Temperature Dependence of Iron-Catalyzed Continued Single-Walled

J. Phys. Chem. C 2009, 113, 159–169

159

Temperature Dependence of Iron-Catalyzed Continued Single-Walled Carbon Nanotube Growth Rates: Density Functional Tight-Binding Molecular Dynamics Simulations Yasuhito Ohta,† Yoshiko Okamoto,† Stephan Irle,*,†,‡ and Keiji Morokuma*,† Fukui Institute for Fundamental Chemistry, Kyoto UniVersity, Kyoto 606-8103, Japan, Institute for AdVanced Research and Department of Chemistry, Nagoya UniVersity, Nagoya 464-8602, Japan ReceiVed: September 24, 2008; ReVised Manuscript ReceiVed: October 27, 2008

The temperature dependence of continued single-walled carbon nanotube (SWNT) growth on an iron cluster is investigated using quantum chemical molecular dynamics simulations based on the density functional tightbinding method. As a model system for continued SWNT growth, a (5,5) armchair-type SWNT seed attached to an iron Fe38 cluster was used. Continuous and rapid supply of C atoms was provided in the vicinity of the nanotube-metal interface area. The simulations were performed at temperatures of 1000, 1500, and 2000 K. The simulations reveal fastest growth at 1500 K, although the differences are moderate. In the observed growth process, formation of polyyne chains at the rim of the nanotube-metal interface efficiently initiates pentagon/hexagon/heptagon ring formations in the carbon sidewall, leading to “lift-off” of the nanotube from the metal cluster. At 1000 K, the SWNT lift-off is suppressed despite the fact that the total number of created rings in the nanotube is comparable to that at 1500 K. In addition, relatively long polyyne chains tend to form extensions from the carbon sidewall to the metal cluster at 1000 K, whereas at 2000 K, deformation of the nanotube becomes more pronounced and diameter narrowing sets in, and polyyne chains at the rim of the nanotube easily dissociate at this high temperature. These physical and chemical events at 1000 and 2000 K can be considered inhibiting factors preventing efficient growth of the nanotube. 1. Introduction The unique structural features of single-walled carbon nanotubes (SWNTs)1 are responsible for their potentially excellent electric, thermal, and mechanical properties,2,3 and relevant studies have induced strong motivation to consider SWNTs as key elements for the development of new technologies. One of the most pressing issues for the technological application of SWNTs is the improvement of mass production techniques of high-quality SWNTs4,5 as well as gaining control over tube chirality6 and diameter7 (and thereby electronic properties) at the time of synthesis. Elucidating the growth mechanism of SWNTs has therefore been an important subject in the academic and industrial materials sciences communities. The most commonly used synthesis techniques of SWNTs are arc-discharge,1,8 laser ablation,9 and chemical vapor deposition,4,5,10-12 with the latter being the most promising technique for large-scale mass productions. Common in all SWNT synthesis methods is the use of transition metal catalysts such as Fe, Co, Ni, Y, and Mo or their bimetallic alloys. However, to achieve SWNT growth it does qualitatively matter whether the metals or alloys are employed themselves or if they are present in the form of metal oxides13 or as minerals;14 recently even noble metals have shown catalytic activity for SWNT growth.15 The role of the metal catalyst is believed (a) to efficiently catalyze the decomposition of feedstock carbon sources such as hydrocarbons,10 CO,11 and alcohol4 in CVD synthesis, (b) to assist in the early stages of SWNT nucleation,10,16 and (c) to prevent the closure of the tube sidewalls during the growth.9 A review on the role of metal catalysts has been given in refs 17 and 18, and recent remarkable * To whom correspondence should be addressed. E-mail: sirle@ iar.nagoya-u.ac.jp (S.I.); [email protected] (K.M.). † Kyoto University. ‡ Nagoya University.

in situ microscopic (environmental transmission electron microscopy, ETEM) studies of Fe-catalyzed19 and Ni-catalyzed20 SWNT nucleation and growth have been reported showing the metal particles “in action”. The most strongly supported mechanism of SWNT formation is the so-called vapor-liquid-solid (VLS) model.21 In this model, free carbons are first generated by vaporization of carbon materials or decomposition of feedstock carbon sources on the metal catalyst. These free carbons then dissolve into the metal catalyst to form a metal carbide. The supersaturation of the metal carbide with carbon triggers precipitation of carbons on the surface of the metal carbide,22 leading to an extrusion of a fullerene cap-like structure as the “moment of SWNT birth”.10,16 Whether it is a requirement for the metal to form a carbide or not is an undecided question,20 but recent X-ray23 and ETEM19 experimental data suggest that carbide formation typically occurs. From a great number of experiments, the growth rate, quality, shape, and product yield of SWNTs are known to be significantly affected by the choices of experimental parameters such as feedstock molecules and feeding speed,7,17,24 type of metal catalysts,8,17,18,25 size of metal catalyst particles,17,26,27 nature of the substrate,28-30 carrier gas and its pressure,31 presence of water5,32 or reducing etching additives such as H2 and/or NH3,33 furnace temperature,34 and so on, depending on the types of the synthetic techniques. One of the most critical parameters for the synthesis of SWNTs is the environmental temperature, which can range from as low as 350 °C in CVD35 to the thermal conditions encountered in plasma synthesis.36 It is reported that increase in the growth temperature tends to generate SWNTs with larger diameters,4,16,37,38 although absolute values of temperatures differ depending on experimental techniques. At furnace temperatures above 1500 K, high-temperature pulsed arc discharge synthesis produces preferentially double-walled carbon nanotubes.34 At

10.1021/jp808493f CCC: $40.75  2009 American Chemical Society Published on Web 12/09/2008

