Frustration in the absence of Gaussian Curvature: what we learned from colloidal crystallization on a cylinder

We demonstrate the effects of a closure constraint on a crystal in the absence of Gaussian curvature. Most studies on closure constraints have focused on crystals on the surface of a sphere, in which case both Gaussian curvature and topology affect the crystallization dynamics. To separate the effects of topology from Gaussian curvature, we study crystallization of colloidal spheres on the surface of a cylinder experimentally, because a cylinder has zero Gaussian curvature, but has a surface that loops back on itself. We find that chiral structures and line-slip defects emerge owing to the closure constraint. We also find that owing to anisotropic crystal growth on a thin and long cylinder, line-slip defects with smaller chiral angles become frustrated, incorporating kinks and fractional vacancies that do not relax in experimental timescale. We show a connection between crystal morphology and growth dynamics, which may elucidate the assembly mechanism of tubular crystalline materials, such as rod-like viruses, bacterial S-layers, and nanotubes.