Modelling gas-phase synthesis of single-walled carbon nanotubes on iron catalyst particles

Abstract

A simple model for the gas-phase synthesis of carbon nanotubes on iron catalyst particles has been developed. It includes a growth model for the catalyst particles and describes nanotube growth processes through carbon monoxide disproportionation and hydrogenation. Models for particle–particle interactions and sintering are also included. When carbon arrives at a catalyst particle it can either dissolve in the particle until a saturation limit is reached, or form a graphene layer on the particle, or go on to form a nanotube. Two models for incipient nanotube growth are considered. The first allows nanotubes to form once a catalyst particle reaches the saturation condition. The second only allows nanotubes to form on the collision of two saturated particles. The particle system is solved using a multivariate stochastic solver coupled to the gas-phase iron chemistry using an operator splitting algorithm. Comparison with experimental data gives a good prediction of the nanotube length, and reasonable values of catalyst particle diameter and nanotube diameter. A parametric study is presented in which the carbon monoxide reaction rate constants are varied, as is the fraction of carbon allowed to form nanotubes relative to surface layers. The assumptions of the coagulation and sintering models are also discussed.