FREEDERICKSZ TRANSITIONS IN NEMATIC LIQUID-CRYSTALS IN ANNULAR GEOMETRIES

This paper investigates the stability of simple static orientation pat terns 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 orthogon al) magnetic field and initial director field are either radial, azimu thal or axial. A classification is given of the threshold fields for F reedericksz transitions for these six cases, with either strong anchor ing or weak anchoring at the boundaries, with or without an 'easy axis ' specified. The weak anchoring cases are of particular interest, sinc e they lead to a dependence of the critical fields on the elastic cons tant k(24) and on various anchoring constants, thereby providing possi ble means of measuring these quantities.