Mechanisms of Carbon Nanotubes and Graphene Growth: Kinetics versus Thermodynamics

Thermodynamics must be favorable for the growth of carbon nanotubes (CNTs) and graphene to take place, but a kinetic study is required to find the operating mechanism. In fact, thermodynamics indicates whether a reaction is possible; however, the route prevailing is not necessarily the most thermodynamically favorable, but the fastest one. Detailed kinetic studies state that there are three alternative routes operating under different temperature and pressure rates. The modes and rates of diffusion of carbon (C) atoms and noble metals have been known since the 1930s, but proof of C bulk diffusion operating in CNT growth came from detailed kinetic studies performed in the early 1970s, when reversible versus irreversible C formation was discussed with examples. The reason for interstitial C bulk diffusion in transition metals is evidenced based on the values of covalent radius. The reason for operating under steady-state conditions (linearity of the weight versus time) when searching for the operating mechanism is discussed herein. The steady-state C formation process operates sometimes with two different solid phases at each side of the catalyst particle (e.g., Ni and Ni3C), with thicknesses proportional to 1/D of the respective C bulk diffusivities when the carbon bulk diffusion step is the rate-determining one.