Résumé:

Liquid crystals shells exhibit fascinating behaviors, for instance, they display topological defects in their ground states. The number and distribution of these defects depend on factors such as shell thickness, anchoring of the liquid crystal at the boundaries, or the type of liquid crystal phase considered. In this work, we study the dramatic consequences of inducing a nematic-smectic phase transition in a liquid crystal shell. Our nematic shells are double emulsions produced in a microfluidic capillary device [1]. The middle fluid is a thermotropic liquid crystal, 4-n-octyl-4-cyanobiphenyl (8CB), while the outer and inner fluids are aqueous solutions containing polyvinyl alcohol (PVA), which stabilizes the double emulsion and forces the nematic molecules to be tangentially anchored at the interface. In the nematic phase, far from the nematic-smectic phase transition temperature (TNS) we observe a configuration with four s = +1/2 defects, as predicted by theory [2]. Since experimental shells are typically heterogeneous in thickness, the four defects appear grouped together at the thinnest part of the shell in an almost square arrangement, Fig. 1(a). By contrast, when approaching TNS, the defects reorganize themselves along a great circle of the sphere, Fig. 1(g), confirming recent theoretical and simulation results [3]. The transition between these two limiting configurations proceeds continuously through a series of equilibrium states in which the defects associate in two pairs to depict the diagonals of a rhombus, Fig. 1(b) and (c). By means of numerical simulations, Fig. 1(d-f), we show that these new defect structures stem from the elastic anisotropy of the system: K3 diverges with respect to K1 when T approaches TNS. Novel types of defects, not observed in shells before, appear when the nematic order is replaced by smectic order [4]. In particular, we observe the formation of primary, secondary, and tertiary curvature walls, which provoke a wavy modulation of the smectic layers. We provide recent results which show that the number of curvature walls and the wavelengths of the associated undulations are correlated to the thickness of the shell. REFERENCES: [1] A.S. Utada, E. Lorenceau, D.R. Link, P.D. Kaplan, H.A. Stone, and D.A. Weitz, Monodisperse Double Emulsions Generated from a Microcapillary Device, Science. 308, 537 (2005). [2] T. Lopez-Leon, V. Koning, K.B.S. Devaiah, V. Vitelli and A. Fernandez-Nieves, Frustrated Nematic Order in Spherical Geometries, Nature Phys. 7, 391 (2011). [3] T. Lopez-Leon, A. Fernandez-Nieves, M. Nobili and C. Blanc, Nematic-Smectic Transition in Spherical Shells, Phys. Rev. Lett. 106, 247802 (2011). [4] T. Lopez-Leon, A. Fernandez-Nieves, M. Nobili and C. Blanc, Smectic Shells, J. Phys.: Condens. Matter 24, in press (2012).