Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes

Transcription

1 Copyright 2006 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Nanoscience and Nanotechnology Vol. 6, 1 12, 2006 Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes Perla B. Balbuena, 1 Jin Zhao, 1 Shiping Huang, 1 Yixuan Wang, 1 Nataphan Sakulchaicharoen, 2 and Daniel E. Resasco 2 1 Department of Chemical Engineering, Texas A&M University, College Station, TX 77843, USA 2 School of Chemical Engineering and Materials Science, University of Oklahoma, Norman, OK 73019, USA Classical molecular dynamics simulations are carried out to analyze the physical state of the catalyst, and the growth of single-wall carbon nanotubes under typical temperature and pressure conditions of their experimental synthesis, emphasizing the role of the catalyst/substrate interactions. It is found that a strong cluster/substrate interaction increases the cluster melting point, modifying the initial stages of carbon dissolution and precipitation on the cluster surface. Experiments performed on model Co Mo catalysts clearly illustrate the existence of an initial period where the catalyst is formed and no nanotube growth is observed. To quantify the nature of the Co Mo 2 C interaction, quantum density functional theory is applied to characterize structural and energetic features of small Co clusters deposited on a (001) Mo 2 C surface, revealing a strong attachment of Co-clusters to the Mo 2 C surface, which may increase the melting point of the cluster and prevent cluster sintering. Keywords: Catalyst Substrate Interaction, Catalyzed Carbon Nanotube Growth, Molecular Dynamics Simulations, Model Catalysts, Melting Points of Nanocatalysts. 1. INTRODUCTION The presence of a transition metal has been found a necessary condition for the synthesis of single-wall carbon nanotubes (SWNTs) using arc discharge, 1 pulsed laser vaporization, 2 or any of the chemical vapor deposition (CVD) techniques. 3 It is interesting to notice that the first two methods use a form of pure carbon (graphite) that after vaporization produces SWNTs among other carbon structures, whereas CVD methods use a carbon-containing source that generates C atoms after catalytic decomposition. In both cases, transition metal nanoparticles are needed to generate SWNTs. Moreover, the best of those transition metal catalysts are the ones able to form metastable carbides (such as Co, Ni, and Fe), instead of those that form very stable carbides (such as Mo and others from groups IV to VI), or those that do not form carbides at all (for example Pt, Pd, Rh, Ru, Ir, Cd). 4 Thus, it could be inferred that such metal nanoparticle is most likely the catalyst that promotes the formation of singlewall carbon nanotubes in a variety of synthesis processes at temperatures in the order of 1000 K for CVD processes and 1200 K for carbon vaporization processes. Authors to whom correspondence should be addressed. Present address: Beijing University of Chemical Technology, Beijing, P. R. China. But the specific role of the catalyst in the nanotube growth process is not clear. Several growth mechanisms have been proposed, among them those where growth is expected to take place at base and tip locations with respect to the nanotube, have received partial evidences from experimental and theoretical studies. The main difference between them is given by the behavior of the C-metal nanoparticle during the growth process. If the particle remains attached to the substrate, new carbon will be added to the nascent nanotube edge in contact with the substrate (base growth), 5 but if the catalyst separates from the substrate being lifted up to the top of the nanotube then a kite or tip growth is most likely found. 6 Further, it has been reported that it is possible to change the growth mechanism from tip mode to base mode just by changing the substrate properties. 4 Detailed reviews and analyses of the various growth modes have been reported recently. 7 9 Integration of theoretical and experimental information provides the best route to identify reaction mechanisms in complex processes. Here we address several topics related to the understanding of the physical state of the catalyst and its interactions with the substrate in relation to the SWNTs growth process. Using classical molecular dynamics (MD) simulations, we analyze the effect of the substrate on the shape and morphology of metal nanoparticles J. Nanosci. Nanotechnol. 2006, Vol. 6, No /2006/6/001/012 doi: /jnn

2 Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes Balbuena et al. at the CVD synthesis temperature and pressure, and discuss how this morphology would affect the SWNT growth process. New experimental data of the rate of growth for the CoMoCAT process 10 illustrates aspects of the sequence of events preceding and during the nanotube growth. To further understand the nature of the catalyst, we report density functional theory calculations of the structure of a Mo 2 C surface and its interactions with small Co clusters. 2. METHODOLOGY 2.1. Classical MD Simulations MD Simulation of Nanotube Growth Classical MD simulations are carried out in a periodic box of fixed volume, at temperatures in the range of the experimental synthesis, 11 between 800 K and 1300 K. A metal nanoparticle (Ni 80 or Ni 48 ) deposited on a substrate is placed in the simulation box. We have chosen Ni as a typical good catalyst for this reaction, to capture the main features of the process. The Langevin equations of motion are integrated according to the Verlet algorithm, 12 with a time step of 0.5 fs. In Langevin dynamics two terms are added to Newton s second law in order to account for neglected degrees of freedom. 