Equilibrium locations for nested carbon nanocones

Potentially, carbon nanostructures are very important as ideal components to create many novel nano-devices. Such devices including nano-oscillators, ultra-fast optical filters and nano-bearings, are based on the unique mechanical and electronic properties of carbon nano-structures. Common carbon nanostructures used are usually C₆₀-fullerenes, carbon nanotubes, carbon nano-bundles and carbon nanotori. In the synthesis and production of carbon nanostructures, carbon nanocones tend to occur less frequently, and it is known that five different size cones may occur, depending on the number of pentagons in the atomic network. However, the simple geometric structure of carbon nanocones certainly facilitates calculations for their potential energy. Here, the Lennard–Jones potential energy function and the usual continuum approximation are employed to determine the energy for two such nested carbon nanocones which are located co-axially. We show graphically the energy profiles for any two carbon nanocones arising from the five possible structures. For both two distinct cones and two identical cones, we find that the equilibrium location moves further away from the vertex as the number of pentagons is increased. However, we observe that the equilibrium position occurs such that one cone is always inside the other, and therefore, we might expect that nested double-cones are formed according to these results.