Wetting and energetics in nanoparticle etching of graphene

Molten metallic nanoparticles have recently been used to construct graphene nanostructures with crystallographic edges. The mechanism by which this happens, however, remains unclear. Here, we present a simple model that explains how a droplet can etch graphene. Two factors possibly contribute to this process: a difference between the equilibrium wettability of graphene and the substrate that supports it, or the large surface energy associated with the graphene edge. We calculate the etching velocities due to either of these factors and make testable predictions for evaluating the significance of each in graphene etching. This model is general and can be applied to other materials systems as well. As an example, we show how our model can be used to extend a current theory of droplet motion on binary semiconductor surfaces.