The structures and electronic states of Na+ trapped on graphene were investigated by means of density functional theory in order to clarify the nature of the interaction between Na+ and graphene. Graphene composed of 37 benzene rings was used as a model. The calculations showed that the sodium ion was stabilized in hexagonal sites and was located about 2.230Å from the graphene surfaces. The calculations showed that the Na+ ion diffused freely on the graphene surface, but the ion did not approach the edge region due to a high potential barrier near to the edge region.

DFT and Direct MD Study of the Diffusion of Sodium Ion on Graphenes. Tachikawa, H., Kawabata, H.: Thin Solid Films, 2009, 518[2], 873-6