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Pleats on Crystals on Curved Surfaces

Electrically charged polymer colloids attracted to the surface of water droplets of different shapes crystallize on their curved surfaces.

ŸThe curvature frustrates perfect crystallization and defects must be added such as the familiar twelve pentagons which decorate the otherwise hexagonal faces of a soccer ball. The pentagons/disclinations strongly relax curvature.

ŸWe have found a gentler way to relax curvature - Pleats. Pleats add width as one moves down their length both in skirts and in crystals. Our experiments indicate that pleats in crystals correspond to grain boundaries (lines of dislocations) which vanish on the surface. Allowed off the surface they form a set of steps which decrease circumference with height as on the crown of the Chrysler building in NY.