12 The first term is a frictional force and the second term is a random force. For the stage of nanotube growth it was found that Langevin dynamics can search conformations more efficiently that Newtonian molecular dynamics, and thus help to overcome barriers generating stable growth patterns. The initial configuration of the metal nanoparticle is a local minimum generated via energy minimization of the structure. The rest of the volume is occupied with molecules of the precursor gas initially randomly distributed, at a constant density in the range from to molecules/å 3. Assuming ideal gas conditions, such gas densities are equivalent to pressures in the range atm for temperatures between 800 and 1300 K (typical experimental pressures in the CoMoCAT synthesis are in the range of 1 5 atm). 11 The temperature is kept constant with a simple thermostat where atomic velocities of the precursor phase, the metal cluster, and the catalyzed carbon are separately rescaled to the target temperature at every step of the simulation. It is assumed that as soon as the precursor gas is in contact with the metal particle, it is catalyzed and converted into carbon atoms. Together with the high density condition, this assumption greatly accelerates the simulated growth process, making possible to observe the nanotube growth process at the same temperature of the experiment, in tens of nanoseconds at the lowest density ( molecules/å 3 ), and even in shorter times at the highest density ( molecules/å 3 ). We have developed a set of effective force fields to describe C C, C Ni, and Ni Ni interactions, incorporating information from density functional theory (DFT) calculations of model systems to already existent potentials. A detailed description of our force fields is reported elsewhere; here we briefly describe the main interaction potentials and provide their physical meaning in relation to the simulated synthesis process. For the C C interactions, we have adopted the recently revised second-generation reactive empirical bond order (REBO) potential developed by Brenner et al. 15 However, we have introduced a weighting factor to describe the relative weakness of the C C interactions inside the metal cluster obtained from DFT results. Such weighting factor varies according to the coordination number of C with respect to the metal atoms. Metal metal interactions are described using a many-body potential including Morse-type repulsive and attractive terms. 16 The distance parameters were taken from published data 16 and the energy parameters were fitted to the description given by the Sutton-Chen potential 17 for Ni clusters 14 Probably the most crucial potential for this system is that representing metal carbon interactions. We adopted a many-body Morse-type potential similar to that used for metal metal interactions, as originally proposed by Maruyama et al., 16 where crossed-terms were used to account for the influence of the number of C atoms surrounding a metal atom. Additionally, we included the dependence on the presence of metal atoms surrounding a C atom, which may be singleor double-bonded to other C atoms, as determined by DFT calculations Further refinements of the potential were done considering the effect of the sp 2 -carbon/metal bond on the formation of caps evaluated from analyses of MD trajectories. For the metal-substrate interactions we use a Lennard-Jones potential, the strength of the energy parameter was varied in order to represent different substrates MD Simulation of Physical Properties of Metallic Nanoclusters Classical MD simulations are also used to determine the effects of size and shape on melting points, structural transitions, and atomic diffusion coefficients of Pt clusters with initial cube-octahedral, cubic, and spherical structures. The Sutton-Chen many-body potential is used for the Pt Pt interactions with parameters as published in the original references. The simulations are carried out in a weak coupling heat bath system with constant temperature using the Berendsen thermostat, 19 the temperature relaxation time is 0.4 ps for the simulation system to approach the canonical ensemble, 20 constant number of particles N, constant volume V, without periodic boundary conditions. The cubic simulation box has a volume (6L), 3 where L is the nanocluster side based on a cubic shape. Simulations are performed at temperatures in the range of 0 K 1400 K, with temperature increases every 100 K, but close to the melting point the increments are reduced to 10 K. The Newton equations of motion were integrated using the Verlet leapfrog method 12 with a time step of 1 fs, with equilibration times of 400 ps at each temperature and 2 J. Nanosci. Nanotechnol. 6, 1 12, 2006

3 Balbuena et al. Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes 200 ps for production time when data is collected for analyses, using the DL_POLY code. 21 In order to determine the melting temperature, the heat capacity C v in a weak coupling heat bath system can be written as 20 k B E p 2 C v = k B T 2 2 E p 2 /3N where represents the time average. Thus, C v is related to fluctuations in the potential energy E p. is the ratio of the fluctuation of the kinetic and potential energies, and approaches zero when the simulation system is close to the canonical ensemble. 