Continuum and atomistic modeling of interacting graphene layers

To investigate multishell models of multiwalled carbon nanotubes, we consider the buckling of a pair of graphene layers interacting by van der Waals forces. The layers are modeled as continuum sheets whose interaction is determined by a Lennard-Jones interatomic potential. Important in our treatment is the effect of nonequilibrium spacing between the layers, an issue whose physical and technological importance is suggested by a number of recent articles [see in particular, J. Zou , Nano Lett. 6, 430 (2006), and the references therein]. Using standard local bifurcation techniques, we construct bifurcation curves that describe the deformation of the layers as the edges of the layers are compressed. The bifurcation curves agree qualitatively with the sequence of deformations predicted by atomistic simulations. This agreement suggests the validity of multishell continuum models of multiwalled carbon nanotubes.