The cholesteric defect structure near the smectic A transition

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Abstract
We study in detail the defect structure observed in a cylindrical geometry near the smectic A-cholesteric transition. The orientation of the molecules at the capillary surface is radial. We propose that the cholesteric phase grows from the smectic A phase via a spiralling S = + 2 disclination. Unlike a nematic which requires only a single unit vector, n, to describe completely its symmetry, a cholesteric requires three mutually orthogonal vectors n, ν and ν x n. We argue that although the defect we have observed is non-singular from the nematic viewpoint, i.e. the configuration of n is non-singular, energy considerations imply a core for an S = 2 type line defect for a cholesteric. Specifically, we show that the escape of ν is concentrated in a region of order p, the pitch, and not dispersed throughout the volume of the material. We interpret this to mean that the S = 2 has a core and therefore must be considered singular from the cholesteric viewpoint. This conclusion disagrees with previous topological arguments which predict for cholesterics that line defects of order two are non-singular