Focal Conics Domains in Smectics

Abstract

A lamellar phase constituted by equidistant flat layers presents typical structural defects called Focal Conic Domains (FCD), in which the layers (Dupin cyclides) are folded around two conjugated lines. The aim of this paper is to give a complete review of the geometrical and energetical aspects of FCDs. Also, some typical textures will be described. After a brief historical recall of the discovery of FCD’s by G. Friedel, we describe the conformation of the layers in the FCD’s. We consider the different fundamental types of structural defects of the lamellar phase, pointing out the topological differences between them. An analytical description of the Dupin cyclide is made, in particular we introduce their curvature, which is the starting point of the energy’ s calculation of the FCD. We complete the description with a number of physical situations.