Colloidal crystallization on a cone

We study the self-assembly of colloidal spheres on the surface of a cone, which has zero Gaussian curvature but varying mean curvature. Therefore, we expect that a colloidal crystal growing on a cone must self-intersect at an angle and is limited to a finite size. In our experimental system, colloidal particles assemble by short-ranged depletion interactions onto a pulled microcapillary tube. For a cylindrical tube of constant mean curvature, defects form where the crystalline grain self-intersects. These defects, called line-slip defects, consist of particle pairs with five-fold coordination along the defect line. However, as we increase the cone angle of the tube, a gap opens up along the defect line. This gap, or fractional vacancy, has varying width along the length of the defect. We show that the varying width of the fractional vacancy corresponds with the cone angle. When we increase the cone angle to a critical value, the system reaches a jammed state.