Calculating carbon nanotube–catalyst adhesion strengths Peter Larsson, 1 J. Andreas Larsson, 2 Rajeev Ahuja, 1 Feng Ding, 3,4 Boris I. Yakobson, 4 Haiming Duan, 3, * Arne Rosén, 3 and Kim Bolton 3,5 1 Condensed Matter Theory Group, Department of Physics, Uppsala University, P.O. Box 530, SE-751 21 Uppsala, Sweden 2 Tyndall National Institute, University College Cork, Lee Maltings, Prospect Row, Cork, Ireland 3 Physics Department, Göteborg University, Göteborg, SE-412 96, Sweden 4 ME&MS Department, Rice University, Houston, Texas 77005, USA 5 School of Engineering, University College of Borås, Borås SE-501 90, Sweden Received 7 November 2006; published 20 March 2007 Density-functional theory is used to assess the validity of modeling metal clusters as single atoms or rings of atoms when determining adhesion strengths between clusters and single-walled carbon nanotubes SWNTs. Representing a cluster by a single atom or ring gives the correct trends in SWNT-cluster adhesion strengths Fe  Co  Ni, but the single-atom model yields incorrect minimum-energy structures for all three metals. We have found that this is because of directional bonding between the SWNT end and the metal cluster, which is captured in the ring model but not by the single atom. Hence, pairwise potential models that do not describe directional bonding correctly, and which are commonly used to study these systems, are expected to give incorrect minimum-energy structures. DOI: 10.1103/PhysRevB.75.115419 PACS numbers: 68.43.Bc, 68.43.Fg, 73.22.-f, 73.63.Fg INTRODUCTION Since their discovery in 1993, 1,2 there has been an im- mense amount of research into the growth and applications of single-walled carbon nanotubes SWNTs. One of the most challenging applications is in electronics, 3 where both the metallic and semiconducting properties of the SWNTs are exploited. For this to be realized, one needs to separate or selectively grow SWNTs based on their electronic properties. Although significant advances have been made in this area, 4–8 there are still no efficient methods for SWNT sepa- ration, and all production methods yield a mixture of metal- lic and semiconducting nanotubes. Computational methods complement experiment by deep- ening our understanding of the SWNT growth mechanism, and hence can help to identify ways to control the metallicity through the chirality of the SWNTs. Computations have an advantage over experiment in that they allow complete con- trol, manipulation, and monitoring of the atomic positions, but they often require approximations. For example, molecular-dynamics methods rely on the validity of the force fields, 9,10 and density-functional theory DFT methods— where the interatomic forces are handled accurately—are of- ten based on static, zero Kelvin structures or very short dy- namic simulations of small systems. 11–15 One therefore needs to be aware of these approximations and the effect that they may have on the relevance of the results, since SWNTs are usually produced at high temperatures and with added com- plexity e.g., inclusion of carbon feedstock, alloyed catalysts with defects, and interactions with the surface for supported catalysts. 16 It is known that the size of the computational model may affect the results. For example, previous work has shown that electronic properties of short SWNTs depend on the nano- tube length, 17 and hence sufficiently long nanotubes need to be used in the calculations. In this work, we focus on the adhesion between SWNTs and metal clusters. These systems are relevant to SWNT growth since sufficiently strong adhe- sion is necessary to maintain an open end—and hence the continued growth—of SWNTs. 10,18 Our studies show that metals that are commonly used to catalyze SWNT growth, Fe, Co, and Ni, have large adhesion energies, and subse- quently, these metals are the focus of the present work. In particular, we investigate the effect of the SWNT length and what model is used for the catalyst metal nanoparticle— whether it is represented as a complete stable cluster, a ring, or as a single atom—on the adhesion energy and structure of the SWNT-metal cluster complex. In addition to the lower computational costs, the motivation to model the cluster as an atom or ring is that previous studies related to SWNT growth have used the former model, 13 whereas we propose the latter model as a simplification compared to the use of full clusters, since the ring model allows for all SWNT dan- gling bonds to be bonded to metal atoms, as is the case with the cluster. In addition to the size of the model affecting the results, we have also checked that different density function- als, one-electron basis, and other model parameters do not lead to conflicting conclusions. METHOD The Vienna ab initio simulation program 19–21 VASP has been used in this work. Calculations were performed with the PW91 Ref. 22 functional and an ultrasoft pseudopoten- tial with a plane-wave cutoff of 290 eV for the single metal atom and ring models and the projector augmented wave method with a plane-wave cutoff of 400 eV for the metal clusters. Spin-polarized and nonpolarized calculations yield very similar adhesion energies, which are important since the cluster, which is magnetic at 0 K Refs. 23 and 24, is molten and hence nonmagnetic under typical growth conditions. 25 We have also obtained similar trends in preliminary calcula- tions with TURBOMOLE Ref. 26 using atom-centered Gauss- ian basis sets and the Perdew-Burke-Ernzerhof 27 PBE func- PHYSICAL REVIEW B 75, 115419 2007 1098-0121/2007/7511/1154196 ©2007 The American Physical Society 115419-1