Molecular Orientations and Optical Patterns of Rotating Nematics

Abstract

The equation of motion of director for nematic liquid crystal flowing in the azimuthal direction with axial symmetry (as in e.g. torsional flow) is derived from the Ericksen-Leslie theory. When specialized to the case of homeotropic nematics in a circular cell. in the steady state, the two-dimensional equation may be simplified to a one-dimensional ordinary differntial equation under the assumption that either the cell is thick (Model A) or the director angle varies very slowly with the dimensionless radial coordinate R (Model B). Both these two cases are analysed. For Model B, multiple solutions are found and discussed. Spatial distribution of the director is studied and the corresponding optical interference patterns of transmitted monochromatic light are calculated. When compared with experiments of Wahl and Fischer we found that the theoretical positions of the bright rings and the total number of bright rings lying within a radius of R are in agreement with experiments for R < 10 and <R < 130. respectively.

In addition, the theoretical analysis of Wahl and Fischer which differs from ours is examined in detail and found to contain errors in its mathematical derivations. When these errors are properly corrected the domain of validity of Wahl and Fischer's theory is still only half that of ours. Also, the ratio of elastic constants deduced from their own experimental data using their theory is unreliable.