The Fréedericksz transition is a field-driven orientational instability of a confined nematic liquid crystal. Elasticity and surface anchoring resist the electric field or magnetic torque; a lowest allowed distortion mode becomes unstable at a finite threshold. Positive dielectric anisotropy of a nematic permits a normal electric field to tilt a planar anchored director.
For planar strong anchoring and a quarter-turn base profile, and . Expanding the one-dimensional twisted nematic energy through quadratic order gives . The lowest zero-endpoint mode is . Its coefficient vanishes at the displayed threshold, with , provided the bracket and anisotropy are positive. Halving the electric coupling doubles .
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The Fréedericksz transition refers to a phenomenon observed in liquid crystals, particularly in systems subjected to an electric or magnetic field. It describes the change in the orientation of liquid crystal molecules when an external field is applied, leading to a change in the director configuration of the liquid crystal. In equilibrium, liquid crystal molecules are often aligned parallel to a certain direction (the director, often aligned with the surfaces of a cell).