Aqueous dispersions of exfoliated, bile-salt stabilized single-wall carbon nanotubes exhibit a first order transition to a nematic liquid-crystalline phase. The nematic phase presents itself in the form of micron-sized nematic droplets also known as tactoids, freely floating in the isotropic host dispersion. The nematic droplets are spindle shaped and have an aspect ratio of about four, irrespective of their size. We attribute this to a director field that is uniform rather than bipolar, which is confirmed by polarization microscopy. It follows that the ratio of the anchoring strength and the surface tension must be about four, which is quite larger than predicted theoretically but in line with earlier observations of bipolar tactoids. From the scatter in the data we deduce that the surface tension of the coexisting isotropic and nematic phases must be extremely low, that is, of the order of nN/m.

Nematic liquid crystals are typically composed by anisotropic molecules that orientate along a preferred direction n called the director. Due to the existence of internal order, these systems are dramatically affected by confinement and curvature. One of the most outstanding consequences is the presence of topological defects in the ground state of the system. For a spherical nematic shell, the equilibrium defect structure depends on several factors, such as the thickness of the shell, the molecular anchoring at the two confining surfaces, or the elastic constants of the liquid crystal [1, 2]. Here, we show the fascinating transitions that take place when we change: i) the geometry of the shell, and ii) the elastic constants of the nematic phase. To make spherical shells of liquid crystal we generate double emulsions using an axi-symmetric microfluidic device [3]. Both the inner and outer fluids are aqueous solutions that contain poly-vynil-alcohol (PVA), which stabilizes the double emulsion and enforces planar boundary conditions for the nematic. The middle fluid is pentyl-cyano-biphenyl, 5CB. In order to modify the original thickness of the shell, we induce a difference in osmotic pressure between the inner and outer phases, which allows us to swell or de-swell the inner droplet in a controlled way. For thin shells, we observe a continuous transition in which the defects progressively increase their separation distance as the shell becomes thinner. Conversely, we observe a discontinuous transition in thicker shells, where only two equilibrium defect structures exist. More complex transitions arise when using 4-n-octyl-4-cyanobiphenyl (8CB) as liquid crystal. In that case, the decreasing of temperature towards the nematic-to-smectic phase transition temperature provokes a dramatic change in the elastic constants of the system. References: [1] A. Fernandez-Nieves, V. Vitelli, A.S. Utada, D.R. Link, M. Marquez, D.R. Nelson and D.A.Weitz, Phys. Rev. Lett. 99, 4 (2007) [2] T. Lopez-Leon and A. Fernandez-Nieves, Phys. Rev. E 79, 5 (2009) [3] A.S. Utada, E. Lorenceau, D.R. Link, P.D. Kaplan, H.A. Stone, D.A. Weitz, Science 308, 537 (2005)