Shape and director-field transformation of tactoids

Tactoids are droplets of a nematic phase that under suitable conditions form in dispersions of elongated colloidal particles. We theoretically study the shape and the director-field configuration of such droplets for the case where a planar anchoring of the director field to the interface is favored. A minimum of four regimes can be identified in which the droplets have a different structure. Large droplets tend to be nearly spherical with a director field that is bipolar if the surface tension is strongly anisotropic and homogeneous if this is not so. Small droplets can become very elongated and spindlelike if the surface tension is sufficiently anisotropic. Depending on the anchoring strength, the director field is then either homogeneous or bipolar. We find that the more elongated the tactoid, the more strongly it resists the crossing over from a homogeneous to a bipolar structure. This should have implications for the nucleation rate of the nematic phase. Our calculations qualitatively describe the size dependence of the aspect ratio of tactoids found in recent experiments.