Theory of Liquid Crystals

A formalism based on cluster expansion for non-uniform fluid is found useful for the discussion of various thoeries of liquid crystals. Using the general formalism the equations which determine the order parameters for transtions in three-dimensional liquid crystals are derived. The proof by Lakatos that there is no phase transition within the approximation of the Onsager integral equation is found not to be correct in general. The isotopicnematic and nematic-smectic transitions in a two-dimensional system of rod-like molecules are estmated, the latter transition point agrees with what Alder and Wainwright estimate for a hard-sphere molecule in two-dimensions.