Thermodynamic analysis of nucleation of carbon deposits on metal particles and its implications for the growth of carbon nanotubes

By considering the catalytic mechanisms underlying the formation of various nanocarbon deposits on catalytic metal surfaces, we conclude that the majority of these mechanisms include some common steps. The most important of these is the nucleation of the carbon deposit on the metal surface. On the basis of experimental and literature data, we propose that the nucleus has the form of a flat saucer with its edges bonded to the metal surface. A thermodynamic analysis of the carbon nucleation on the metal surface is then performed to obtain an analytical equation for the dependence of the critical radius of the nucleus on the reaction parameters. This equation demonstrates that a variation of the reaction parameters, such as the temperature and the nature of the metal catalyst and promoters, can lead to the formation of different carbon deposits, such as filamentous carbon, multiwall nanotubes or single-wall nanotubes (SWNTs). The performed analysis allows us to conclude that SWNT growth is likely to proceed on liquid metal particles.