Layer undulations induced by a magnetic or electric field in concentric cylindrical layers of smectic-A liquid...

This paper derives theoretical results for the onset of Helfrich-Hurault-type transitions in samples of smectic-A liquid crystals arranged in concentric cylindrical layers [J. Chem. Phys. 55, 839 (1971); 59, 2068 (1973)]. A magnetic field is applied in the azimuthal direction, parallel to the layers. The governing equilibrium equation is solved in order to derive the critical magnitude H(c) of the magnetic field above which the onset of periodic smectic layer distortions is expected. The distortion solution is shown to be energetically favorable for H>H(c). Some examples of critical thresholds are given, by means of figures, for relevant physical parameters. The qualitative features of the solution at H(c) are displayed via the plot of a typical variable solution to the equilibrium equation in a particular case. The consequences of the results, especially the relationship between H(c) and the radial depth, are explored, and comparisons are drawn with known results for infinite planar aligned smectic-A samples. The results are also interpreted for the case of an electric field which follows the plane of the layers in the usual wedge geometry. Critical applied voltage magnitudes U(c) are derived for various radial sample depths and wedge angles.