In this Letter, the authors inve´stigate the interaction of various atoms/ions with a graphene sheet and two parallel graphene sheets using the continuous approximation and the 6–12 Lennard-Jones potential. The authors assume that the carbon atoms are smeared across the surface of the graphene sheet so that the total interaction between the single atom/ion and the graphene sheet can be approximated by a surface integration over the graphene sheet. They determine the equilibrium position for the atom/ion on the surface of the graphene sheet and the minimum intermolecular spacing between two graphene sheets. This minimum spacing is by symmetry twice the value for the equilibrium positions for a single graphene sheet and is such that the atom/ion undergoes no net force. The same methodology together with basic statistical mechanics are also employed to investigate the diffusion of the atom/ion from a central location to the edge of the graphene sheet at different temperatures. The results presented in this Letter are consistent with a similar study adopting a molecular dynamics simulation approach. Possible applications of the present study might include the development of future drug delivery systems and future high-performance alkali battery design using nanomaterials as components.