Orientation-Balances for Liquid Crystals and Their Representation by Alignment Tensors

Abstract

Abstract Up to now there are three different phenomenological concepts suitable to describe liquid crystals: The first one is the well known Ericksen-Leslie theory4 whose balance equations are formulated by use of a macroscopic director for needleshaped molecules with totally relaxed internal degrees of freedom. This macroscopic director is not well defined microscopically: It can not be identified with the orientation of a single molecule because the orientation of the molecules is statistically distributed. Therefore we need a distribution function for describing the orientation in the fluid, or we restrict ourselves to the case of total alignment. In that case the macroscopic director of the Ericksen-Leslie theory coincides with the common alignment of all molecules. Key Words: liquid crystalsalignment tensorsorientation-balances