Crystallization in carbon nanostructures

Abstract:

I will present a simple interaction potential capable of describing crystallization in carbon nanostructures such as graphene, nanotubes, and fullerenes. This energy consists in the sum both a two- and three-body interaction terms. Planar energy minimizers are proved to be graphene patches and the ground state energy is explicitly quantified. By recasting the minimization problem in three-space dimensions, one checks that ground states are necessarily nonplanar and, in particular, rolled-up structures like nanotubes are favored.
Eventually, we present a stability proof for some fullerenes.