Liquids with conics

Abstract

A red thread marks the history of liquid crystals from the start; it is the concept of focal conic domains in smectic phases. Discovered by G. Friedel and F. Grandjean early in the beginning of the 20^th century, focal conic domains still attract the attention of researchers in the field. The presence of focal conic domains is a touchstone of layered media. They rightly excited the interest of P.-G. de Gennes in a seminal paper about the Apollonius tiling of toric focal conic domains. In this paper we shall review the development of this notion over the last one hundred years, firstly emphasising its importance in the appearance and broadening of the concept of order and of its singularities in liquid crystals and beyond in condensed matter physics, through the renewed notions of dislocations, disclinations, grain boundaries, kinks and focal conic domain imperfections, then describing the empirical evidence of focal conic domains in various liquid crystalline materials, and finally how they have inspired research in visualisation methods and molecular architectures.

Keywords:

• Smectic A
• focal conic domains
• disclinations
• kinks
• double helices
• 3D microscopy

Acknowledgements

We thank C. Blanc, P. Boltenhagen, C. Meyer, I. Smalyukh, and Yu. Nastishin for collaboration on various aspects of FCDs and Jacques Friedel for reading the manuscript and fruitful suggestions. This is IPGP contribution # 2487 (MK); ODL acknowledges the support of NSF DMR 0504516.

Notes

¹We recall that a wedge disclination line segment is a line segment parallel to the rotation vector, here denoted by Ω; a twist disclination line segment is perpendicular to the rotation vector Ω (cf. ( 23 )).