Nucleation and Growth of Carbon Nanostructures

Experimental data and molecular dynamic simulations [1-3] suggest that defects are required for the nucleation and growth of carbon nanostructures. However, the defects strongly deteriorate the properties of nanostructures. We investigated the role of defects in the formation of carbon nanostructures by folding of graphite sheets in the gas phase. The process of defect elimination was studied in the gas phase and compared with that on the catalyst surface.

Although the energy barrier for the folding of a graphite sheet is very high (about 20 eV), our molecular dynamics simulations have shown that it proceeds for about 1 ns at 3500 K (Fig. 1). This is explained by the formation of numerous defects, which increases system entropy and, hence, substantially reduces its free energy at high temperatures.

The simulation has demonstrated that the most important reactions of defect transformation are surface reactions with breaking only one bond; their barrier is about 3 eV. The mechanism of defect penetration into the interior of the graphite sheet is most likely associated with the formation of small defects adjacent to a ten-membered or a larger ring. Based on the elementary processes examined, we proposed a simple scheme of defect formation at sheet edges and used it to determine the equilibrium densities of defects. According to this scheme, the minimum temperature at which the folding of graphite sheets can be observed experimentally is 2500 K.

After the folding process is completed, the further relaxation of the structure was shown to proceed via the Stone–Wales rearrangements of defects. It was found that the addition of carbon atoms and dimers to an imperfect fullerene does not reduce the number of defects. Based on the calculated reaction pathway of the Stone–Wales rearrangements of defects (Fig. 2), we have found that defect-free nanostructures should form in the temperature range from 1800 to 3200 K.

To investigate the reactions of defects on the catalyst surface, we applied a multilevel approach. First, the DFT calculations of the energies of different carbon species on the (111) Ni and Pt surfaces were performed. These studies have shown that the aggregation of carbon adatoms proceeds relatively easily on Ni and is hindered on Pt, which explains the low catalytic activity of Pt in the synthesis of nanotubes. Using the results of these first-principles calculations, we constructed an empirical potential for the Ni-C system. This potential was demonstrated to describe pure Ni systems and carbon structures on the Ni surface. The developed potential was used to investigate the Stone-Wales rearrangement of defects on the catalyst surface (Fig. 4). It was shown that the catalyst reduces the minimum temperature of the formation of defect-free nanostructures to 1200 K.