Symmetric scrolled packings of multilayered carbon nanoribbons

Scrolled packings of single-layer and multilayer graphene can be used for the creation of supercapacitors, nanopumps, nanofilters, and other nanodevices. The full atomistic simulation of graphene scrolls is restricted to consideration of relatively small systems in small time intervals. To overcome this difficulty, a two-dimensional chain model making possible an efficient calculation of static and dynamic characteristics of nanoribbon scrolls with allowance for the longitudinal and bending stiffness of nanoribbons is proposed. The model is extended to the case of scrolls of multilayer graphene. Possible equilibrium states of symmetric scrolls of multilayer carbon nanotribbons rolled up so that all nanoribbons in the scroll are equivalent are found. Dependences of the number of coils, the inner and outer radii, lowest vibrational eigenfrequencies of rolled packages on the length $L$ of nanoribbons are obtained. It is shown that the lowest vibrational eigenfrequency of a symmetric scroll decreases with a nanoribbon length proportionally to $L^{-1}$. It is energetically unfavorable for too short nanoribbons to roll up, and their ground state is a stack of plane nanoribbons. With an increasing number k of layers, the nanoribbon length $L$ necessary for creation of symmetric scrolls increases. For a sufficiently small number of layers $k$ and a sufficiently large nanoribbon length $L$, the scrolled packing has the lowest energy as compared to that of stack of plane nanoribbons and folded structures. The results can be used for development of nanomaterials and nanodevices on the basis of graphene scrolled packings.