The low bending rigidity of graphene facilitates the formation of folds into the structure. This curvature change affects the reactivity and electron transport of the sheet. One novel extension of this is the intercalation of small molecules into these folds. We construct a model incorporating a single-walled carbon nanotube into a sheet of folded graphene. Variational calculus techniques are employed to determine the minimum energy structure and the resulting curves are shown to agree well with molecular dynamics study. Graphical Abstract Using calculus of variations, the elastic bending energy and van der Waals energy are minimised giving rise to Euler-Lagrange equation for which analytical solutions are derived to determine the optimal curved sturctures of graphene wrapped around carbon nanotubes . Overall agreement between the analytical solutions (with different values of bending rigidities) and results from molecular dynamics simulations (grey) is shown here for (6,6), (8,8) and (10,10) armchair nanotubes, respectively.
Keywords: Calculus of variations; Carbon nanotubes; Elastic energy; Graphene; van der Waals force.