160 J. Phys. Chem. C, Vol. 113, No. 1, 2009 this moment, it is not known why this is so. In experiment, temperature is directly related to pressure,39 which makes a systematic study difficult. Theoretical simulations of SWNT nucleation and growth processes meet a number of formidably challenging problems. (a) The time scale for carbide formation and subsequent selforganization process of a carbon nanocap and following sidewall growth in experiment is beyond the reach even for classical reactive empirical bond order (REBO)40-42 force field-based MD simulations. (b) The energy stabilization gained by expanding π-conjugation in the molecular orbitals (MOs) of the growing SWNT system cannot be described by the REBO force field by definition yet can be expected to play a crucial role in sidewall defect healing. (c) The electronic state of metal nanoclusters is difficult to describe in any quantum chemical method due to the large density of states (DOS) near the Fermi level. Almost all the atomic-level theoretical studies of SWNT growth dynamics on metal clusters have employed variations of the classical REBO-type potential.43-49 Regarding the temperature dependence of the SWNT nucleation process on Fe clusters, Ding et al. have reported that the carbon diffusion into the metal and subsequent incorporation into the nanotube is accelerated with increasing temperature, while at lower temperature carbon atoms involved in surface diffusion can also contribute to the nucleation and growth process.50 Several REBO-based MD studies of metal nanoparticle melting with and without substrate have been reported, indicating that the melting point of the metal particle is strongly dependent on its size48 and the interaction with support surfaces influences melting temperatures as well.46,49 Since first-principle MD simulations based on the Car-Parrinello (CPMD) approach22,51-53 is computationally too expensive to reach time scales beyond 10-25 ps, combined REBO MD/DFT54 or the use of highly educated guess geometries for DFT geometry optimizations of intermediate structures presumed to occur during SWNT growth55 have become increasingly popular for the inclusion of electronic effects in the growth simulations. For instance, Zhu et al. have shown that pentagon/ heptagon pairs in a growing SWNT can become very stable in the vicinity of an Fe55 particle and can therefore cause changes in tube chirality and increases (not decreases) in diameter.55 Grand-canonical MD simulations of SWNT growth on Ni surfaces have been reported using a tight-binding potential, illustrating the importance of C-chains during the hexagon network formation.56 Recently, we have reported the first successful MD simulation of continued growth starting from a seed SWNT on a metal cluster,57 employing the self-consistent-charge density-functional tight-binding (DFTB) approach with parameters for Fe-Fe and Fe-C interactions developed in our group.58 DFTB/MD is an approximationtodensityfunctionaltheory(DFT)Born-Oppenheimer MD and perhaps 3 orders of magnitudes faster; therefore longer simulation times can be reached compared to CPMD without sacrificing the full quantum chemical description of the system. We have revealed that gas-phase carbon atoms are easily incorporated at the metal-nanotube boundary to form short polyyne chains and that a delicate interplay of dynamics and energetics of rim-attached polyyne chains, sidewall, and metal cluster is essential for the efficient growth of a SWNT on the metal cluster. In sharp contrast to REBO-based simulations, we never found incorporation of long-lasting four- or eightmembered rings into the sidewall, no kink deformations, and no long-lasting free valences on carbon present in the grown sidewalls.

Ohta et al.

Figure 1. Model structure for the growth of a nanotube seed on an iron cluster. The (5,5) armchair-type carbon nanotube is attached to the Fe38 cluster where gray, cyan, and brown spheres represent hydrogen, carbon, and iron, respectively.

The successful simulations motivated us to employ the previously implemented rapid continued SWNT+Fe38 growth methodology to a wider range of environmental temperatures from 1000 to 2000 K to investigate the temperature dependence of continued growth under otherwise fixed conditions. We report here a variety of reaction processes between feedstock carbon atoms and the nanotube-metal cluster during the growth process of the nanotube. The temperature dependence of the primary reaction dynamics is analyzed using growth rates and phenomenological observations. We find that relatively long polyyne chains tend to extend from the SWNT sidewall at the lower temperature of 1000 K, while near structural collapse of the nanotube starts to play a role at the higher temperature of 2000 K. These features are attributed to inefficient growth at these temperatures under the present simulation conditions. 2. Computational Methodology A. Model System. The present model system was inspired by the length amplification experiment of a seed SWNT initiated by Smalley et al.59,60 They successfully prepared short SWNT seeds where both ends of the SWNT fragment were terminated by Fe particles and from which micrometer-long SWNTs have been grown while maintaining the tube diameter. Figure 1 shows our model system for continued growth simulations of a short SWNT seed attached to an iron cluster. The open-ended (5,5) armchair-type seed nanotube with a length of 7.2 Å and a diameter of 6.7 Å contains 60 carbon atoms in which one end of the nanotube was terminated by ten hydrogen atoms to saturate dangling bonds of carbon atoms and the other end was covalently bound to a truncated octahedron Fe38 cluster. The initial geometry of the magic-number iron cluster was cut out from a face-centered cubic (fcc) crystal structure61 to model the iron γ-phase known to be stable in bulk Fe above 1189 K. The motion of the end C and H atoms were frozen during the molecular dynamics simulations to avoid unessential reactions between diffusive gas-phase carbon atoms and the truncated nanotube. This initial structure is identical to the one used by us in ref 57. B. Quantum Chemical Molecular Dynamics Simulations. In the present DFTB/MD simulations, the self-consistent-charge DFTB (SCC-DFTB) method in combination with a finite electronic temperature approach62-64 with Te ) 10000 K was employed to evaluate the quantum chemical potential on the fly. The electronic temperature allows the occupancy of each molecular orbital to change smoothly from 2 to 0 depending on its energy and effectively incorporates the open-shell nature of the system due to near-degeneracy of iron d orbitals as well

Temperature Dependence of Iron-Catalyzed SWNTs

Figure 2. Initial positions of the incident carbons. G is the center of mass of the target candidate carbons. The incident carbon and target candidate carbons were highlighted by cyan spheres.

as carbon dangling bonds. We previously found that without electronic temperature the iron cluster is very low in reactivity and does not promote the growth of nanotube.65 In the molecular dynamics simulations the velocity Verlet integrator was used with a time step of 1 fs, and nuclear temperature was controlled by connecting the Nose-Hoover chain thermostat66 to the degrees of freedom of the present model system. The geometry shown in Figure 1 was used as initial starting structure for annealing simulations at 1000, 1500, and 2000 K for 10 ps, and ten geometries and associated velocities were randomly extracted between 5 and 10 ps from these annealing runs as starting geometries with letters A to J for identification purposes to initiate carbon-supply simulations at the respective temperature for 45 ps. Thus, the investigation in this work is comprised of a total of 30 trajectories plus a large number of less systematic supplementary simulations. Cartesian coordinates of the final 30 trajectories at 45 ps are available as Supporting Information and the Cartesian coordinates of the full trajectories will become available at http://kmweb.fukui.kyoto-u.ac.jp/nano at the time of publication. C. Carbon Supply Simulations. In concern for the feeding procedure in the carbon-supply simulations, a single C atom was supplied around the C-Fe boundary area between the nanotube and the metal cluster every 0.5 ps, increasing the number of carbon atoms in the system from initially 60 to 150 at the end of the 45 ps simulations. Figure 2 shows how initial positions of the successively supplied carbon atoms are characterized. To randomly select initial positions of the incident carbon atoms, a target carbon atom was first randomly chosen from “target candidates” (rim SWNT carbon atoms) at the C-Fe interface. The requirement for SWNT carbon atoms to become a target candidate is the existence of a C-Fe bond or sp hybridization with a covalent bond to a single neighbor C atom. A point O (see Figure 2) is then determined by the extension of the line from the center of mass of the target candidates to the chosen target carbon atom. The length of the line D is an input parameter in our supply routine and was fixed to D ) 5 Å in the present simulations. The positions of the incident C atoms were randomly distributed in a sphere around the point O using the polar coordinates r, θ, and φ, where the maximum value of r was set to 3 Å. The initial velocity vector was directed to the position of the target carbon atom with a magnitude of 0.052 eV, which corresponds to the kinetic energy equivalent of an “atomic carbon nuclear temperature” of 600 K. Although the selection of the incident energy of the C atoms is rather arbitrary, we have confirmed that growth dynamics were not significantly affected by the magnitude of the incident energy,

