Microseparation and tactoid formation in liquid crystal nanocomposites

Tactoids are droplets of liquid crystal (LC) immersed in an isotropic host fluid. Due to energetic competition between the elasticity of the liquid crystal and the surface tension, the morphology of a tactoid may be nonspherical. This is in contrast to that of isotropic droplet, which necessarily forms an spherical shape. But what happens when the host fluid is also a liquid crystal, potentially with very different properties? Such a scenario may emerge from microphase separation, for example. To understand the space of possible morphologies in such a system, we build a finite element model of a LC droplet immersed in a host LC fluid using morpho, a program for shape optimization, and characterize the solution space by minimizing the free energy with respect to the order parameters of interior and host fluids as well as the shape of the tactoid. Potential applications of this model will be discussed in the talk, and we consider a candidate exemplar system whereby a tactoid structure is formed by the non-equilibrium self-assembly of quantum dots in a chromonic liquid crystal during the isotropic-to-nematic phase transition.