Existing literature has focused on experimental investigations of CNT/CNF flame synthesis. 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 steady carbon deposition and filament growth occurs once there is a stable carbon cluster size due to nucleation. 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.

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