J. Phys. Chem. C, Vol. 113, No. 1, 2009 161 at least within the range of ∼0.1 eV, by performing 30 supplemental simulations. In our simulations it is assumed that C atoms were generated by the decomposition of carbon precursors on the metal cluster or by evaporation of carbon fragments as commonly occurring in the laser ablation technique. Under the experimental conditions, it is reported that common species besides carbon atoms are C2 and C3,67 and therefore we also implemented C2-supply simulations with a feeding rate of 1 ps, which results formally in the same carbon density increase as in the C-atom supply simulations with a feeding rate of 0.5 ps. However, supply of C2 molecule around the C-Fe boundary area caused rapid formation of highly entangled carbon complexes around the metal cluster, which we deemed unlikely to lead to the growth of SWNTs (perhaps first stages of encapsulation, also observed for instance by Raty et al.52). We think that the use of less reactive and less mobile C2 molecules as feedstock carbon source requires longer annealing time in order to successfully contribute to the growth of the SWNT sidewall. Since the required longer feeding simulations are computationally too demanding even for DFTB/MD simulations, we settle for now with C atoms as a feedstock carbon source. 3. Results and Discussion A. Role of Polyyne Chains and Metal Cluster for Growth of the Nanotube. In the present carbon-supply simulations, we observed rapid growth behavior of the nanotube for all the temperatures where the construction of the sidewall of the nanotube is mainly initiated by the formation of the polyyne chains between the iron cluster and the nanotube. Figure 3 shows typical polyyne dynamics during the growth process of the nanotube, here encountered in trajectory E at 1500 K. At 10.60 ps, an incident C atom approaches an edge carbon in the nanotube to form a C-C bond. The C-C bond at 10.80 ps is then promptly drawn to an iron atom to complete formation of the C-C-Fe structure so that its principal molecular axis becomes parallel to the nanotube axis. The embedded incident C atom between the edge carbon and the Fe atom has a high kinetic energy due to the exothermic addition to the carbon network and can switch binding to different iron sites, frequently breaking and reforming the C-Fe bond. The neighbor C2 chain dangling at the rim of the nanotube also experiences frequent C-Fe bond-breaking/formation, allowing it to migrate along different iron sites. Around 12 ps, the dangling C atom and the short C2 chain approach each other to form a stable sixmembered ring. Five- and seven-membered rings were also created by the similar process during the growth simulations. The intermittent occurrence of such carbon polygon formations at the rim area of the nanotube is assisted by thermal fluctuation of catalytic iron atoms, leading to the main construction process of extending the tube sidewall during the continued SWNT growth. B. Temperature Dependence of the Growth Rate. We compare the results at 1000, 1500, and 2000 K for the time variation of the tube length in Figure 4. The tube length was estimated by the quantity |GC-GFe| - RFe where GC is the center of mass of ten frozen carbon atoms terminated by edge hydrogen atoms at the side of the SWNT opposite to the metal particle, GFe the center of mass of the Fe38 cluster, and RFe the average radius of Fe38, which was assumed to be steady with approximately 3.6 Å. Table 1 lists the average growth rate of the nanotube and statistics for the structural features of the resulting nanotubes after 45-ps simulations. The growth rate was determined by linear regression analysis of the tube length as a

162 J. Phys. Chem. C, Vol. 113, No. 1, 2009

Ohta et al.

Figure 3. Typical six-membered ring formation in the carbon sidewall during SWNT growth. Pink spheres highlights carbon atoms involved in the hexagon formation process. The snapshots are obtained from the trajectory E at 1500 K (see Figure 7).

Figure 4. Time variations of the tube length at T ) 1000, 1500, and 2000 K.

function of time for the ten trajectories. As shown in Figure 4, the increase in tube length at 1000 K is visibly slower compared to that at 1500 and 2000 K, and the distribution of trajectories is narrower compared to those at 1500 and 2000 K, although the growth-rate difference (0.0094 Å/ps) between 1500 and 2000 K is not negligible compared to that (0.0065 Å/ps) between 1000 and 2000 K. The average total number of carbon atoms at 2000 K is about 10% lower than that for 1000 and 1500 K, and the number of carbon chains attached to the sidewall also

decreases with increasing temperature. These results indicate a more dissociative behavior of carbon chains attached to the nanotube at higher temperatures. Regarding the ring-count statistics, it is notable that the number of the seven-membered rings is comparable to that of the five-membered rings at all temperatures as we had reported earlier.57 This observation contrasts with that in our previous fullerene formation simulations where five- and six-membered rings were dominant over heptagons in the compositions of giant fullerenes.68,69 The initial SWNT seed contains 20 six-membered rings, and thereby the net increase of the total number of the six-membered rings after 45 ps simulation is 2.5, 1.9, and 1.7 for 1000, 1500, and 2000 K, respectively. These numbers are remarkably smaller than the corresponding total numbers of the 5- and 7-membered rings at respective nuclear temperature. We found that the large contribution of the seven-membered rings to the carbon sidewall in the present simulations is mainly due to the insertion reaction of gas-phase carbon atom into the hexagonal sidewall of the nanotube. We will describe this reaction in more detail as well as other primarily chemical events observed between 1000-2000 K. C. Formation and Dissociation of Polyyne Chains on the Sidewall of SWNT. In the present carbon-supply simulations, we observed that about 50% of the incident carbon atoms reacts with the sidewall of the nanotube, giving rise to structural modifications. One of the more frequently observed reactions is the insertion of an incident carbon atom into the carbon sidewall, creating heptagons and hexagons by addition to hexagons and pentagons, respectively. Another noticeable event along the rim of the SWNT sidewall is the formation and dissociation of short carbon chains. The sp-hybridized carbon chain formation is initiated by the incident C atom captureinduced creation of a deformed heptagon in the carbon sidewall. Figure 5a shows a reaction process of an incident carbon atom targeting a hexagon ring in the nanotube. When the carbon atom approaches the sidewall, a CC adatom triangular structure is created with the incident carbon atom becoming a bridge located on top of a hexagon C-C bond. The attack of another carbon atom to the C-adatom opens two possibilities for further reactions: one where a C2 molecule is detaching from the carbon sidewall and the other where a longer polyyne chain is formed on the carbon sidewall. Figure 5b shows the dissociation process of such a C2 unit produced as the result of the aforementioned CC adatom mechanism at 7.28 ps. Immediately after dissociation, the sidewall of the nanotube recovers the original hexagon, which is preferable over a defective SWNT sidewall even at the prevalent high temperatures. The growth of longer sp carbon chains attached to the carbon sidewalls on the other hand is a result of successive reactions of multiple incident carbon atoms as shown in Figure 5c. Eventually, the carbon chains attached


J. Phys. Chem. C, Vol. 113, No. 1, 2009 163

Figure 5. Reaction dynamics on the sidewall of the nanotube. (a) Insertion reaction of the incident C atom into the carbon sidewall. (b) C2 dissociation process. (c) C3 sp carbon chain formation process. The snapshots of parts a and b were obtained from trajectory A at T ) 1000 K and those of part c from trajectory H at 1000 K (see Figure 6).

