User:Meursault 2009

Focal Conic defects are the most commonly observed defect structures in smectic liquid crystals. The defect consists of smectic layers arranged in parallel surfaces, each of which is a Dupine cyclide. Focal Conic defects were first discovered by Friedel and Grandjean in 1910. Since focal conics are composed of layers of Dupin cyclides, they only have line singularities, and no surface singularities. Hence, they involve little energetic cost as opposed to other defects, and hence they are the most commonly observed defects in smectic samples.

Structure of Focal Conic Defect
Focal Conic defects can be visualized as layers of molecules wrapped around a hyperbola. Each layer is a Dupine cyclide. The resulting structure has another line of singurity, a parabola formed on the plane at right angles to each other. The hypoerbola and the parabola passes through the focus of each other, thus giving the name "Focal Conic".

Energy of a Focal Conic Defect
The energy of a focal conic defect consists mainly of three different parts: 1.Energy due to layer curvature 2.Surface Anchoring Energy 3.Core Energy

The energetic cost due to layer curvature can be calculated from the geometry of the focal conics