Rolling up of graphite sheet: Energetics of shell formation

The energetics of transformation of a planar fragment of a graphite monolayer into a spherical cluster is studied. The path considered is that a flat cluster rolls up into a segment of a spherical shell. The energy landscape of the process is presented. A simple model, formerly invented for calculating the carbon nanocluster formation energy, is used to evaluate the energies of intermediate states. Although the spherical-shell closed cluster has the lowest energy, curving of a plane fragment into a segment has an energy barrier. The barrier height goes to zero for clusters with the number of atoms greater than some $N_{\rm th}$, for which the cluster size is found analytically.