TABLE 1: Average Growth Rate of the SWNT and Statistics for the Structural Feature of the Nanotube after 45-ps Simulationsa growth rate total T [K] [Å/ps] carbons chain carbons 1000 1500 2000

0.0348 0.0507 0.0413

112.9 110.1 102.7

3.9 0.3 0.2

five-, six-, and seven-membered rings 4.7 5.7 5.7

22.5 21.9 21.7

4.8 5.2 5.3

a Total carbons: average total number of carbon atoms constituting the nanotube. Chain carbons: average total number of carbon chains formed on the sidewall of the nanotube. Five-, six-, and seven-membered rings: total number of respective rings in the resulting SWNT carbon structure.

to the sidewall proceed to either dissociation from the sidewall or further growth by incorporating additional incident carbons every time they are attacked by gas-phase carbon atoms. D. Carbon Dynamics on the Sidewall of SWNT at T ) 1000 K. As mentioned in the previous subsection, most short carbon chains such as C2 and C3 sticking on the sidewall of the nanotube frequently dissociated at all temperatures, typically as a consequence of an attack of subsequent incident carbon

atoms. However, as shown in Table 1, we observed that relatively long polyyne chains or carbon branches tend to form on the carbon sidewall in the case of lower temperature of T ) 1000 K. Figure 6a displays the snapshots of the ten trajectories at T ) 1000 K after 45-ps simulations. In the structures C, E, H, and I, the polyyne chains or carbon branches are attached to the nanotube sidewall. Structure C especially possesses a notable feature where a carbon complex creates a bridging structure extending from the carbon sidewall to the metal surface. The formation of such bridging structures was also observed at the higher temperatures, but in these cases they were short-lived as the carbon chains easily dissociated from the carbon sidewall. Figure 6b shows the formation process of the aforementioned bridging structure in trajectory C. At 29.52 ps, a long polyynechain complex is formed on the carbon sidewall by incident carbon atom capture. This long polyyne chain exerts largeamplitude movements that one could compare to the swaying of “seaweed” and gradually curls up with the free end approaching the metal surface. After several “failed attempts”, at 45 ps, the end of the carbon chain finally attaches to the metal surface creating the bridging structure that now extends from the carbon sidewall to the metal surface. Since the carbon chain is mostly


Ohta et al.

Figure 6. Results at T ) 1000 K. (a) Snapshots of ten trajectories after 45-ps simulations. (b) Bridging structure formation observed in the trajectory C.

composed of reactive sp carbons, it will easily incorporate gasphase carbon atoms leading to the formation of larger carbon complex. Probably, the amorphous nature of such a carbon complex would increase as more carbon atoms become incorporated into such a carbon complex. It is conceivable that further carbon condensation around the metal-tube boundary area causes formation of large carbon complexes and that such a process can become an inhibiting factor for growth (carbon encapsulation, “death of the catalyst”). E. Description of Carbon Dynamics on the Sidewall of SWNT at T ) 1500 K. The present carbon supply simulations at all the nuclear temperatures were implemented with the incident energy of 0.052 eV. As for the T ) 1500 K case, we previously performed similar growth simulations with the incident energy of 0.13 eV.57 However, the results were not significantly affected by the values of incident energies, and for both cases we have clearly observed rapid growth behavior of the nanotube on the metal cluster. The reaction between the incident carbon and the nanotube or the metal cluster are highly exothermic, with the reaction energy typically being in the order of several electronvolts, which is several orders of magnitude larger than the incident carbon energies used in the present simulations. Therefore, the reaction dynamics is mainly governed by the large exothermicity and is insensitive to the choice of the incident carbon energy. Figure 7a shows 10 snapshots after 45-ps simulation at T ) 1500 K. The frequency of the polyyne-chain formation on the carbon sidewall at 1500 K noticeably dropped compared to the case of T ) 1000 K. At T ) 1500 K, the majority of the polyyne chains promptly dissociates from the sidewall, leaving the carbon sidewall relatively inert to further carbon additions. Some of the dissociated polyyne chains were recaptured on the surface

of the metal cluster where they formed Fe-Cn-Fe bridging structures. The increasingly frequent dissociation events of polyyne chains on the carbon sidewalls lower the possibility of the formation of longer carbon branches which could possibly evolve into larger amorphous carbon complexes. Avoiding the formation process of such larger carbon complex on the sidewall may be one of key factors for efficient growth of the nanotube. However, we note that the formation of the polyyne chains at the rim of the nanotube is essential for the efficient growth of the nanotube as mentioned above. In fact, we observed rapid pentagon, hexagon, and heptagon ring formation from short carbon chains which “wobble” at the rim of the nanotube during the growth simulations. Figure 7b shows successive rapid formation of hexagon and pentagon by the reaction of an incident C atom with the rim area of the nanotube. At t ) 38.88 ps, an incident C atom approaches an edge C atom of the nanotube to bring about the C-C bond breaking of the heptagon in the carbon sidewall. The cleaved heptagon generates C3 and C4 polyyne chains at the adjacent sites of the rim of the nanotube at t ) 39.08 ps. These polyyne chains promptly approach each other to form a hexagon at 39.32 ps, which snaps closed a new adjacent pentagon at 39.52 ps. Such ring formations repeatedly occurred in a concerted manner with the lift-off of the nanotube sidewall from the metal cluster. Considering the fact that the growth rate at 1500 K is faster than that at 1000 K as shown in Table 1 despite comparable average numbers of rings in the nanotube, 1500 K may be more favorable for rapid polygon sidewall construction and subsequent lift-off of the nanotube on the Fe cluster. F. Description of Carbon Dynamics on the Sidewall of SWNT at T ) 2000 K. Figure 8 shows snapshots after 45-ps simulation at T ) 2000 K. The notable feature observed at T )



Figure 7. (a) Snapshots of ten trajectories after 45-ps simulations at T ) 1500 K. (b) Rapid formations of carbonaceous hexagon and pentagon observed in the trajectory E. Pink spheres represent carbon atoms involved in the polygonal formation reaction.

2000 K is the pronounced structural deformation of the nanotube. Obviously, increase in temperature promotes defect creation in the carbon sidewall due to the increase in the atomic kinetic energies of constituent carbon atoms. The structures C and D especially exhibit significant deformation of the nanotube where their diameters around the metal-nanotube contact area are becoming narrower. This tendency seems to contrast the previous reports on the increasing behavior of the nanotube diameter with temperature.16,37,38 Their experimental observations have been explained by the kinetics of condensation of the metal particles. In the present simulations, the total number of iron atom is fixed, and thus such condensation effect of the metal particle is not involved. Interestingly, Bhowmick et al. have recently observed both increasing and decreasing behavior of the tube diameter with increasing growth temperature in their SWNT synthesis using the floating catalyst method.70 They have explained that distribution of narrow diameter SWNT is due to thermodynamic effect on the curvature of the nanotube. Our findings at T ) 2000 K seems to be in line with their suggestion although further study would be necessary to clarify the temperature dependence of diameter of SWNTs. It is worth to note that the calculations by Zhu et al. predicted that diameter narrowing should be thermodynamically unfavorable.55 We also note that mobility of Fe atoms significantly increases with temperature. The large fluctuation of Fe atoms brings about more frequent bond breaking and formation of the C-Fe bonds around the boundary area between the nanotube and the metal

