Optical Microscopy Observations and Construction of Dupin Cyclides at the Isotropic/Smectic A Phase Transition

Abstract

In this work, we are interested in the nucleation of bâtonnets at the Isotropic/Smectic A phase transition of 10CB liquid crystal. Very often, these bâtonnets are decorated with a large number of focal conics. We present here an example of a bâtonnet obtained by optical crossed polarized microscopy in a frequently observed particular area of the sample. This bâtonnet presents bulges and one of them consists of a tessellation of ellipses. These ellipses are two by two tangent, one to each other, and their confocal hyperbolas merge at the apex of the bâtonnet. We propose a numerical simulation with Python software to reproduce this tiling of ellipses as well as the shape of the smectic layers taking the well-known shape of Dupin cyclides within this particular bâtonnet area.

Lyotropic Liquid-Crystalline Phases of Sophorolipid Biosurfactants

“…The latter grows within the former as anisotropic rod-like birefringent domains (Figure c), called “bâtonnets de Friedel-Grandjean” (French for “Friedel and Grandjean rod-like objects”) . The microscopic organization of these objects, which are quite characteristic of the lamellar (or smectic A) mesophase, results both from the requirement of keeping the lamellar period constant and from the director anchoring condition at the lamellar/isotropic liquid interface. , …”

“…30 The microscopic organization of these objects, which are quite characteristic of the lamellar (or smectic A) mesophase, results both from the requirement of keeping the lamellar period constant and from the director anchoring condition at the lamellar/isotropic liquid interface. 31,32 By using an optical compensator, the birefringence of a small aligned part of the sample, n, was estimated to be on the order of 6×10 -4 , which, taking the dilution into account, provides the value of the specific birefringence of the biosurfactant membranes, nsp  8×10 -4 . This value is lower than that, nsp  4×10 -3 , reported for the sodium decylsulfate anionic surfactant system, 33 which might suggest a larger conformational disorder of the biosurfactant compound (1), or could be due to the sample being only partially aligned.…”