An analytical geometrical model for quasi onedimensional graphene nanomaterials

We construct an analytical geometrical model for quasi one-dimensional (1D) graphene nanomaterials. The general carbon nanoscrolls (CNSs) model is characterized by a Archimedes spiral line with two construction parameters, the interlayer distance t and the inner radius. Graphene nanoribbons (GNRs) and carbon nanotubes (CNTs) are included in the model for two special cases. A set of analytical expressions are derived for all the coordinates of carbon atoms in a supercell under a three-dimensional (3D) coordinate system. This general geometrical model can be further used to first-principles calculations and simulations of material properties.