cluster, contributing to the deformation and collapse of the nanotube. We observed that the polyyne chains which dangle at the rim of the nanotube often dissociate from the nanotube and then migrate onto the surface of the metal cluster. At T ) 2000 K, carbon chains are hardly formed on the sidewall of the nanotube. Most of the C2 units “wobbling” on the carbon sidewall were abstracted by an incident carbon atom without forming longer carbon chains, while several C chains spontaneously dissociated from the carbon sidewall with a lifetime of ∼ 1 ps as well, similar to the case at T ) 1500 K. As we mentioned in the case of T ) 1000 K, the formation of polyyne chains on the carbon sidewall can initiate the formation of larger carbon complexes with greater amorphous nature, inducing inefficiency for the growth of the nanotube. The less frequent polyyne chains on the carbon sidewall at T ) 2000 K thereby seem to remove an inhibiting factor for efficient growth. However, as shown in Figure 8b, large kinetic energy at T ) 2000 K also causes more frequent dissociations of polyyne chains at the rim of the nanotube, which are responsible for extending the sidewall. Therefore, the net efficiency of nanotube growth at T ) 2000 K is lower than that of 1500 K due to polyyne-chain dissociation on the nanotube. G. Description of Early-Stage Carbide Formation. To understand nonequilibrium dynamics between the supplied carbons and the metal cluster in more detail, we analyzed Mulliken atomic charges71,72 of the present system. Figure 9 shows a typical time variation of atomic Mulliken charges during


Ohta et al.

Figure 8. (a) Snapshots of ten trajectories after 45 ps simulations at T ) 2000 K. (b) Dissociation of C2 molecule from the rim of the nanotube observed in the trajectory G. Dissociating C2 is highlighted by pink spheres.

the growth process of the SWNT seed for trajectory E at 1500 K. At t ) 0, without carbon supply, one can see some charge transfer around the contact area from the Fe cluster to the nanotube. Because of this back-donation of the electrons, the C-C bonds in the Fe-attachment region of carbon sidewall is weakened due to the population of π* MOs of the nanotube. During the C atom supply simulations, several tens of C atoms were captured on the surface of the Fe cluster, eventually reacting with each other to form C2 molecules after a period of surface diffusion. The C2 molecules typically form a Fe-C-C-Fe structure on the metal surface and exhibit wobbling behavior by frequently breaking their C-Fe bonds, as we had described elsewhere.73 The wobbling C2 molecules also migrate and react with the other C molecules, leading to the formation of polyyne chains on the metal surface. Both ends of the polyyne chains are typically bound to Fe atoms, forming frequently Fe-Cn-Fe bridging structures, but the chains remain able to diffuse on the metal surface through intermittent C-Fe bond breaking/ formation. The Mulliken charge at t ) 20 ps in Figure 9 clearly shows that C molecules accept electrons from the iron atoms, making the Fe-C bonds strongly polar. The lack of electrons in the Fe cluster weakens the Fe-Fe bond and allows C atoms to penetrate into the inside of the Fe cluster. At t ) 45 ps, the Fe cluster suffered disintegration, allowing incursion of several C atoms into its subsurface layers, while polyyne chains remain in the outer region of the Fe cluster. The mobility of the penetrated C atoms was much lower than those on the surface of the Fe cluster. Therefore, we did not observe incorporation of subsurface C atoms into the nanotube.

H. Average Number of Fe-C and Fe-Fe bonds. Figure 10 shows average coordinate number of the Fe atoms as a function of time. As a common trend in all the temperatures, the number of Fe-C bonds per Fe atom almost monotonically increases with increasing number of carbon atoms as shown in Figure 10a, and accordingly the number of Fe-Fe bonds per Fe atom decreases as shown in Figure 10b. Most notable is that the total Fe valence (number of nearest neighboring atoms within a given distance) also monotonically decreases with increasing number of carbon atoms, as shown in Figure 10c. This feature is related to the disintegration of the Fe cluster initiated by the enhanced interaction of Fe atoms with carbons due to the high concentration of carbons on the metal surface. We expect that such disintegration would be suppressed in a larger cluster with more than 38 metal atoms owing to the decrease in surface effect of the metal cluster. We note that the total average Fe valence at higher temperature is always smaller than that at lower temperature as well, along with the numbers of Fe-Fe and Fe-C bonds. Obviously the Fe cluster expands more at higher temperatures due to the increased kinetic energies of its constituent atoms. Such spatial expansion with temperature makes the Fe cluster vulnerable to disintegration. 4. Summary and Conclusions In summary, we have performed rapid growth simulations of a SWNT seed on an iron cluster by means of a quantum chemical molecular dynamics method based on the densityfunctional tight-binding (SCC-DFTB) method with a finite electronic temperature approach. The results have been com-



Figure 9. Time variation of atomic Mulliken charges during SWNT growth (taken from trajectory E at 1500 K). (a) Atomic charges of the nanotube-metal cluster. (b) Extracted carbon and hydrogen atomic charges. (c) Extracted Fe atomic charges.

pared for the nuclear temperatures of 1000, 1500, and 2000 K in order to investigate temperature dependence of the growth process of SWNT on metal cluster. At all three temperatures, we have observed rapid growth behavior of the seed nanotube, indicating that carbon supply around the boundary area between the nanotube and the metal cluster can be an efficient pathway for the feedstock carbon atoms to contribute to the growth of a nanotube. The grown nanotubes consist of pentagons, hexagons, and heptagons, with no or only intermittently occurring few fouror eight-membered rings, with few to no stable valence defects, in contrast to classical REBO simulations such as in refs 43-50. SWNT sidewall growth does not proceed in an ordered fashion, with the (n,m) chirality maintained in the interface region at all times. Rather, as our quantum chemical MD simulations show, short carbon chain and polyyne dynamics allow for intermediate creation of pentagons and heptagons with a near 1:1 ratio, and therefore annealing through Stone-Wales transformations74 to all-hexagon networks can be expected, leading to the experimentallyobservedtubestructureswithuniform(n,m)characteristics. Regarding temperature dependence of SWNT, at 1000 K we have found that relatively long polyyne chains or carbon branches tend to form from the sidewall of the nanotube to the surface of the metal cluster. SWNT “lift-off” from the metal particle is suppressed despite the fact that the total number of created pentagon/hexagon/heptagon rings in the nanotube is comparable to that at 1500 K. 1500 K seems to represent an ideal balance between disordered growth mediated by small carbon chains and polyynes on one hand and structural deformations on the other. At 2000 K, pronounced deformations

Figure 10. Time variation of average coordination number of Fe atoms. (a) Average Fe-C bonds per Fe atom. (b) Average Fe-Fe bonds per atom. (c) Total Fe valences.

