Steps of Nanocluster Formation: Energetical Predictions for Catalytic Mechanism

The two-parameter phenomenological model allows to calculate formation energies of di erent nanotubes. The energy, geometry and size of the optimal tube were found. This tube has the minimal formation energy at the de nite number of atoms. A region of energetical stability of tubes in respect with planar fragment of graphite sheet was investigated. We accounted for the possible dangling bond energy passivation, which essentially changes the energetics of formation process. We analyze an energy di erence between a planar round piece of graphite sheet (which is optimal in a sense) and an optimal tube of the same number of atoms. This value shows which con guration is more stable energetically: the planar or cylindrical one. It is well known experimentally that the tube is readily grown at some metal particle. In order to explain the abnormally small nuclei size we propose the catalytical mechanism of the tube formation. We suppose that the role of the metal is to decrease the dangling bond energy or to bound completely the bond. Then the resulting perimeter energy decreases in some times (the new parameter of the model). It results in the increasing of the nuclei size.