Effect of Surface Tension on Carbon Diffusion into a Catalyst Nanoparticle

Abstract—The synthesis of carbon nanotubes by chemical-vapor deposition (CVD) using a thin-film nickel-based catalyst is studied. An analysis of the size distributions of catalyst nanoparticles is carried out and compared with the distribution of particles from which the growth of carbon nanotubes is observed. The experiment shows that carbon nanotubes grow mainly from particles with sizes from 7 to 19 nm; nanotubes do not grow from particles of other sizes. A thermodynamic model of the solubility of carbon in a nickel nanoparticle is developed. This theoretical model is based on minimizing the Gibbs free energy of the system of nanoparticles that appear after the catalyst film melts. A critical minimum size of the catalyst nanoparticle exists for each set of parameters of the synthesis process, such that, under these conditions, it is able to dissolve a carbon atom.