Mechanics of the scrolling and folding of graphene

The competition between the out-of-plane rigidity and the van der Waals interaction leads to the scrolled and folded structural configurations of graphene. These configuration changes, as compared with the initially planar geometry, significantly affect the electronic, optical and mechanical properties of graphene, promising exciting applications in graphene-nanoelectronics. We propose a finite-deformation theoretical model, in which no presumed assumptions on the geometries of deformed configurations are required. Both the predicted deformed profiles and the critical conditions show great agreements with molecular dynamics simulations results when compared with existing studies with simple geometrical assumptions. Moreover, MD simulations are performed to explore the morphology transitions between different configurations. It is observed that the folded configuration is energetically favorable for a short graphene sheet, while a long graphene sheet tends to scroll. Of particular interest, we observe the morphology transition from a Fermat scroll to the Archimedean scroll for the bi-scrolled graphene. These findings are useful for understanding the stability of graphene and may provide guidance to the design of programmable graphene-nanoelectronics.