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Nanoparticle Shape Selection By Repulsive Interactions: Metal Islands on Few Layer Graphenes

Metal atoms adsorbed on few layer graphenes condense to form nanometer-size droplets whose growth is size limited by a competition between the surface tension and repulsive electrostatic interactions from charge transfer between the metal droplet and the graphene. For situations where the work function mismatch is large and the droplet surface tension is small, a growing droplet can be unstable to a family of shape instabilities. We observe this phenomenon for Yb deposited and annealed on few layer graphenes and develop a theoretical model to describe it by studying the renormalization of the line tension of a two dimensional droplet by repulsive interparticle interactions. Our model describes the onset of shape instabilities for nanoparticles where the growth is size-limited by a generic repulsive potential and provides a good account of the experimentally observed structures for Yb on graphene.