Generalized Fréedericksz transition in nematics. Geometrical threshold and quantization in cylindrical geometry

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Abstract
Using the continuum theory of curvature elasticity of nematics in the small deformation approximation, the occurrence of magnetic field induced static periodic deformation (PD) relative to that of the aperiodic deformation (AD) is studied with the nematic (in Couette geometry) assumed to be confined between two coaxial cylinders and the director firmly anchored at the sample boundaries. When the initial director orientation is azimuthal and the field radial, PD is similar to a static Taylor instability. In the absence of a field PD is shown to possess a geometrical threshold like that predicted earlier for AD. When the initial director orientation is axial, a radial field may induce PD whose azimuthal domain wave vector qψ can take only integral values. In this geometry, qψ is found to vary discontinuously over certain ranges of material parameters and sample radii — a situation somewhat reminiscent of the Barkhausen effect in ferromagnetic materials. A third configuration in which director distortion above threshold may suffer azimuthal modulation is briefly discussed
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