A detailed model for the flame synthesis of carbon nanotubes and nanofibers

Many experimental investigations of CNT/CNF flame synthesis have been recently reported. However, there are as yet no comprehensive models regarding their formation, growth or structure. Herein, a CNT/CNF growth rate model is proposed that is applicable for any method of CNT/CNF production (although our particular interest lies in flame synthesis in ethylene/air flames). While it is usual for most existing models to consider only a single carbon-carrying gas that contributes towards carbon deposition, our extended model can consider a complex hydrocarbon mixture that can mimic a flame environment. The model shows that before carbon nucleation is initiated, the surface density of carbon atoms increases as they are added through diffusion from the leading face of the catalyst nanoparticle. Over time, the diffusion potential decreases due to a reduction in the carbon atom concentration gradient. However, with the onset of nucleation and growth, diffusion is reinstated as the major driving potential for carbon atom transport through the nanoparticle. Steady carbon deposition and filament growth occurs once there is a stable carbon cluster size due to nucleation. The results support our hypothesis that flame synthesis can be a much faster and higher throughput process than CVD. The CNT/CNF growth rate decreases with increasing height above the burner. Decreasing temperature at higher locations leads to slower catalyst deactivation, but the CO concentration, which is the major contributor to carbon deposition, also decreases with increasing height above the burner. One of the major findings in this work is the contribution of CO to CNT formation by flame synthesis. The concentration of hydrocarbons in the vicinity of the toroidal zone near, which most of the CNT growth is observed, is negligible compared to CO concentration. Our results provide a basis to conduct future multiscale simulations of CNT/CNF growth.