Thermodynamics approach of the formation of Ni catalyst particles for carbon nanotubes growth

Size-dependent thermodynamic parameters, such as Gibbs free energy, enthalpy and entropy, for the transition of a Ni nanofilm to catalyst particles for subsequent carbon nanotube growth have been explored. In this investigation, we consider the derived equations of the size-dependent melting temperature of nanosolids based on our previous works. Using this thermodynamic approach, it is found that the diameter of Ni particles is 3 times greater than the thickness of the original film. From the critical and stable sizes of transformed Ni nanoparticles, a minimum film thickness for transformation of film to nanoparticles was obtained. Our predictions are in good agreement with experimental results.