Freedericksz transitions in nematic liquid crystals in annular geometries

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 k24 and on various anchoring constants, thereby providing possible means of measuring these quantities.