of the nanotube have been observed around the nanotube-metal contact as well as dissociation behavior of polyyne chains at the rim of the carbon sidewall. In addition, the Fe38 cluster becomes more liquidlike, allowing penetration by carbon atoms (carbide formation), and tends to disintegrate at this temperature. These physical and chemical events observed at 1000 and 2000 K can be regarded as inihibiting factors preventing efficient SWNT growth. Of course, such an estimate has to be viewed in the light of the simulation conditions. Experimental conditions involve slower addition of less reactive molecular carbon C2, C3, etc., species as well, and thus more time for annealing is available to “clean” the tubes and metal particles from amorphous carbon by the sidewall growth process occurring at the Fe-C interface, especially at lower temperatures. Acknowledgment. This work was in part supported by a CREST (Core Research for Evolutional Science and Technology) grant in the Area of High Performance Computing for Multiscale and Multiphysics Phenomena from the Japan Science and Technology Agency. S.I. also acknowledges support by the Program for Improvement of Research Environment for Young Researchers from Special Coordination Funds for Promoting Science and Technology commissioned by the Ministry of Education, Culture, Sports, Science and Technology of Japan. The simulations were performed in part using the computer resources at the Research Center for Computational Science, Okazaki Research Facilities, National Institutes for Natural Sciences.

168 J. Phys. Chem. C, Vol. 113, No. 1, 2009 Supporting Information Available: Cartesian coordinates of the final snapshots of 30 trajectories at 45 ps. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Iijima, S.; Ichihashi, T. Single-Shell Carbon Nanotubes of 1-Nm Diameter. Nature 1993, 364 (6439), 737–737. (2) Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Science of Fullerenes and Carbon Nanotubes; Academic Press: New York, 1996. (3) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Physical properties of Carbon Nanotube; Imperial College Press: London, 1998. (4) Maruyama, S.; Kojima, R.; Miyauchi, Y.; Chiashi, S.; Kohno, M. Low-temperature synthesis of high-purity single-walled carbon nanotubes from alcohol. Chem. Phys. Lett. 2002, 360 (3-4), 229–234. (5) Hata, K.; Futaba, D. N.; Mizuno, K.; Namai, T.; Yumura, M.; Iijima, S. Water-assisted highly efficient synthesis of impurity-free single-waited carbon nanotubes. Science 2004, 306 (5700), 1362–1364. (6) Bachilo, S. M.; Balzano, L.; Herrera, J. E.; Pompeo, F.; Resasco, D. E.; Weisman, R. B. Narrow (n,m) Distribution of Single-Walled Carbon Nanotubes Grown Using a Solid Supported Catalyst. J. Am. Chem. Soc. 2003, 125 (37), 11186–11187. (7) Lu, C.; Liu, J. Controlling the Diameter of Carbon Nanotubes in Chemical Vapor Deposition Method by Carbon Feeding. J. Phys. Chem. B 2006, 110, 20254–20257. (8) Journet, C.; Maser, W. K.; Bernier, P.; Loiseau, A.; de la Chapelle, M. L.; Lefrant, S.; Deniard, P.; Lee, R.; Fischer, J. E. Large-scale production of single-walled carbon nanotubes by the electric-arc technique. Nature 1997, 388 (6644), 756–758. (9) Thess, A.; Lee, R.; Nikolaev, P.; Dai, H. J.; Petit, P.; Robert, J.; Xu, C. H.; Lee, Y. H.; Kim, S. G.; Rinzler, A. G.; Colbert, D. T.; Scuseria, G. E.; Tomanek, D.; Fischer, J. E.; Smalley, R. E. Crystalline ropes of metallic carbon nanotubes. Science 1996, 273 (5274), 483–487. (10) Cheng, M. H.; Li, F.; Su, G.; Pan, H. Y.; He, L. L.; Sun, X.; Dresselhaus, M. S. Large-scale and low-cost synthesis of single-walled carbon nanotubes by the catalytic pyrolysis of hydrocarbons. Appl. Phys. Lett. 1998, 72, 3282–3284. (11) Dai, H.; Rinzler, A. G.; Nikolaev, P.; Thess, A.; Colbert, D. T.; Smalley, R. E. Single-wall nanotubes produced by metal-catalyzed disproportionation of carbon monoxide. Chem. Phys. Lett. 1996, 260, 471–475. (12) Murakami, Y.; Chiashi, S.; Miyauchi, Y.; Maruyama, S. Direct synthesis of single-walled carbon nanotubes on silicon and quartz-based systems. Jpn. J. Appl. Phys. 2004, 43 (3), 1221–1226. (13) Rummeli, M. H.; Borowlak-Palen, E.; Gemming, T.; Pichler, T.; Knupfer, M.; Kalbac, M.; Dunsch, L.; Jost, O.; Silva, S. R. P.; Pompe, W.; Bucher, B. Novel Catalysts, Room Temperature, and the Importance of Oxygen for the Synthesis of Single-Walled Carbon Nanotubes. Nano Lett. 2005, 5, 1209–1215. (14) Kawasaki, S.; Shinoda, M.; Shimada, T.; Okino, F.; Touhara, H. Single-walled carbon nanotubes grown on natural minerals. Carbon 2006, 44, 2139–2141. (15) Takagi, D.; Homma, Y.; Hibino, H.; Suzuki, S.; Kobayashi, Y. Single-Walled Carbon Nanotube Growth from Highly Activated Metal Nanoparticles. Nano Lett. 2006, 6 (12), 2642–2645. (16) Kataura, H.; Kumazawa, Y.; Maniwa, Y.; Ohtsuka, Y.; Sen, R.; Suzuki, S.; Achiba, Y. Diameter control of single-walled carbon nanotubes. Carbon 2000, 38 (11-12), 1691–1697. (17) Moisala, A.; Nasibulin, A. G.; Kauppinen, E. I. The role of metal nanoparticles in the catalytic production of single-walled carbon nanotubes - a review. J. Phys.: Condens. Matter 2003, 15 (42), S3011–S3035. (18) Gavillet, J.; Thibault, J.; Stephan, O.; Amara, H.; Loiseau, A.; Bichara, C.; Gaspard, J. P.; Ducastelle, F. Nucleation and growth of singlewalled nanotubes: The role of metallic catalysts. J. Nanosci. Nanotechnol. 2004, 4 (4), 346–359. (19) Yoshida, H.; Takeda, S.; Uchiyama, T.; Kohno, H.; Homma, Y. Atomic-Scale In-situ Observation of Carbon Nanotube Growth from Solid State Iron Carbide Nanoparticles. Nano Lett. 2008, 8 (7), 2082–2086. (20) Hofmann, S.; Sharma, R.; Ducati, C.; Du, G.; Mattevi, C.; Cepek, C.; Cantoro, M.; Pisana, S.; Parvez, A.; Cervantes-Sodi, F.; Ferrari, A. C.; Dunin-Borkowski, R.; Lizzit, S.; Petaccia, L.; Goldoni, A.; Robertson, J. In situ Observations of Catalyst Dynamics during Surface-Bound Carbon Nanotube Nucleation. Nano Lett. 2007, 7 (3), 602–608. (21) Harris, P. J. F. Solid state growth mechanisms for carbon nanotubes. Carbon 2007, 45 (2), 229–239. (22) Gavillet, J.; Loiseau, A.; Journet, C.; Willaime, F.; Ducastelle, F.; Charlier, J.-C. Root-Growth Mechanism for Single-Wall Carbon Nanotubes. Phys. ReV. Lett. 2001, 87 (27), 275504–1. (23) Stolojan, V.; Tison, Y.; Chen, G. Y.; Silva, R. Controlled GrowthReversal of Catalytic Carbon Nanotubes under Electron-Beam Irradiation. Nano Lett. 2006, 6 (9), 1837–1841.

