In this paper, a new model based on kinetic theory of gases and longitude oscillations of metallic nanocluster on single carbon nanotube (CNT) in addition to phononvibrations of CNT on substrate is presented to describe the growth mechanism of ultra-long CNT in chemical vapor deposition (CVD).Interaction between CNT and catalyst is investigated by Lennard-Jones potential. Simulations demonstrate that metal nanocluster makes and keeps the carbon atoms at tip end reactive. So carbon nanotube can grow more than 1 cm. In addition, results show carbon nanotubes with larger diameter grow less owing to higher damping factors. Furthermore, effect of temperatureand type of catalyst on growth is discussed and it is shown thatthere is an optimum temperature and an optimum catalyst for growth process. Also, it is shown that the optimum temperature is changed by using different catalysts. Finally, effect of the partial pressure of decomposed hydrocarbons on the growth is also discussed. It is demonstrated that increasing partial pressure leads to the longest CNTs and influence of partial pressure on CNTs with smaller diameter is stronger. All results from the model are in good agreement with reported experimental results.
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