Kinetics of Carbon Nanotube Forest Growth by Chemical Vapor Deposition

A theoretical study of carbon nanotube (NT) forest growth by chemical vapor deposition is given, including (i) ballistic mode of C species impingement into the NT surface, (ii) C diffusion over NT surface and through the metal nanoparticle and (iii) the temperature drop at the NT tip occurring with increase in NT length. The presence of a metal nanoparticle is shown to shift NT growth from being surface diffusion controlled to being controlled by bulk diffusion through the nanoparticle. For typical growth conditions the growth rate is shown to be controlled simultaneously by surface diffusion over NT surface and bulk diffusion of C through metal nanoparticle. Even in specific cases where NT growth rate is controlled by bulk diffusion through the nanoparticle the initial stage may be controlled by surface diffusion, as revealed by the exponential change in NT length with time. A parametric study of the growth rate of NT forest with metal nanoparticles held at the NT tips as a function of temperature reveals the existence of a maximum near 1050-1100 K, agreeing with reported experiments. A thermal analysis based upon the heat conductance equation shows that with NT forest growth the temperature of the NT tips decreases, leading to growth deceleration and termination, suggesting that the larger the pressure the smaller the forest height that may be grown.