Statistical properties of carbon nanostructures

We look at modeling carbon nanostructures from a theoretical graph network view, where a graph has atoms at a vertex and links represent bonds. In this way, we can calculate standard statistical mechanics functions (entropy, enthalpy, and free energy) and matrix indices (Wiener index) of finite structures, such as fullerenes and carbon nanotubes. The Euclidean Wiener index (topographical index) is compared with its topological (standard) counterpart. For many of these parameters, the data have power law behavior, especially when plotted versus the number of bonds or the number of atoms. The number of bonds in a carbon nanotube is linear with the length of the nanotube, thus enabling us to calculate the heat of formation of capped (5,5) and (10,10) nanotubes. These properties are determined from atomic coordinates using MATLAB routines.