We consider carbon nanostructures that consist of one or more graphene sheets. Each graphene sheet is a one-atom thick and contains carbon atoms arranged in a hexagonal lattice. Neighboring atoms within a sheet interact via strong covalent bonds, making graphene essentially inextensible, but amenable to large elastic bending deformation. The interaction between the sheets is of a weak Van-der-Waals-type and allows for a relatively easy sliding.
When upscaled to the macroscopic level, each graphene sheet can be represented by an elastic shell and the energy of interactions within a sheet reduces to an elastic energy. The macroscopic analog of weak interactions is typically thought of as a pressure-type term that depends only on the local distance between the sheets.
In my talk, I will demonstrate that this reduction is not always correct as the weak interactions also depend on relative arrangements of atoms of the neighboring shells. I will discuss how one can borrow from the idea of a Gamma-development from calculus of variations to obtain a macroscopic Ginzburg-Landau-type model for carbon nanostructures. I will also connect mathematical predictions to experimental observations.