20 The self-diffusion coefficient D is obtained from D i = 1 ri t + s r 6 t i s 2 (2) where r i t + s is the vector position of the i-th atom, the average is over atoms of type i and over choices of the time origin s Density Functional Theory Calculations Periodic density functional theory calculations are performed with the CPMD program, Version The code implements density functional theory (DFT) in the Kohn- Sham formulation with a plane-wave basis set and a norm-conserving pseudopotential (PP) for the interactions between the valence electrons and the ionic cores. The DFT method and the PPs used through the present simulation are the PBE type of generalized-gradient approximation density functional, 23 and the Goedecker pseudopotentials, 24 respectively. In order to accurately treat open shell systems, spin states are polarized. In the Goedecker scheme, Mo, Co, and C have 14 (4s 2 4p 6 4d 5 5s 1, 9 (3d 7 4s 2 ), and 4 (2s 2 2p 2 ) valence electrons, respectively. The wavefunction is expanded in plane wave basis sets with a kinetic energy cutoff of Ry. Only the -point is used in the Brillouin zone (BZ) sampling generated from the basis vectors of the supercell. In order to validate the employed Goedecker pseudopotentials, density functional theory calculations (PBE, LANL2DZ ECP and basis set 25 ) are also conducted for a variety of small cluster systems, such as Co n (n = 1 3), Mo m (m = 3, 4), and Co n Mo m, using Gaussian The electronic structures and geometries obtained with CPMD and Gaussian for the tested clusters are in reasonable agreement, as discussed in Section 3.5. The adsorptions of Co n (n = 1 3) clusters are investigated on the bulk surface of -Mo 2 C(001). To model the surface, the supercell approach was used, with fourlayer slabs 27 and a 11 Å vacuum space between any two successive slabs. For most of the CPMD optimizations, the surface was fixed at their experimental bulk lattice constant of Mo 2 C (a = 4 73 Å, b = 6 03 Å and c = 5 20 Å). 28 A couple of optimizations performed with a (1) totally relaxed surface indicates that surface relaxation effects are not significant as found by previous calculations for other extended systems. 29 Partial atomic charges for the optimized structures are estimated by the method of Hirshfeld RESULTS AND DISCUSSION 3.1. Growth of SWNTs on a Supported Catalyst Nanocluster Significant effort has been devoted to study the growth of SWCNTs on metal clusters floating in a vapor of the precursor gas, using classical MD simulations. In all these simulations it is found that carbon first dissolves into the metal cluster, and after saturation or oversaturation of the C inside the cluster, C precipitates on the surface forming various structures ending with the formation of a cap which evolves separating from the cluster and forming a single-wall carbon nanotube. In all cases, the simulated nanotubes are closed by the cap in one end and attached to the metal cluster in the other end, just like those observed in base growth mode. 4 In our previous work 13 we also reported that the growth process on a weakly interacting substrate is not significantly altered from that of a nanocatalyst floating in a vapor. However, new simulations done for a cluster deposited on a strongly interacting substrate indicate that such interaction modifies the stages of nucleation and growth with respect to those found in identical metal clusters floating in a vapor phase. The most significant features are illustrated by snapshots shown in Figure 1. The strong substrate/cluster interaction favors a more rigid cluster structure which modifies the initial stage of C dissolution. Even though C still dissolves into the cluster, the amount is lower than that obtained when the metal cluster is completely unrestrained. Note that the effect is similar to a reduction in temperature. The related literature usually discusses the need of an initial supersaturation, 33 defined as the ratio of the actual amount of C dissolved in the metal to the equilibrium concentration. However, both the actual and the equilibrium C concentrations are functions of the metal particle size, temperature, and pressure, and the simultaneous dissolution and deposition of C on the surface cannot be discarded. 34 In fact, supersaturation is a metastable transient phenomenon, which would be difficult to detect experimentally and also by simulations, especially if the simulated rate of C addition is artificially high. Under the effect of a strong surface-metal cluster interaction, we do not observe supersaturation, and in addition we observe simultaneous C dissolution and deposition on the surface. Thus, C deposits on the surface at the same time that some atoms dissolve in the interior, initially forming chains that then interact with each other forming sp 2 polygons, and finally fullerene-type structures partially cover the surface, and a cap is formed that leads to the nanotube growth. J. Nanosci. Nanotechnol. 6, 1 12,

4 Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes Balbuena et al. Fig. 1. Time evolution of nanotube growth calculated by classical MD simulations using a reactive force field. Ni 48 is interacting with a substrate via a LJ potential, the density of precursor atoms is molecules/å 3, and the temperature is 1023 K. Initially the C atoms either dissolve in the cluster or deposit on the surface, then chains are formed, followed by fullerene structures, and finally a cap is formed that develops into the nanotube. At the conditions of pressure and temperature shown in Figure 1, the nanotube formed has several imperfections and those are most likely due to the fast rate of carbon addition artificially imposed by our simulations. It is interesting to add that while this report was under review, we became aware of ab initio molecular dynamics simulations 35 that basically agree with our findings. In the ab initio MD study, 35 the metal cluster is kept fixed, and hydrogen atoms are added to the bottom part of the metal structure to emulate the effect of the substrate. It is found that a cap is formed without carbon atoms being dissolved in the cluster interior, as expected from our discussion for a strongly interactive substrate that causes the cluster to adopt a rigid structure avoiding the penetration of C atoms. The most significant aspect extracted from these MD simulations is that the physical state of the cluster and its interactions with the substrate can significantly influence the nanotube growth. Thus, in the next sections we focus on various aspects of the catalyst characterization, using computational and experimental techniques Physical Properties of Metallic Nanoclusters at High Temperatures and Pressures At the high temperature conditions of the SWNT synthesis process and under the effect of moderate to high pressures, nanoclusters may have significant changes of morphology and structure. 