Ohta et al. (24) Mora, E.; Pigos, J. M.; Ding, F.; Yakobson, B. I.; Harutyunyan, A. R. Low-Temperature Single-Wall Carbon Nanotubes Synthesis: Feedstock Decomposition Limited Growth. J. Am. Chem. Soc. 2008, 130, 11840– 11841. (25) Li, X.; Tu, X.; Zaric, K.; Welsher, K.; Seo, W. S.; Zhao, W.; Dai, H. Selective Synthesis Combined with Chemical Separation of SingleWalled Carbon Nanotubes for Chirality Selection. J. Am. Chem. Soc. 2007, 129, 15770–15771. (26) Schaffel, F.; Kramberger, C.; Rummeli, M. H.; Grimm, D.; Mohn, E.; Gemming, T.; Pichler, T.; Rellinghaus, B.; Buchner, B.; Schultz, L. Nanoengineered Catalyst Particles as a Key for Tailor-Made Carbon Nanotubes. Chem. Mater. 2007, 19, 5006–5009. (27) Kobayashi, K.; Kitaura, R.; Kumai, Y.; Goto, Y.; Inagaki, S.; Shinohara, H. Synthesis of single-wall carbon nanotubes grown from sizecontrolled Rh/Pd nanoparticles by catalyst-supported chemical vapor deposition. Chem. Phys. Lett. 2008, 458, 346–350. (28) Chakraborty, A. K.; Jacobs, J.; Anderson, C.; Roberts, C. J.; Hunt, M. R. C. Chemical vapor deposition growth of carbon nanotubes on Si substrates using Fe catalyst: What happens at the nanotube/Fe/Si interface. J. Appl. Phys. 2006, 100, 084321/1–6. (29) Wang, Y.; Li, B.; Ho, P. S.; Yao, Z.; Shi, L. Effect of supporting layer on growth of carbon nanotubes by thermal chemical vapor deposition. Appl. Phys. Lett. 2006, 89, 183113/1–3. (30) Rummeli, M. H.; Schaffel, F.; Kramberger, C.; Gemming, T.; Bachmatiuk, A.; Kalenczuk, R. J.; Rellinghaus, B.; Buchner, B.; Pichler, T. Oxide-Driven Carbon Nanotube Growth in Supported Catalyst CVD. J. Am. Chem. Soc. 2007, 129, 15772–15773. (31) Nishide, D.; Kataura, H.; Suzuki, S.; Tsukagoshi, K.; Aoyagi, Y.; Achiba, Y. High-yield production of single-wall carbon nanotubes in nitrogen gas. Chem. Phys. Lett. 2003, 372 (1-2), 45–50. (32) Zhang, G.; Mann, D.; Zhang, L.; Javey, A.; Li, Y.; Yenilmez, E.; Wang, Q.; McVittie, J. P.; Nishi, Y.; Gibbons, J.; Dai, H. Ultra-high-yield growth of vertical single-walled carbon nanotubes: Hidden roles of hydrogen and oxygen. Proc. Natl. Acad. Sci. 2005, 102 (45), 16141–16145. (33) Ting, J.-M.; Lin, S.-H. Growth and characteristics of carbon nanotubes obtained under different C2H2/H2/NH3 concentrations. Carbon 2007, 45, 1934–1940. (34) Sugai, Y.; Yoshida, H.; Shimada, T.; Okazaki, T.; Shinohara, H. New Synthesis of High-Quality Double-Walled Carbon Nanotubes by HighTemperature Pulsed Arc Discharge. Nano Lett. 2003, 3 (6), 769–773. (35) Cantoro, M.; Hofmann, S.; Pisana, S.; Scardaci, V.; Parvez, A.; Ducati, C.; Ferrari, A. C.; Blackburn, A. M.; Wang, K.-Y.; Roberson, J. Catalytic Chemical Vapor Deposition of Single-Wall Carbon Nanotubes at Low Temperatures. Nano Lett. 2006, 6 (6), 1107–1112. (36) Kim, K. S.; Cota-Sanchez, G.; Kingston, C. T.; Imris, M.; Simard, B.; Soucy, G. Large-scale production of single-walled carbon nanotubes by induction thermal plasma. J. Phys. D. Appl. Phys. 2007, 40, 2375–2387. (37) Bandow, S.; Asaka, S.; Saito, Y.; Rao, A. M.; Grigorian, L.; Richter, E.; Eklund, P. C. Effect of the growth temperature on the diameter distribution and chirality of single-wall carbon nanotubes. Phys. ReV. Lett. 1998, 80 (17), 3779–3782. (38) Kumar, M.; Ando, Y. Controlling the diameter distribution of carbon nanotubes grown from camphor on a zeolite support. Carbon 2005, 43 (3), 533–540. (39) Einarsson, E.; Murakami, Y.; Kadowaki, M.; Maruyama, S. Growth dynamics of vertically aligned single-walled carbon nanotubes from in situ measurements. Carbon 2008, 46, 923–930. (40) Brenner, D. W. Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor-Deposition of Diamond Films. Phys. ReV. B 1990, 42 (15), 9458–9471. (41) Brenner, D. W. Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. [Erratum to document cited in CA114(6):53045x]. Phys. ReV. B 1992, 46, 1948. (42) Brenner, D. W.; Shenderova, O. A.; Harrison, J. A.; Stuart, S. J.; Ni, B.; Sinnott, S. B. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter 2002, 14, 783–802. (43) Maruyama, S.; Shibuta, Y. Molecular dynamics in formation process of SWNTs. Mol. Cryst. Liq. Cryst. 2002, 387, 311–316. (44) Shibuta, Y.; Maruyama, S. Molecular dynamics simulation of generation process of SWNTs. Physica B 2002, 323 (1-4), 187–189. (45) Shibuta, Y.; Maruyama, S. Molecular dynamics simulation of formation process of single-walled carbon nanotubes by CCVD method. Chem. Phys. Lett. 2003, 382 (3-4), 381–386. (46) Shibuta, Y.; Maruyama, S. A molecular dynamics study of the effect of a substrate on catalytic metal clusters in nucleation process of singlewalled carbon nanotubes. Chem. Phys. Lett. 2007, 437 (4-6), 218–223. (47) Ding, F.; Bolton, K.; Rosen, A. Nucleation and growth of singlewalled carbon nanotubes: A molecular dynamics study. J. Phys. Chem. B 2004, 108 (45), 17369–17377. (48) Ding, F.; Rosen, A.; Bolton, K. Size dependence of the coalescence and melting of iron clusters: A molecular-dynamics study. Phys. ReV. B 2004, 70 (7), 075415/1–075415/6.

