Adsorption and diffusion of lithium-ion on and between graphene layers are investigated by an analytical model, employing a pairwise potential, which can be approximated by the Lennard–Jones potential to express the interaction between lithium-ion and each carbon atom of graphene. The equilibrium position and binding energy of lithium-ion at three particular adsorption sites (hollow, bridge, and top) are calculated, and the adsorption stability is discussed. The results show that hollow site is the most stable adsorption site, and top site is the most unstable. The adsorption and diffusion of lithium-ion on different sizes of monolayer graphene are investigated and proved to be size and edge dependent. Moreover, lithium-ion would rather diffuse on the surface of graphene than through a hexagonal carbon ring to the other side no matter what the graphene sheet size is. In addition, two kinds of vacancy defects in graphene are considered to study the diffusion of lithium-ion. The vacancy defect can improve energy barrier, and if a vacancy defect is big enough, lithium-ion migrating through the vacancy area from one layer to another is feasible. The possible applications of present study include rechargeable lithium-ion graphene battery and Li storage in carbon material.

Theoretical investigations are made on adsorption and diffusion of atoms/ions on graphene surface based on an analytical continuous model. An atom/ion interacts with every carbon atom of graphene through a pairwise potential which can be approximated by the Lennard‐Jones (L‐J) potential. Using the Fourier expansion of the interaction potential, the total interaction energy between the adsorption atom/ion and a monolayer graphene is derived. The energy‐distance relationships in the normal and lateral directions for varied atoms/ions, including gold atom (Au), platinum atom (Pt), manganese ion (Mn²⁺), sodium ion (Na¹⁺), and lithium‐ion (Li¹⁺), on monolayer graphene surface are analyzed. The equilibrium position and binding energy of the atoms/ions at three particular adsorption sites (hollow, bridge, and top) are calculated, and the adsorption stability is discussed. The results show that H‐site is the most stable adsorption site, which is in agreement with the results of other literatures. What is more, the periodic interaction energy and interaction forces of lithium‐ion diffusing along specific paths on graphene surface are also obtained and analyzed. The minimum energy barrier for diffusion is calculated. The possible applications of present study include drug delivery system (DDS), atomic scale friction, rechargeable lithium‐ion graphene battery, and energy storage in carbon materials.