Article pubs.acs.org/JPCA
Reactive Sites for Chiral Selective Growth of Single-Walled Carbon Nanotubes: A DFT Study of Ni55−Cn Complexes Qiang Wang,†,‡,§ Hong Wang,† Li Wei,† Shuo-Wang Yang,‡ and Yuan Chen*,† †
School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, Singapore 637459, Singapore ‡ Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore § Department of Applied Chemistry, College of Science, Nanjing University of Technology, Nanjing 210009, P. R. China ABSTRACT: The physical and electronic properties of single-walled carbon nanotubes (SWCNTs) are determined by their chirality. The chirality selection mechanism in SWCNT growth is not fully understood. In this study, the interaction between near-armchair (n,5), where n = 6, 7, 8, and 9, zigzag (9,0), and armchair (5,5) nanotubes and a fully relaxed Ni55 metal cluster during the early stage of growth is studied by density functional theory calculations. We found that kink sites at the end edge of (n,5) nanotubes are more reactive than other sites based on the charge transfer analysis at the Ni−C interface. The frontier orbitals of the (6,5) and (7,5) caps are localized on their kink-step sites, which stretch outward from the carbon cap surface, having typical 2pz orbital feature of carbon atom with high reactivity. Such favorable frontier orbital spatial orientation and location is ideal to incorporate more carbon species. These reactive sites may lead to the faster growth rate, resulting in the chirality selectivity toward the (6,5) and (7,5) nanotubes. In contrast, the frontier orbitals of (8,5) and (9,5) caps spread over the entire carbon cap surface. Adding carbon species at these sites may lead to the chirality change or formation of other carbon structures. Our results showed that the spatial distribution and orientation of frontier orbitals is useful in explaining the chiral selectivity. Engineering catalyst clusters to control these reactive sites has high potential to further improve chirality control in SWCNT synthesis.
1. INTRODUCTION The physical and electronic properties of single-walled carbon nanotubes (SWCNTs) are determined by their chirality, which depends on nanotube diameter and rolling angle of graphene sheets (chiral angle).1,2 Chiral selective growth of SWCNTs is an essential precondition for many of their applications.1,2 In recent years, a number of experimental3−17 and theoretical14−29 studies have explored the chiral selectivity in SWCNT growth. Theoretical studies have attributed the chiral selectivity to different aspects of the interaction between metal clusters and growing carbon structures. Experimental results show that the size, morphology, and composition of metal clusters contribute to the chiral selective growth of SWCNTs.30−35 Electron microscope studies illustrated that carbon caps first sprout on metal surfaces, and then lift themselves by incorporating more carbon atoms, eventually growing into well-defined tubes.36−40 Among the proposed chiral selection mechanisms, Reich et al. suggested that the chirality control may be achieved by matching a SWCNT cap with specific local crystalline lattices on metal surfaces.18,19 We showed that changing the ratio between single carbon atoms and carbon dimers in carbon precursors could lead to either SWCNT length extension or chirality changes.41 Ding et al. found that a strong adhesion between SWCNTs and catalyst particles is needed to sustain the growth of nanotubes.42 Yakobson et al. proposed a dislocation growth mechanism, which correlates the chirality selectivity observed in several experimental studies to the different growth rate of (n,m) SWCNTs.43 The dislocation © 2012 American Chemical Society
growth mechanism has recently been corroborated by several experimental studies.44,45 The difference in SWCNT growth rates is related to the incorporation of carbon atoms into growing carbon structures. It is critical to understand where and how carbon atoms are incorporated, as well as when the chirality of SWCNTs is determined during the growth. In our previous study, we studied the growth of (5,5), (6,5), and (9,0) nanotubes on a relaxed Ni55 cluster. We showed that charges are transferred from metal catalysts to the growing end edges of nanotubes.46 Different chiral nanotubes display distinct reaction active sites. The (5,5) nanotube has five identical doublecarbon active sites, while the (9,0) nanotube has nine singlecarbon active sites. The (6,5) nanotube has a kink site with the highest reaction activity based on the electronic density of states analysis. If carbon atoms are incorporated into carbon structures through the kink site, other chiral nanotubes, such as (8,5) and (9,5), are more favorable in growth because they have more kink sites at their end edges. However, the chiral selectivity toward (8,5) and (9,5) nanotubes is seldom found in experimental studies. A better understanding of the characteristics of these reactive kink sites is very useful, and it may lead to novel ideas of improving chirality control in SWCNT synthesis. Received: August 15, 2012 Revised: October 4, 2012 Published: October 30, 2012 11709
