Scaling laws for multi-walled carbon nanotube growth by catalyzed chemical vapor deposition

The synthesis of C nanotubes by catalyzed chemical vapor deposition at 600 °C is investigated, using yield and purity degree of C deposits to monitor the reaction outcome. From the reaction, carried out in C4H10-H2-He environment over Al2O3 supported Fe catalysts, multi-walled C nanotubes are attained, which, after purification, are analyzed by routinely-used diagnostics techniques. In order to clarify the role of the growth parameters, various experiments are performed changing flow rates of reactive gases, as well as, amount, metal load and reduction temperature of Fe/Al2O3 catalysts in the ranges 15-90 cc/min, 0.25-2.00 g, 10-40 wt% and 500-700 °C, respectively. Correspondingly, carbon yield varies between 47 wt% and 913 wt%, while purity degree between 56 wt% and 93 wt%. Owing to the lack of any correlation between these changes, it is initially quite difficult to envisage the effect, produced by any change of the growth conditions, on the final reaction outcome. The problem is solved by applying a semi-empirical approach, through which the "original" growth variables are combined to give dimensionless arguments (scaling laws for the reaction parameters), able to account for all the variation of yield and purity in the ranges considered. As final result, the growth issue can be easily predicted because carbon yield and purity degree can be approximated through very simple functions of the "new" process variables.