Growth kinetics of a single-walled carbon nanotube: Exact and simulation results

Abstract

The single walled (SW) carbon nanotube (CNT), discovered in 1991, is a fascinating system for studying key processes relevant to nanomaterials synthesis. It has crucial technological applications, in particular in biomedecine, sensors and telecom networks. In this work, we study numerically the growth kinetics and surface roughness of a hexagonal SWCNT with zero chiral angle using Glauber dynamics. The SWCNT growth kinetics are described in terms of Markov processes whose states are given by its upper edge profile that we mapped onto a 5-vertex model. The model parameters considered are the supersaturation of the fluid phase or driving force and the temperature. The kinetic equation of the system is solved exactly by means of the transition matrix method for small samples and the steady state growth velocity is calculated. Kinetic Monte Carlo (KMC) simulations based on the Bortz–Kalos–Lebowitz (BKL) update algorithm are used to extract some large scale properties of the model.