JNL: JPD PIPS: 268628 TYPE: PAP TS: NEWGEN DATE: 7/2/2008 EDITOR: MM IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS J. Phys. D: Appl. Phys. 41 (2008) 000000 (6pp) doi:10.1088/0022-3727/41/1/000000 A model for catalytic growth of carbon nanotubes Sayangdev Naha and Ishwar K Puri 1 Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA E-mail: ikpuri@vt.edu (I. K. Puri) Received 26 December 2007, in final form 24 January 2008 Published Online at stacks.iop.org/JPhysD/41 Abstract Despite the utility and promise of carbon nanotubes (CNTs), their production is generally based on empirical principles. There are only a few CNT formation models that predict the dependence of their growth on various synthesis parameters. Typically, these do not incorporate a detailed mechanistic consideration of the various processes that are involved during CNT synthesis. We address this need and present a model for catalytic CNT growth that integrates various interdependent physical and chemical processes involved in CNT production. We validate the model by comparing its predictions with one set of experimental measurements from a previous study for cobalt (Co) catalyzed growth. A brief parametric study is presented subsequently. From an application perspective, the model is able to predict the growth rate of the CNT length and its dependence on the ambient temperature and gas-phase feedstock partial pressure. 1. Introduction The literature pertaining to carbon nanotubes (CNTs) is mostly experimental and there are few available models that can predict their growth. A number of the existing models focus on catalysis alone and do not combine all of the different processes that contribute to CNT formation. Kuwana and Saito [1] described nanoparticle growth from ferrocene and provided a two-step catalytic reaction model for the formation of Fe nanoparticles. Zavarukhin and Kuvshinov [2] proposed a model for the production of nanofibrous carbon from a methane–hydrogen mixture using Ni as catalyst. Scott [3] provided a chemical model based on soot nucleation kinetics that simulates the nucleation and growth of carbon– nickel clusters and single-wall CNTs. Dateo et al [4] presented a model for CNT production considering high pressure carbon monoxide as precursor by considering the decomposition of the catalyst precursor Fe(CO) 5 , catalyst growth and decomposition, CNT formation and overcoating of the catalyst. Zhang and Smith [5] provided a model for methane decomposition and the formation of filamentous carbon on a supported Co catalyst. They considered the 1 Author to whom any correspondence should be addressed. effects of catalyst deactivation, metal particle size and the carbon density profiles through the catalyst particle at different reaction times. In a previous study [6] we discussed a model for CNT growth on Fe catalyst substrates placed in a co-annular ethylene/air nonpremixed flame reactors. Herein, we present a more detailed model that predicts CNT growth in terms of length and handles catalyst poisoning in a more representative manner. 2. Model The model includes a mechanism for CNT production based on a previous diamond nucleation model [7] that now also contains additional details about the adsorption energies, bulk diffusion energies and sticking coefficients. The overall mechanism considers (a) the impingement of carbon atoms from the predominant carbon-containing species in the ambient, (b) their adsorption and desorption at the catalyst– gaseous hydrocarbon interface, (c) surface and bulk diffusions, (d) nucleation and (e) separation of solid undissolved carbon in nanostructured form. The schematic of figure 1 illustrates the modelled processes that lead to the catalyzed formation of CNTs. Salient features of the model are described below. 0022-3727/08/000000+06$30.00 1 © 2008 IOP Publishing Ltd Printed in the UK