Arrested Coarsening in Liquid Crystalline Phase Separation

Recent experiments have shown that liquid-liquid phase separation in complex environments is a promising tool for engineering and may play a role in organization within biological cells. Motivated by these findings, we study the phase separation behavior of Cahn-Hilliard droplets coupled to a liquid crystalline degree of freedom. We find that both parallel and perpendicular anchoring of the liquid crystal and droplet interfaces can arrest coarsening, regardless of whether the liquid crystal is isotropic or ordered. Furthermore, we show that the onset of arrest and size selection of the droplets can be predicted by a reduction in effective surface tension due to the interaction. These results suggest routes to controlling phase separation in engineered systems or complex environments like the interior of cells.