The Construction of the Dupin Cyclides in a Smectic A Polygonal Texture

Claire Meyer,Coline Penaud,Brice Jonckheere

doi:10.1155/2014/145375

Abstract

We report experimental observations with optical microscopy of the usual so-called polygonal texture. We have made simulations of the Dupin cyclides in one small region of the sample.

Highlights

Many experiments on smectic A phases of liquid crystals report on the existence of macroscopic defective textures since the pioneer work of Friedel and Grandjean of 1910 [1]
Because of the nature of the singular lines in a smectic phase, two confocal lines both located in perpendicular plans, smectic layers take the shape of Dupin cyclides in order to keep their equidistance
We have presented a picture of the smectic layers inside a sample made with a polygonal texture

Summary

Introduction

Many experiments on smectic A phases of liquid crystals report on the existence of macroscopic defective textures since the pioneer work of Friedel and Grandjean of 1910 [1]. The equations of the two different sets of singular lines are given in (1) for the ellipse and the confocal hyperbola and in (6) for the circle and the straight line going through the center of the circle: x = a cos u, y = a sin u, z = 0, (6)

Results

Conclusion