of the properties of thermotropic nematic liquid crystals based on their molecular structure. For these studies we employ the molecular field approximation, which has been shown to give a good qualitative and semi-quantitative understanding of liquid crystalline properties. In the first chapter we give an introduction to liquid crystals and their properties as it pertains to the theoretical studies of later chapters. In the next chapter we lay the necessary foundations in statistical mechanics and introduce the molecular field approximation as a theoretical framework within which we develop the molecular field theories which we employ subsequently. We begin our studies by considering the application of an electric field to a nematic monodomain, a procedure that has potential applications in the production of non-linear optical devices. The idea is that by polarising a nematic rather than an ordinary liquid, the polarisation is augmented. Thus we seek to probe the theoretical basis of this by estimating the response of the order parameters to the field using molecular field theory. In the next chapter we move on to consider the composition dependence of order parameters in binary mixtures where the solute is less anisotropic than the solvent. This is to investigate the validity of extrapolation procedures commonly used in experiment to obtain values for properties of non-mesogenic compounds intrinsic to the compound in question, in a hypothetical pure nematic state. In the final chapter we undertake to predict the properties of liquid crystal dendrimers, a fascinating new class of highly fiexible mesogenic molecule. Here the problem of the very great conformational fiexibility is addressed and a solution is presented involving a hybrid methodology that draws on both molecular field theory and Monte Carlo computer simulation techniques.

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