Freedericksz transitions in nematic liquid crystals in annular geometries

Abstract

This paper investigates the stability of simple static orientation patterns in a sample of nematic liquid crystal confined to a cylindrical annulus, when a magnetic field is applied. Six different arrangements are considered, covering all the cases in which the (mutually orthogonal) magnetic field and initial director field are either radial, azimuthal or axial. A classification is given of the threshold fields for Freedericksz transitions for these six cases, with either strong anchoring or weak anchoring at the boundaries, with or without an `easy axis' specified. The weak anchoring cases are of particular interest, since they lead to a dependence of the critical fields on the elastic constant and on various anchoring constants, thereby providing possible means of measuring these quantities.