dx.doi.org/10.1021/jp308115f | J. Phys. Chem. A 2012, 116, 11709−11717
The Journal of Physical Chemistry A
Article
The chemical reactivity of carbon structures and Ni55 was studied by the gradient-corrected DFT calculations with the PBE functional and a DFT-based relativistic semicore pseudopotential (DSPP)54 combined with a double numerical basis with polarization functions (DNP) in the DMol3 package.55,56 The structures of various isolated Cn, Ni55, and Ni55−Cn complexes were further reoptimized, followed by their frontier orbital analysis. It should be noted that, in our calculations using the DMol3 package, DSPP calculations gave the same electronic properties for studied complexes as what was obtained by the all-electron core treatments. The Broyden−Fletcher−Goldfarb−Shanno algorithm57 with a convergence criterion of 10−3 a.u. on the displacement, and the gradient of 10−5 a.u. on the total energy was used for the geometry optimization. A convergence criterion of 10−6 a.u. on the total energy and electron density was adapted for the selfconsistent field calculations. All simulated structures are fully relaxed to optimize with no symmetry restriction. A conjugategradient algorithm with a Gaussian smearing of r = 0.02 eV was used to improve the convergence of electronic structures. As illustrated in Figure 1, we studied the growth of several SWCNTs, including the near-armchair (n,5) (n = 6, 7, 8, 9),
The frontier orbital theory has been widely used to study the chemical reactivity of molecules in organic or organometallic reactions.47−49 The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is used as a simple measure for the kinetic stability or chemical reactivity of aromatic molecules. A small or no HOMO−LUMO gap implies a high chemical reactivity. More importantly, the spatial distribution and orientation of frontier orbitals provide critical information about the characteristics of reactive sites on molecules. In this study, we studied the interaction between a series of near-armchair (n,5), where n = 6, 7, 8, and 9, zigzag (9,0), and armchair (5,5) nanotubes and a fully relaxed Ni55 metal cluster at the early stage of SWCNT growth in order to better understand the influences of active kink sites on the growth of SWCNTs. We first examined factors related to nanotube growth, which have been highlighted by previous studies. We compared the adhesion energy of growing carbon structures on the Ni clusters and then evaluated the structure deformation and deformation energies of the various carbon caps and the corresponding Ni clusters. Next, the electronic charge density changes and the electronic structure rearrangements of the Ni55−Cn complexes were studied. Last, but most importantly, we analyzed the frontier orbitals of the Ni55−Cn complexes to understand their characteristics and to explore how they could be relevant to the chirality selectivity in SWCNT growth.
2. CALCULATION METHODS AND MODELS The spin polarized density functional theory (DFT) calculations, with the Perdew−Burke−Ernzerhof (PBE) exchange correlation function,50 were carried out using the Vienna ab initio simulation package.51 The interaction between an atomic core and electrons were described by the projector augmented wave method.52,53 The plane-wave basis set energy cutoff was set to 400 eV. The periodic boundary conditions were implemented with at least 1 nm vacuum to preclude interactions between a cluster and its images (the simulation boxes were 20 × 20 × C Å (with C from 20 to 32 Å) for different calculated systems). The reciprocal space integration was performed with a 1 × 1 × 1 k-point mesh for all the calculated systems with a discrete character. The electron distribution was determined by electron localization function (ELF). All structures were fully relaxed to optimize with no symmetry restriction until their total energies were converged to