Simple model of the interrelation between single- and multiwall carbon nanotube growth rates for the CVD process

Recent time-resolved measurements of carbon nanotube (CNT) growth on Fe and Fe∕Mo catalysts have identified a maximum growth rate and temperature corresponding to the onset of small-diameter, single-wall CNT (SWNT) formation. A simple model described here emphasizes the essential role of the SWNTs in the growth process of CNTs. Remarkably, it shows that the growth rate (i.e., the time derivative of the length) of a multiwalled CNT is the same as that of a SWNT at the carbon flux and diffusion coefficient corresponding to a given temperature. Moreover, below ~7000.2em0ex^∘C, the temperature above which SWNT growth is observed for a 60.3em0exsccm (cubic centimeter per minute at STP) C₂H₂ flow rate, the number of walls as a function of temperature is uniquely determined by the interplay of the incident flux of atomic C and diffusion rates consistent with bulk diffusion. Even partial melting of the catalytic particle is unnecessary to explain the experimental results on growth rate and number of walls. Above 7000.2em0ex^∘C, where severe catalyst poisoning ordinarily begins, the growth rate without poisoning is consistent with recent results of Hata and co-workers [Science 306, 1362 (2004); Phys. Rev. Lett. 95, 056104 (2005)] for ``supergrowth.''