Can Single-Walled\nCarbon Nanotube Diameter Be Defined by Catalyst Particle Diameter?

Abstract

The need of designing and controlling single-walled carbon\nnanotube (SWCNT) properties is a challenge in a growing nanomaterials-related\nindustry. Recently, great progress has been made experimentally to\nselectively control SWCNT diameter and chirality. However, there is\nnot yet a complete understanding of the synthesis process, and there\nis a lack of mathematical models that explain nucleation and diameter\nselectivity of stable carbon allotropes. Here, <i>in situ</i> analysis of chemical vapor deposition SWCNT synthesis confirms that\nthe nanoparticle-to-nanotube diameter ratio varies with the catalyst\nparticle size. It is found that the tube diameter is larger than that\nof the particle below a specific size (<i>d</i>_c ≈ 2 nm) and above this value is smaller than particle diameters.\nTo explain these observations, we develop a statistical mechanics\nbased model that correlates possible energy states of a nascent tube\nwith the catalyst particle size. This model incorporates the equilibrium\ndistance between the nucleating SWCNT layer and the metal catalyst\n(e.g., Fe, Co, and Ni) evaluated with density functional theory (DFT)\ncalculations. The theoretical analysis explains and predicts the observed\ncorrelation between tube and solid particle diameters during growth\nof supported SWCNTs. This work also brings together previous observations\nrelated to the stability condition for SWCNT nucleation. Tests of\nthe model against various published data sets and our own experimental\nresults show good agreement, making it a promising tool for evaluating\nSWCNT synthesis processes.