36 Experimental and theoretical studies have provided ample evidence that melting points of metallic nanoclusters are much lower than the melting temperature of the bulk material, and the change is a function of cluster size, 41 cluster-substrate interactions, cluster composition, 44 and combinations of these effects. Figure 2 illustrates the variation of the melting temperature as a function of the cluster size for Pt nanoclusters of different initial shapes: cubic (fcc), cube-octahedral, and spherical. The phase transition is characterized both by the discontinuity in the potential energy versus temperature and also by the peak in the heat capacity calculated by Eq. (1). The spherical clusters were built defining a cutoff distance from a large Pt metal crystal with fcc structure, whereas the cube-octahedral clusters are a function of R, the ratio of the number of 111 and 100 exposed faces. Results summarized in Figure 3 clearly illustrate the decrease of the melting temperature as the cluster size decreases, with little dependence on the cluster shape for small sizes, and slightly larger differences for intermediate sizes, given by variations in the onset of surface melting due to the nature of the exposed surfaces. In conjunction with the melting transition, another property that is clearly relevant to the SWNT synthesis process is the T-dependence of the self-diffusion coefficient as shown in Figure 4. Very high mobilities are observed in the liquid phase, in agreement with previous studies. As discussed in Section 3.1, for catalysts floating in vapor, or for weak cluster/substrate interactions, at the beginning of the synthesis process, carbon atoms are dissolved in the metal cluster and after some time they start depositing on the surface. The C dissolution continues until the cluster 4 J. Nanosci. Nanotechnol. 6, 1 12, 2006

5 Balbuena et al. Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes (a) E p (ev/atom) (b) C (ev/k) (c) E p (ev/atom) (d) C (ev/k) (e) 5.25 (f) 0.6 E p (ev/atom) C (ev/k) Fig. 2. MD calculated temperature effect on the potential energy (E p, in ev/atom) and specific heat (C, in ev/k) of Pt nanoclusters of different number of atoms as indicated in each graph. (a) and (b) correspond to initial cubic shape, (c) and (d) initial cube-octahedral shape, and (e) and (f) are the results obtained for initial spherical structures. The number of atoms of the nanoclusters in (e) are: (1) 266, (2) 370, (3) 490, (4) 610, (5) 736, and (6) 904. For clarity, only three of these sizes are included in (f). reaches saturation at the given temperature. At higher temperatures more carbon atoms are able to be dissolved in the more open and highly dynamic cluster structures therefore slowing down the process of carbon deposition on the cluster surface, which in turn permits the continuous growing of the metal cluster. However, as the metal/substrate interaction strength increases, the melting temperature of the cluster increases. We note that once carbon is dissolved in the small metal cluster, the formation of a carbide or simply the physical mixture C-metal would also alter (usually reducing) the melting temperature of the C-metal cluster. Thus, a sufficiently strong metal/substrate interaction is needed to control the cluster melting temperature and cluster growing, and to avoid particle sintering. We emphasize that although the discussion and results presented in Sections 3.1 and 3.2 refer to Ni and Pt nanoparticles respectively, the conclusions are valid for other transition metals, in particular for Co and Fe, which are the most common catalysts in SWNTs synthesis processes. In the next section we provide experimental insights yielded by experiments in model systems that emulate the CoMoCAT synthesis, and in the last two sections simulation results related to the Co Mo system attempt to quantify the strength of the Co MO 2 C interaction Experimental Observations of Model Co Mo Catalysts In this section we report electron microscopy and Raman studies conducted on model Co Mo catalysts prepared on TEM grids, in order to obtain direct observations of the onset of the nanotube growth, as well as the J. Nanosci. Nanotechnol. 6, 1 12,

6 Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes Balbuena et al. Melting Temperature (K) Cube-octahedral Cube Spherical Number of Atoms in the Cluster Fig. 3. Melting points as functions of size for Pt nanoclusters of spherical, cube-octahedral, and cubic shape, calculated from MD simulations. The diameter (in nm) of the spherical cluster is marked by a number in blue, and the ratio of the number of 111 to 100 exposed surfaces in the cube-octahedral particle is denoted by a pink number. transformations undergone by the catalyst under the precursor gas as a function of time. Although the catalyst formulation (Co/Mo ratio, support composition) and reaction conditions attempt to mimic those of the CoMo- CAT process, the resulting particle size and diameter of the nanotube produced are not exactly the same as those obtained on the high-surface area support. Nevertheless, the observed behavior is expected to be qualitatively the same as that in the real process. One of the uniqueness of the CoMoCAT process compared to the rest of the catalytic decomposition methods is the stabilization of highly dispersed Co species that are generated under the reaction on the solid substrate. The effect of the Co stabilization by the Mo carbide species is dramatic. The strong interaction between Co and its substrate (oxidic Mo that becomes Mo carbide under reaction) inhibits the D ( m 2 /s) Fig. 4. MD calculated atomic self-diffusion coefficient in Pt nanoclusters of initial spherical shape with 266, 370, and 904 atoms, and predicted melting