Temperature Dependence of Iron-Catalyzed SWNTs (49) Ding, F.; Rosen, A.; Curtarolo, S.; Bolton, K. Modeling the melting of supported clusters. Appl. Phys. Lett. 2006, 88, 133110/1–133110/3. (50) Ding, F.; Rosen, A.; Bolton, K. Dependence of SWNT growth mechanism on temperature and catalyst particle size: Bulk versus surface diffusion. Carbon 2005, 43 (10), 2215–2217. (51) Car, R.; Parrinello, M. Unified Approach for Molecular-Dynamics and Density-Functional Theory. Phys. ReV. Lett. 1985, 55 (22), 2471–2474. (52) Raty, J. Y.; Gygi, F.; Galli, G. Growth of carbon nanotubes on metal nanoparticles: A microscopic mechanism from ab initio molecular dynamics simulations. Phys. ReV. Lett. 2005, 95 (9), 96103. (53) Raty, J. Y.; Galli, G.; Bostedt, C.; van Buuren, T. W.; Terminello, L. J. Quantum confinement and fullerenelike surface reconstructions in nanodiamonds. Phys. ReV. Lett. 2003, 90 (3), 37401. (54) Ding, F.; Larsson, P.; Larsson, J. A.; Ahuja, R.; Duan, H.; Rosen, A.; Bolton, K. The Importance of Strong Carbon-Metal Adhesion for Catalytic Nucleation of Single-Walled Carbon Nanotubes. Nano Lett. 2008, 8 (2), 463–468. (55) Zhu, W.; Rosen, A.; Bolton, K. Changes in single-walled carbon nanotube chirality during growth and regrowth. J. Chem. Phys. 2008, 128, 124708. (56) Amara, H.; Bichara, C.; Ducastelle, F. Understanding the Nucleation Mechanisms of Carbon Nanotubes in Catalytic Chemical Vapor Deposition. Phys. ReV. Lett. 2008, 100, 056105/1–4. (57) Ohta, Y.; Irle, S.; Okamoto, Y.; Morokuma, K. Rapid growth of a single-walled carbon nanotube on an iron cluster: Density-functional tightbinding molecular dynamics simulations. ACS Nano 2008, 2, 1437–1444. (58) (a) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Self-consistent-charge densityfunctional tight-binding method for simulations of complex materials properties. Phys. ReV. B 1998, 58 (11), 7260–7268. (b) Zheng, G.; Witek, H. A.; Bobadova-Parvanova, P.; Irle, S.; Musaev, D. G.; Prabhakar, R.; Morokuma, K.; Elstner, M.; Ko¨hler, C.; Frauenheim, T. Parameterization of Transition Metal Elements for the Spin-Polarized Self-Consistent-Charge Density-Functional Tight-Binding Method: Parameterization of Sc, Ti, Fe, Co, and Ni. J. Chem. Theor. Comput. 2007, 3, 1349–1367. (59) Wang, Y.; Kim, M. J.; Shan, H.; Kittrell, C.; Fan, H.; Ericson, L. M.; Hwang, W.-F.; Arepalli, S.; Hauge, R. H.; Smalley, R. E. Continued Growth of Single-Walled Carbon Nanotubes. Nano Lett. 2005, 5 (6), 997– 1002. (60) Smalley, R. E.; Li, Y. B.; Moore, V. C.; Price, B. K.; Colorado, R.; Schmidt, H. K.; Hauge, R. H.; Barron, A. R.; Tour, J. M. Single wall carbon nanotube amplification: En route to a type-specific growth mechanism. J. Am. Chem. Soc. 2006, 128 (49), 15824–15829.

J. Phys. Chem. C, Vol. 113, No. 1, 2009 169 (61) Zhang, Q. M.; Wells, J. C.; Gong, X. G.; Zhang, Z. Y. Adsorption of a carbon atom on the Ni-38 magic cluster and three low-index nickel surfaces: A comparative first-principles study. Phys. ReV. B 2004, 69 (20), 205413. (62) Weinert, M.; Davenport, J. W. Fractional Occupations and DensityFunctional Energies and Forces. Phys. ReV. B 1992, 45 (23), 13709–13712. (63) Wentzcovitch, R. M.; Martins, J. L.; Allen, P. B. Energy Versus Free-Energy Conservation in 1 St-Principles Molecular-Dynamics. Phys. ReV. B 1992, 45 (19), 11372–11374. (64) Wagner, F.; Laloyaux, T.; Scheffler, M. Errors in HellmannFeynman forces due to occupation-number broadening and how they can be corrected. Phys. ReV. B 1998, 57 (4), 2102–2107. (65) Irle, S.; Okamoto, Y.; Ohta, Y.; Zheng, G.; Morokuma, K. NCCDFTB Molecular Dynamics Study of Fe/Co/Ni Catalyst Particle Melting in Carbide Formation During SWCNT Nucleation. In DFT calculations on fullerenes and carbon nanotubes; Basiuk, V., Irle, S., Eds.; Research Signpost, T. C.: Trivandrum, India, 2008; under release. (66) Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nose-Hoover Chains - the Canonical Ensemble Via Continuous Dynamics. J. Chem. Phys. 1992, 97 (4), 2635–2643. (67) Arepalli, S.; Scott, C. D.; Nikolaev, P.; Smalley, R. E. Electronically excited C-2 from laser photodissociated C-60. Chem. Phys. Lett. 2000, 320 (1-2), 26–34. (68) Irle, S.; Zheng, G.; Wang, Z.; Morokuma, K.; Elstner, M. The C60 Formation Puzzle “Solved”: QM/MD Simulations Reveal the Shrinking Hot Giant Road of the Dynamic Fullerene Self-Assembly Mechanism. J. Phys. Chem. B 2006, 110, 14531–14545. (69) Irle, S.; Wang, Z.; Zheng, G.; Morokuma, K. “Shrinking hot giant” road of dynamic fullerene self-assembly in hot carbon vapor. Nano 2007, 2, 21–30. (70) Bhowmick, R.; Clemens, B. M.; Cruden, B. A. Parametric analysis of chirality families and diameter distributions in single-wall carbon nanotube production by the floating catalyst method. Carbon 2008, 46 (6), 907–922. (71) Mulliken, R. S. J. Chim. Phys. 1949, 46, 497. (72) Mulliken, R. S. J. Chim. Phys. 1949, 46, 675. (73) Zheng, G.; Irle, S.; Morokuma, K. J. Nanosci. Nanotechnol. 2006, 6, 1259–1270. (74) Stone, A. J.; Wales, D. J. Theoretical Studies of Icosahedral C60 and Some Related Species. Chem. Phys. Lett. 1986, 128 (5,6), 501–503.

JP808493F

Temperature Dependence of Iron-Catalyzed Continued Single-Walled

Recommend Documents