BALANCE LAWS AND CONSTITUTIVE-EQUATIONS OF MICROSCOPIC RIGID BODIES -A MODEL FOR BIAXIAL LIQUID-CRYSTALS

A reasonably general model of a liquid crystal is achieved by a contin uum consisting of microscopic rigid bodies. Within this model it is po ssible to deal with chiral molecules as well as simple rod-like partic les forming a conventional nematic liquid crystal. The configuration s pace of a rigid body is the rotation group SO(3); the configuration sp ace of a ''nematic'' is - with regard to the head-tail symmetry the pr ojective plane P(2). By replacing both manifolds by their universal co verings (S-3 and S-2, resp.) the internal symmetry of the fluid can be represented by a generalized (non-normalized) director. Within this m athematical framework mesoscopic balance equations are formulated whic h are applicable in the biaxial case of chiral molecules and in the un iaxial case of rod-like particles. Finally it is shown how constitutiv e equations can be derived by calculating averages of mesoscopic quant ities with respect to an orientation distribution function which chara cterizes the orientational order of the liquid crystal.