Modeling of the Heterogeneous Formation of Ni Catalyst Particles for Carbon Nanotube Growth

Abstract

Size dependent thermodynamic parameters (Gibbs free energy, entropy, enthalpy, and surface energy) have been calculated for the heterogeneous transition of Ni nanofilms to nanoparticles. Such particles are often used as catalysts for carbon nanotube formation, and particle size controls the carbon nanotube diameter. The resultant equations are based upon the size dependent melting temperature of nanosolids derived in our previous works, and the results are compared with our recent calculations on the homogeneous formation of Ni catalyst particles. Using this thermodynamic approach, a relation between the minimum diameter of Ni particles and the thickness of the original film is found, and we predict the optimum Ni film thickness to form particles with diameter 20−30 nm. We illustrate that the calculated critical and stable sizes of Ni heterogeneously formed nanoparticles are a function of the wetting angle. For further comparison, a 5 nm Ni film was deposited on a Si substrate and heat treated at 923 K. Atomic force microscopy showed that Ni nanoparticles with spherical cap diameters of 20−200 nm were formed, and their wetting angles were used to confirm the derived equations. The predictions are in good agreement with the experimental results.