Layer distortions induced by a magnetic field in planar samples of smectic C liquid crystals

Abstract

This article derives theoretical results for the onset of the Helfrich-Hurault transition in smectic C liquid crystals induced by a magnetic field applied parallel to the smectic layers. A suitable quadratic energy in terms of the smectic layer displacement u is derived from the nonlinear version of the smectic C energy. This energy is minimized via averaging to enable the calculation of a critical field strength H _c for the onset of layer distortions. Comparisons are made with known results for the corresponding geometry in the smectic A case. An estimate for the value of the smectic C elastic constant A ₁₂ can also be made by considering characteristic length scales.