Colloidal crystallization on a cone

We study the self-assembly of colloidal spheres on the surface of a cone. For a flat surface with zero Gaussian curvature, colloidal monolayers form hexagonal crystals. However, a cone has zero Gaussian curvature everywhere except its apex -- a delta function of positive Gaussian curvature, which introduces a novel source of geometrical frustration for colloidal crystallization.

Using confocal microscopy, we watch colloidal particles assemble by short-ranged depletion interactions onto a tapered glass fiber. For a cone with a low opening angle, the fiber is approximately cylindrical. In this case, we find that defect-free crystals wrap around the fiber, forming seams when they meet themselves. At slightly larger opening angles, the seams open, forming wedge-shaped voids. At even larger opening angles, the particles assemble into smaller, seemingly randomly oriented crystalline domains. We will discuss how these structures might arise and how these studies may be used to understand crystal growth on more general curved surfaces.