temperatures of 880, 970, and 1090 K respectively. formation of large metallic aggregates. These large metallic aggregates, present in other CVD methods have the disadvantage of getting encapsulated in graphite layers, which remain in the product and are more difficult to remove. In the development of the CoMoCAT process it was found that silica-supported Co Mo catalysts with low Co:Mo ratio exhibit excellent performance in the temperature range C under the CO disproportionation reaction. We have explained this performance on the basis of the Co Mo interaction. Co is stabilized by the Mo in an oxidized form of the type CoMoO 4 and remain as such even at high temperatures. Only when the carbon containing gas (CO) is contacted with the catalyst, the CoMoO 4 is converted to unstable CoMo carbide; Co is no longer stabilized in this new matrix and starts migrating towards the surface where gets reduced in the form of very small Co metallic clusters that start the SWNT growth. That is, there is an induction period during which carbon is uptaken by the catalyst and the CoMoO 4 species start transforming into Mo carbide and metallic Co, but no nanotube growth should be observed. We attempt here to have a direct observation of this induction period. The real catalyst in the CoMoCAT process is composed of Co Mo species supported on high-surface-area silica. Using a porous high-surface area supports allows for the stabilization of relatively large amounts of catalytically active metals in high state of dispersion and facilitates the scale-up process. However, using porous supports complicates the observation of the catalytic reaction and the evolution of the active species during the various stages of the process. Model catalysts on flat surfaces provide a more direct access and have allowed us to directly observing some of the important transformations that take place. For example, we have prepared Co Mo catalysts directly supported on lacey silicon monoxide membranes TEM grids. Before reaction, the grid was calcined at 500 C for 5 min in order to generate a silica surface on the membrane surface. A solution containing Co and Mo was prepared by dissolving cobalt(ii) acetate tetrahydrate and molybdenum(ii) acetate dimer in ethanol. The solution was then dropped on the calcined grids and further calcined at 400 C for 5 min to decompose the acetate and form the Co Mo metallic oxide species. As illustrated in Figure 5, we have been able to directly observe on these model catalysts the induction period (nucleation) that we have previously proposed. Remarkably, during the first 3 min in contact with CO, no nanotubes were observed on the TEM grid. The TEM/SEM images clearly showed that after the grid was reduced at 500 C and heated up to the reaction temperature (850 C), the structure of the CoMoO 4 species was still crystalline. By contrast, after being in contact with CO for 1 min the particles start changing their morphology and their surface became rougher. This transformation clearly indicates that the CoMoO 4 species began to change into a different species. 6 J. Nanosci. Nanotechnol. 6, 1 12, 2006

7 Balbuena et al. Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes 850 C before CO 3 min under CO 10 min under CO Fig. 5. Evolution of the Co Mo species in a model catalyst directly supported on a TEM grid. Left: SEM images. Right: TEM images. Top: Catalyst heated to 850 C in He, before exposure to CO. Middle: After 3 min in CO at 850 C (induction period); note the change in texture of the catalytic particles, but absence of nanotubes. Bottom: After 10 min in CO, large number of SWNT bundles. Previous EXAFS, XRD, and XPS studies indicate that the new species is a carbide. After 5 minutes exposure to CO a high density of long bundles of SWNTs was detected. These TEM/SEM observations are in perfect agreement with the Raman spectroscopy observations. Figure 6 shows the Raman spectra of the material obtained at 850 Cat different times. The band appearing at about 1580 cm 1 (G band) results from the in-plane stretching mode of ordered crystalline graphite-like structures, while the band appearing at around 1340 cm 1 (D band) represents disordered carbon structure. No G band was observed after 1 minute reaction, and only a weak signal corresponding to the G band was present after 3 minutes reaction, for this particular sample only a few short SWNTs were observed from TEM/SEM. However, after 5 minutes, the Raman spectra changed dramatically displaying a typical 3500 Growth vs. time CO 850 C Growth vs. time CO 850 C Cal 400 C Wave number (cm 1 ) 3 min 1 min Heat 850 C hr 10 min 5 min Wave number (cm 1 ) Fig. 6. Raman spectra as function of process time. Nanotube features revealed by the G mode and the radial breathing modes start at about 3 min and become clear at longer times (right). J. Nanosci. Nanotechnol. 6, 1 12,

8 Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes Balbuena et al. Raman G band Signal Time (min) Fig. 7. Time evolution of the Raman G signal, indicative of nanotube growth, shows the existence of an induction period of 3 5 min before a temperature dependent nanotube growth is detected. Squares: T = 750 C, Triangles: T = 850 C. SWNT spectrum with a high G/D ratio, indicative of good nanotube quality, which correlates very well with the high density of long SWNT observed by TEM/SEM. Figure 6 also illustrates the transformation undergone by the catalyst particles during the initial stages of growth. It is clear that the Raman bands observed on the catalyst before reaction correspond to CoMoO 4 species. After pretreatment to reaction conditions, the cobalt molybdate bands become getting distorted; this change in the Raman spectra might originate from the loss of crystallinity of CoMoO 4 in the first stages of transformation. After 1 minute reaction, the intensity of CoMoO 4 band has greatly decreased, which indicates that the CoMoO 4 phase