Modeling CVD synthesis of carbon nanotubes: Nanoparticle formation from ferrocene

Catalyst nanoparticles play an important role in the synthesis of carbon nanotubes. In this paper, we present a two-equation model that can predict the formation process of iron nanoparticles from ferrocene fed into a CVD reactor. The model, combined with an axisymmetric two-dimensional computational fluid dynamics (CFD) simulation, includes the mechanism of nucleation and surface growth of an iron particle and bi-particle collision. The model predicts that the diameter of a particle will increase with an increase in the reaction temperature or the radial distance from the center of the reactor. Iron particles may deposit on the reactor wall; our model predicts that the thickness of the layer consisting of deposited iron particles will decrease with an increase in the axial distance from the entrance. The first prediction was validated by experimental observations reported by other researchers. In addition to the CFD simulation, a dimensional analysis was conducted to find pi-numbers that govern the process of particle formation; three pi-numbers were identified. Furthermore, one-dimensional governing equations were obtained under the assumptions of constant diffusion coefficient and collision frequency function, and solutions for particle diameter were obtained in qualitative agreement with the earlier CFD simulations.