Focal conic faceting in smectic-A liquid crystals

Abstract

Smectic-A nucleating in the isotropic phase presents various bulk focal conic defects close to the interface, within the “bâtonnets” first described by Friedel and Grandjean in 1910. We experimentally study the stability of the “bâtonnets” in a high-frequency aligning electrical field. Although the external shape appears out-of-equilibrium, the focal conic texture is found stable. We build a model explaining the general interfacial focal conic texture : it participates in the minimization of the interfacial energy by orienting the smectic layers almost perpendicular to the interface, above a critical size l0 comparing layer curvature and surface energies. This model explains new arborescent textures that we observe inside capillary tubes. We then discuss equilibrium shapes of size ∼L. We discuss three regimes : L ≪l0 yields 3D-cristal-like “Wulf” shapes. For L > l0, equilibrium shapes must contains focal conics, although we cannot solve the general solution. In the asymptotic limit L ↦∞, we predict fractal textures of dimension 1 < d < 2 inside “optimal” configurations, spherical as for 3D-liquids. Finally focal conics can be considered as “bulk facets” which pile up to decorate “bâtonnet” and more general interfacial textures. Focal conics appear then an intrinsic defects of Smectic-A materials in contact with their isotropic phase.