either becomes more amorphous or starts to transform into the carbide species. The latter case seems more plausible ε = 1/2 ε o 800 K as revealed by TEM/SEM, as well as by previous characterization conducted on the high surface area catalysts. Figure 7 shows the evolution of the G band with reaction time. It can be seen that the G band intensity increased significantly after the first 3 minutes of induction. As described above, the G band in the Raman spectra arises from ordered crystalline graphite-like structures; this is directly related to the presence of SWNT, as also confirmed by the breathing mode bands. After the nanoclusters of metallic cobalt start being released from the carbide intermediate, SWNTs can grow very fast via the dissolution of carbon atoms into the cluster and deposition on the cluster surface as illustrated in Section 3.1. From these observations, we can conclude that SWNTs grew after the catalyst was in contact with CO for a period of time. An induction time is needed for the CoMoO 4 species transform into a dual carbide, which decomposes into Mo carbide and Co clusters. In the last two sections we discuss the morphology of Co clusters predicted from theoretical calculations when the Co interactions with substrates (graphite and molybdenum carbide) are taken into account Shape and Morphology of Co Clusters as a Function of Co-Substrate Interactions To evaluate the substrate effect on Co-graphite interactions, we analyze the structure obtained from MD simulations of a 48 atom-co cluster deposited on a graphite surface. Results are presented as a function of the metal/ substrate interaction represented by a 12-6 LJ potential. The Sutton-Chen potential was employed for the Co Co interactions, 47 in two possible structures of the Co cluster, ε = 3/4 ε o 800 K ε = ε o 800 K ε = ε o 1023 K Fig. 8. Snapshots from MD simulations of hcp Co clusters of 48 atoms deposited on a graphite substrate. The 12-6 LJ potential function is used to represent the Co C interatomic interactions; in the top two figures the value of the energy parameter was reduced with respect to the calculated o = ev in order to determine its effect on the cluster morphology and structure. 8 J. Nanosci. Nanotechnol. 6, 1 12, 2006

9 Balbuena et al. Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes hexagonal close-packed, hcp, and face-centered cubic, fcc. The Sutton Chen potential for Co Co was fitted to a LJ potential to obtain LJ energy and length parameters for Co Co interactions. Such LJ parameters were then used along with the Lorentz-Berthelot mixing rules, 12 and C C parameters taken from published work, 48 to determine the cross-interaction C Co LJ parameters ( C Co = ev and C Co = Å). The stable structure of bulk Co is hexagonal close packing, hcp. 49 However, experiments indicate that the fcc phase is most stable at high temperatures, 50 and the stable phase is a function of the particle size. Kitakami et al. 51 reported fcc for average particle diameters below 20 nm, mixtures of fcc and hcp for diameters of 30 nm, and almost pure hcp for larger particles, whereas Dassenoy et al. 52 found hcp and non-periodic polytetrahedral structure for Co clusters of 2 4 nm synthesized in the presence of a polymer template. Our MD simulations showed that Co clusters of nanodimensions can exist both as fcc or hcp with very close energies, especially at temperatures close to its melting point. Although we have not determined the melting temperature for Co clusters, by analogy with other transition metals, we speculate that it should be much lower than Co bulk melting temperature, 1768 K. 53 Figure 8 qualitatively shows the effect of the substrate on the melting temperature of an hcp Co 48 structure. When the substrate-cluster interaction strength is half of that of the Co-graphite interaction (Fig. 8, top left), both surface and core atoms have high mobility and the cluster has a melted appearance at 800 K. As the cluster/substrate interaction increases, the cluster adopts a much ordered structure (Fig. 8, top right), and a clear wetting layer is developed (Fig. 8, bottom left) causing a significant change on the overall shape of the cluster and on the nature of the exposed phases. Finally, the structure of Co 48 at 1023 K for an interaction strength corresponding to the Co-graphite system (Fig. 8, bottom right) reveals much higher atomic mobility than at 800 K. In relation to the CoMoCAT synthesis process, we next investigate the strength of the Co Mo carbide interaction, assuming that Co clusters are formed on a Mo carbide substrate as discussed in Section 3.3. Fig. 9. The cell and its partial neighbor periodic images for the bulk surface of -Mo 2 C (Mo atoms are blue spheres, C atoms are grey). Top: Top view. Bottom: Side view. having two carbon atoms coordinated (Mo2), illustrated in Figure 9. The adsorption of one Co atom on the Mo-terminated -Mo 2 C surface was investigated on top, bridge as well as hollow initial configurations. Such adsorption corresponds to 1/4 of a monolayer coverage. Co tends to be adsorbed on both bridge and hollow sites. In the case of bridge adsorption, the distances from Co to the two Mo atoms are 2.63 and 2.65 Å, which they are around 2.83 Å for the hollow adsorption. The adsorption energies are defined as the difference between the energy of the complex adsorbate/adsorbent minus the energy of the adsorbent (slab) minus the energy of the adsorbate Co n (Co cluster of n atoms) E = E Co n Mo 2 C complex) E Mo 2 C slab E Co n (3) Such Es are almost the same for the hollow and bridge different adsorptions for n = 1, 5.80 ev. Charge population analysis indicates that significant charge of 0.9 e is transferred from Mo to Co atoms. As the bulk surface is relaxed, the energy of the complex decreases only slightly by 0.5 ev. The distances between Co and Mo are very comparable to the case of the fixed surface Preliminary Ab Initio Studies of the Mo 2 C/Co Interactions Both experimental and theoretical results show that the most stable -Mo 2 C phase adopts an orthorhombic crystal structure, where Mo atoms are in a slightly distorted close-packed arrangement and carbon atoms occupy half of the ordered positions in lattice octahedral vacancies. Such -Mo 2 C phase was also identified in the CoMoCAT process. In the bulk crystal, the coordination of Mo is three and that of C is six; while in the Mo-terminated surface, Mo atoms have two types of coordination, the first having one carbon coordinated (denoted as Mo1) and the second Fig. 10. Adsorption of Co 3 (left) and Co 2 (right) on a Mo 2 C carbide surface calculated with periodic DFT. For clarity, only the unit cell is shown. J. Nanosci. Nanotechnol. 6, 1 12,

