A model for the catalytic growth of carbon filaments

A two-dimensional model of the growth of filamentous carbon using an iron catalyst is presented. A single catalyst particle in the shape of a pear, producing filament diameters in the range from 30 to 100 nm is considered. The steady-state mass balance on the carbon within the particle is solved numerically. The model predicts the hollow structure of carbon filaments accurately and also indicates a strong dependence of growth rate on diameter. These findings are consistent with previous one-dimensional models and experimental observations. This two-dimensional model refines previous one-dimensional models in that it accounts for the variation in diffusion path length with filament radius, and provides predictive capability both with respect to filament inner radius and growth rate. However, the results are not significantly better than those obtained via one-dimensional approximations, and they require significantly more computational effort.