Charge- and thickness-dependent inplane deformation of multilayer graphene thin films

The charge- and thickness-dependent inplane deformation of multilayer graphene thin films in an electrolyte was studied by joint first-principles/continuum calculations (JFPCC) and the surface eigenstress model. At thermodynamic equilibrium, a multilayer graphene film exhibits initial deformation, which is asymmetric with respect to negative and positive charges, and the thickness-dependent minimal inplane C-C bond length occurs at the same positive charge of about 0.0381 × 10(20) |e| m(-2) for all studied films. The surface eigenstress model was further developed to take the charge-induced deformation into account, which yields analytical formulas. The analytical formulas describe the JFPCC results well for multilayer graphene thin films with a layer number larger than two, and are powerful and user friendly for understanding the charge and thickness dependent deformation in atomistic calculations and sophisticated experiments with multilayer graphene thin films.