10 Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes Balbuena et al. Table I. DFT calculated (PBEPBE/LANL2DZ) ground state electronic energies of small clusters of Co, Mo, and Mo n Co m, with ground state multiplicities (m) indicated, characteristic bond distances R, and binding energies BE (in ev) for the Mo n Co m complexes. BE/Co atom in m (ground states) Energy/au Geometry (Å and degree) Mo n Co m (ev) Co Co Co 3 isosceles triangle , 2.209, Mo Mo Mo 3 isosceles triangle , 2.233, Mo 4 rhombus = 2.297, 2 3 = = 2.298, 4 1 = = 105.1, = 74.8, = 105.1, = 0 Mo 4 pyramid = 2.724, 2 3 = 2.128, 3 4 = 2.719, 3 1 = 2.722, 4 1 = 2.128, 4 2 = = 67.0, = 67.0, = 50.3 Mo 2 _Co isosceles triangle Mo 1 Mo2 = 2.071, Co Mo1 = Co Mo2 = Mo 3 _Co rhombus Mo1 Mo2 = 2.273, Mo2 Mo3 = Mo3 Mo1 = 2.434, Mo3 Co = Mo1 Co = 2.493, Mo1 Mo2 Mo3 Co = 0 Mo 3 _Co pyramid Mo1 Mo2 = 2.381, Mo2 Mo3 = Mo3 Mo1 = 2.320, Mo1 Co = Mo2 Co = 2.426, Mo3 Co = Mo1 Mo2 Mo3 Co = 65.3 Mo 3 _Co 2 square-based Co Co = 2.271, Mo1 Mo2 = 2.288, 2.3 pyramid a Co1 Mo1 = 2.406, Co2 Mo2 = 2.679, Co1 Mo3 = 2.584, Co2 Mo3 = Mo 4 _Co b Co Mo1 = 2.309, Co Mo2 = 2.761, 2.9 Co Mo3 = 2.763, Co Mo4 = 3.965, Mo1 Mo2 Mo4 Mo3 = 37 Mo 4 _Co c trigonal Co Mo1 =2.518, Co Mo2 = 2.566, 3.0 bipyramid Co Mo3 = 2.540, Mo1 Mo3 = Mo 4 -Co d 2 square-based Co Co = 2.277, Co1 Mo1 = 2.473, 2.7 bipyramid Mo3 Co1 = 2.776, Mo3 Co2 = 2.477, Mo1 Mo2 = 2.900, Mo2 Co2 = 2.673, Mo4 Co1 = 2.786, Mo4 Co2 = Mo1 Mo2 Co2 Co1 = 0.0 a Mo1, Mo2 and the two Co atoms constitute the base; b Initial geometries could be considered as rhombus Mo 4 and Co, yet Mo 4 is considerably distorted into a butterfly cluster; c From pyramid Mo 4 and Co; d It may also be considered as octahedron. Mo1, Mo2, and the two Co atoms form the square. Stable adsorption of Co 2 on the Mo-terminated -Mo 2 C surface was also found at the bridge site (Fig. 10, right). The distances between Co and its nearest neighbors are 2.65 and 2.75 Å, and the Co Co bond length is 2.37 Å. The adsorption energy is 5.05 ev/co atom. The net charges carried by the two Co atoms are 0.62 e and 0.45 e. For Co 3 adsorption (Fig. 9, right), the binding energy is 4.1 ev/co atom, and the charges on the Co atoms are 0.68, 0.58, and 0.74 e. To test the performance of the pseudopotentials regarding binding energies, we used DFT to calculate structure and binding energies of small clusters Mo n Co m using the PBE/PBE functional and the LANL2DZ basis set. Results indicate that although similar bonding geometries are obtained, the binding energies (Table I) are approximately half of the values obtained with periodic DFT, but still in the order of 3 ev/co atom, indicative of a Fig. 11. DFT (PBEPBE/LANL2DZ) optimized geometries of clusters. From left to right: Mo 3 Co 2 (m = 5, square-based bipyramid); Mo 4 Co (m = 4, butterfly); Mo 4 Co 2 (m = 5); Mo 3 Co (rhombus, m = 4). See Table 1 for bond lengths, angles, and binding energies. 10 J. Nanosci. Nanotechnol. 6, 1 12, 2006

11 Balbuena et al. Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes very strong interaction between small Co clusters and Mo surfaces. Selected geometries are shown in Figure CONCLUSIONS New simulations done for a cluster deposited on a strongly interacting substrate indicate that such interaction modifies the initial stage of nucleation with respect to that found in identical metal clusters floating in a vapor phase. Simultaneous C dissolution in the metal particle and deposition on the surface take place initially, and the amount dissolved is much lower than that expected at the given temperature. The reason for this phenomenon is that the strong surface/ cluster interaction has the same effect on the process as temperature decreases, reducing not only the cluster mobility, but also its melting point, and the C-solubility inside the particle. To prove such hypothesis, results from molecular dynamics simulations illustrate how mobility and melting point on a metal nanocluster deposited on a surface are significantly reduced both by a temperature decrease and by a strong cluster/surface interaction. Thus, nanotube growth on a strongly interacting metal cluster/substrate would start with simultaneous C deposition on the surface and dissolution in the cluster interior; the surface C atoms initially form chains that then interact with each other forming sp 2 polygons, and finally fullerene-type structures partially cover the surface, and a cap is formed that leads to nanotube growth. Experiments in model systems illustrate the transformation undergone by the catalyst particles during the initial stages of growth. It is clearly shown that after the process is initiated by flowing CO on the catalyst, there is an induction period corresponding with the metal cluster formation which is followed by nanotube growth. A strong interaction of Co-clusters on Mo 2 C surfaces is revealed by DFT calculations, which confirms that Co clusters formed on Mo-carbide surfaces would be very stable against sintering and would favor the formation of SWNTs. In summary, although the complexity of the synthesis process requires a series of approximations both in the