Open Access Kent State (OAKS)

The topological properties of disclinations are quite different for liquid crystals in two dimensions (2D) or three dimensions (3D). In 2D, there are distinct types of disclinations with topological charges or winding numbers of any half-integer or integer. By contrast, in 3D, all half-integer disclinations are topologically equivalent to each other, and integer disclinations are not defects at all. In this study, we use numerical simulations to explore the crossover between 3D and 2D. We show that certain disclination lines between patterned surfaces can exist when the director field is free to rotate in 3D, but not when the director field is forced into the 2D plane (by an electric field applied to a liquid crystal with negative dielectric anisotropy). As a result, these disclinations are expelled from the liquid crystal.