Can single-walled carbon nanotube diameter be defined by catalyst particle diameter?

The need of designing and controlling single-walled carbon nanotube (SWCNT) properties is a challenge in a growing nanomaterials-related industry. Recently, great progress has been made experimentally to selectively control SWCNT diameter and chirality. However, there is not yet a complete understanding of the synthesis process and there is a lack of mathematical models that explain nucleation and diameter selectivity of stable carbon allotropes. Here, in-situ analysis of chemical vapor deposition SWCNT synthesis confirms that the nanoparticle to nanotube diameter ratio varies with the catalyst particle size. It is found that the tube diameter is larger than that of the particle below a specific size (d_c ≈ 2nm) and above this value is smaller than particle diameters. To explain these observations, we develop a statistical mechanics based model that correlates possible energy states of a nascent tube with the catalyst particle size. This model incorporates the equilibrium distance between the nucleating SWCNT layer and the metal catalyst (e.g. Fe, Co, Ni) evaluated with density functional theory (DFT) calculations. The theoretical analysis explains and predicts the observed correlation between tube and solid particle diameters during growth of supported SWCNTs. This work also brings together previous observations related to the stability condition for SWCNT nucleation. Tests of the model against various published data sets and our own experimental results show good agreement, making it a promising tool for evaluating SWCNT synthesis processes.