modeling and in the design of model experiments, we are confident that the essence of the results yielded by our integrated experimental-simulation approach responds to the physics of the SWNT synthesis process. When reporting results from classical molecular simulations, where the electronic structure is represented by effective force fields, one is often left with the question of how realistic are these mathematical functions to describe the physical system. In this work, we have reported a few important points which can be considered independent of the form of the adopted force field because these physical phenomena have been detected by experiments, by a variety of effective force fields, and by ab initio molecular dynamics simulations: (1) the existence of melting and solid solid structural transitions in nanoclusters at the temperatures and pressures of SWNT synthesis; (2) the dependence of these phase transitions on temperature and cluster substrate interactions; (3) the dependence of the C dissolution in the cluster on the structure of the metal cluster, which is a function of temperature and substrate. In this work we intended to connect all these points to the experimental observations in model catalysts and in the real process. Acknowledgment: Financial support from the National Science Foundation (NER/CTS ) is gratefully acknowledged. References and Notes 1. S. Iijima and T. Ichihashi, Nature 363, 603 (1993). 2. T. W. Ebbesen and P. M. Ajayan, Nature 358, 220 (1992). 3. J.-C. Charlier and S. Iijima, Topics in Applied Physics 80, 55 (2001). 4. R. G. Coltters, Mat. Sci. Eng. 76, 1 (1985). 5. Y. Li, W. Kim, Y. Zhang, M. Rolandi, D. Wang, and H. Dai, J. Phys. Chem. B 105, (2001). 6. S. Huang, M. Woodson, R. Smalley, and J. Liu, Nano Lett. 4, 1025 (2004). 7. J. Gavillet, J. Thibault, O. Stephan, H. Amara, A. Loiseau, C. Bichara, J.-P. Gaspard, and F. Ducastelle, J. Nanosci. Nanotechnol. 4, 346 (2004). 8. O. Jost, A. Gorbunov, X. Liu, W. Pompe, and J. Fink, J. Nanosci. Nanotechnol. 4, 433 (2004). 9. S. Pannala and R. F. Wood, J. Nanosci. Nanotechnol. 4, 463 (2004). 10. D. E. Resasco, W. E. Alvarez, F. Pompeo, L. Balzano, J. E. Herrera, B. Kitiyanan, and A. Borgna, J. Nanoparticle Res. 4, 131 (2002). 11. J. E. Herrera and D. E. Resasco, J. Phys. Chem. B 107, 3738 (2003). 12. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Oxford University Press, Oxford (1990). 13. J. Zhao, A. Martinez-Limia, and P. B. Balbuena, Nanotechnology 16, S575 (2005). 14. A. Martinez-Limia, J. Zhao, and P. B. Balbuena (2005), to be submitted. 15. D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. Stuart, B. Ni, and S. B. Sinnott, J. Phys: Condens. Matter 14, 783 (2002). 16. Y. Yamaguchi and S. Maruyama, Eur. Phys. J. D 9, 385 (1999). 17. A. P. Sutton and J. Chen, Phil. Mag. Lett. 61, 139 (1990). 18. H. Rafii-Tabar and A. P. Sutton, Phil. Mag. Lett. 63, 217 (1991). 19. H. J. C. Berendsen, J. P. M. Postma, W. F. v. Gunsteren, A. D. Nola, and J. R. Haak, J. Chem. Phys. 81, 3684 (1984). 20. T. Morishita, J. Chem. Phys. 113, 2976 (2000). 21. F. L. Hirshfeld, Theor. Chim. Acta 44, 129 (1977). 22. CPMD. Copyright IBM Corp , Copyright MPI fuer Festkoerperforschung, Stuttgart, (2003). 23. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 78, 1396 (1997). 24. S. Goedecker and K. Maschke, Phys. Rev. A 45, 88 (1992). 25. P. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 270 (1985). 26. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, J. Nanosci. Nanotechnol. 6, 1 12,

12 Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Wallingford, CT (2004). 27. P. Liu and J. A. Rodriguez, J. Chem. Phys. 120, 5414 (2004). 28. T. P. St. Clair, S. T. Oyama, D. F. Cox, S. Otani, Y. Ishizawa, R.-L. Lo, K.-I. Fukui, and Y. Iwasawa, Surf. Sci. 426, 187 (2001). 29. A. Michaelides and P. Hu, J. Am. Chem. Soc. 123, 4235 (2001). 30. F. Ding, K. Bolton, and A. Rosen, J. Phys. Chem. B 108, (2004). 31. F. Ding, A. Rosen, and K. Bolton, Chem. Phys. Lett. 393, 309 (2004). 32. Y. Shibuta and S. Maruyama, Physica B 323, 187 (2002). 33. V. L. Kuznetsov, A. N. Usol tseva, and Y. V. Butenko, Kinetics and Catalysis 44, 726 (2003). 34. A. Moisala, A. G. Nasibulin, and E. I. Kauppinen, J. Phys. Condens. Matter 15, S3011 (2003). 35. J. Raty, F. Gygi, and G. Galli, Phys. Rev. Lett. 95, (2005). 36. E. J. Lamas and P. B. Balbuena, J. Phys. Chem. B 107, (2003). 37. P. Jensen, Rev. Mod. Phys. 71, 1695 (1999). 38. Y. Qi, T. Cagin, W. L. Johnson, and W. A. Goddard, J. Chem. Phys. 115, 385 (2001). Balbuena et al. 39. C. L. Cleveland, W. D. Luedtke, and U. Landman, Phys. Rev. Lett. 81, 2036 (1998). 40. J. M. Petroski, Z. L. Wang, T. C. Green, and M. A. El-Sayed, J. Phys. Chem. B 102, 3316 (1998). 41. W. H. Qi and M. P. Wang, Mat. Chem. Phys. 88, 280 (2004). 42. S.-P. Huang and P. B. Balbuena, Mol. Phys. 100, 2165 (2002). 43. S.-P. Huang, D. S. Mainardi, and P. B. Balbuena, Surf. Sci. 545, 163 (2003). 44. S.-P. Huang and P. B. Balbuena, J. Phys. Chem. B 106, 7225 (2002). 45. F. Ercolesi, W. Andreoni, and E. Tosatti, Phys. Rev. Lett. 66, 911 (1991). 46. Y. Wang, S. Teitel, and C. Dellago, Chem. Phys. Lett. 394, 257 (2004). 47. Z. A. Kaszkur and B. Mierzwa, Phil. Mag. A 77, 781 (1998). 48. W. A. Steele, The Interaction of Gases with Solid Surfaces, Pergamon Press, Oxford (1974). 49. W. D. Callister, Materials Science and Engineering: An Introduction, John Wiley and Sons, New York (1994). 50. H. Sato, O. Kitakami, T. Sakurai, Y. Shimada, Y. Otani, and K. Fukamichi, J. Appl. Phys. 81, 1858 (1997). 51. O. Kitakami, H. Sato, Y. Shimada, F. Sato, and M. Tanaka, Phys. Rev. B 56, (1997). 52. F. Dassenoy, M.-J. Casanove, P. Lecante, M. Verelst, E. Snoeck, A. Mosset, T. O. Ely, C. Amiens, and B. Chaudret, J. Chem. Phys. 112, 8137 (2000). 53. D. R. Lide (ed.), Handbook of Chemistry and Physics, CRC Press, Boca Raton (1997). Received: 23 May Revised/Accepted: 19 October J. Nanosci. Nanotechnol. 6, 1 12, 2006