Weak-anchoring effects on a Freedericksz transition in an annulus

Abstract

This paper investigates the effect of weak anchoring on static orientation patterns in a sample of nematic liquid crystal confined to a cylindrical annular geometry, in the presence of a magnetic field. The particular arrangement considered in detail is that in which a magnetic field is applied in the azimuthal direction to a sample of liquid crystal that is initially uniformly aligned parallel to the cylindrical axis and is weakly anchored at the inner cylinder, but strongly anchored at the outer cylinder. A static solution of the non-linear continuum equations is presented which suggests a possible experiment for evaluating the surface elastic coefficient k ₂₄. In addition, a linear stability analysis based on the dynamic theory yields results for critical phenomena in agreement with those derived from the non-linear solution.