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Molecular Dynamics Simulation of the Diffusion of Au and Pt Nanoclusters on Carbon Nanotubes Dong Hwa Seo, Hyun You Kim, Ji Hoon Ryu, and Hyuck Mo Lee* Department of Materials Science and Engineering, KAIST, Gwahangno 335, Yuseong-gu, Daejeon, Korea 305-701 ReceiVed: January 29, 2009; ReVised Manuscript ReceiVed: March 29, 2009
The diffusive nature of Au and the Pt clusters supported on various carbon nanotubes (CNTs) is studied through molecular dynamics simulation. We found out that the cluster-CNT interface is essential and the matching between the diffusion pathways on the CNT and the linear atomic arrangements of the bottom layer of the clusters controls the diffusion behavior of the clusters. The atomic arrangement of the cluster bottom layer is independent of the kind of CNTs. The direction and the gap of the diffusion pathways on the CNTs were however quite dependent on the chirality and radius of the CNTs. Based on careful investigations, we propose a strategy for minimizing the aggregation of CNT-supported nanoclusters that worsen the catalytic properties. Introduction Transition metal nanoclusters supported on carbon nanotubes (CNTs) have recently attracted considerable interest due to the unique properties of both CNTs1,2 and nanoclusters3-8 and the possibility that these properties can be enhanced when CNTs and nanoclusters are used in a composite.9,10 This type of a composite nanostructure is used in various fields, such as nanoelectric devices,11-17 sensors,18-21 and catalysts.1,22-24 The overall properties of CNT-supported nanoclusters are determined by the type of cluster, the cluster size and shape, and the degree of cluster dispersion.9,25,26 Especially the diffusion and aggregation of CNT-supported nanoclusters over time significantly influences system properties.25,27,28 A better understanding of the dynamics of CNT-supported nanoclusters would therefore help us to improve our insight into the overall properties. The dynamic properties can be difficult to measure experimentally because of the short diffusion period of CNT-supported nanoclusters. Accordingly, molecular dynamics (MD) simulation is often used to understand the details of atomic-scale dynamics because it deals with the dynamic evolution on a picosecond time scale. In our previous works, we used MD simulations to study the thermodynamic, static, and dynamic properties of graphitesupported Pt nanoclusters.29,30 The diffusion rate of the Pt nanoclusters mainly depends on the morphology of the bottom layers of the nanocluster and the periodic lattice matching between the bottom layer and the graphite. We found that, besides the lateral diffusion, Pt nanoclusters with a rectangular or imperfect hexagonal shaped bottom layer tend to wag or rotate themselves.30 Many theoretical studies have focused on the diffusion and aggregation of nanoclusters as well as adatoms on graphite.31-36 They reportedly found that the mismatch between the lattice parameters of the nanocluster and the substrate,32 the misfit between the bottom layer of the nanocluster and the substrate,35 * Corresponding author. Electronic mail:
[email protected]. Telephone: +82-42-350-3334. Fax: +82-42-350-3310.
and the lattice structure of the bottom layer of the nanocluster36 are essential. Other factors such as the CNT curvature and the adsorptive nature of adatoms and clusters may also effect the diffusion of adatoms and nanoclusters supported on CNTs. Zhang et al. experimentally observed that adatoms which interact weakly with a CNT, such as Au, migrate and merge together to form large clusters on the CNT, whereas adatoms which interact strongly, such as Pt, are relatively immobile and form small clusters on the CNT.37,38 In another experimental study, Wu et al. observed the cluster formation of Ag adatoms on CNTs: vigorous diffusion of the Ag adatoms on the CNT induces the early formation of small clusters, and these clusters migrate and merge into larger clusters.39 From these experimental results, we speculate that the diffusion of small nanoclusters as well as adatoms is important for the aggregation of CNT-supported nanoclusters. In this work, we address the essential factors that affect the diffusion of nanoclusters physisorbed on a CNT. Using a MD simulation method, we study the diffusive nature of 100-atom Au and Pt clusters supported on an (8,0) CNT and then extend our understanding to other CNTs of different size and chirality. Computational Details We carried out classical MD simulations in canonical ensemble conditions (NVT). To integrate the equation of motion, which is governed by Newton’s second law, we used a velocity rescaling algorithm with a time step of 0.001 ps. The quantum Sutton-Chen potential40 was used to model Au-Au and Pt-Pt interactions.41 The interactions of the Au and Pt atoms with the carbon atoms of a CNT are described by a 12-6 Lennard-Jones (LJ) potential.27,41,42 The LJ potential does not correctly describe the quantitative interaction between the metal atoms and carbon atoms of a CNT. However, when supported on a pristine CNT, the metal nanoclusters are weakly adsorbed in contrast to the adatoms.43 We therefore postulate that the LJ potential is sufficient for a qualitative study of the diffusion of nanoclusters on a CNT.27 All the MD simulations were conducted on a single walled carbon nanotube, the CNT axis of which is parallel to
10.1021/jp900862t CCC: $40.75 2009 American Chemical Society Published on Web 05/21/2009
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Figure 1. Schematic of the directional diffusion of a cluster on a CNT: (a) translation along the CNT axis and (b) revolution on the CNT. These diffusions are represented as Dt and Dr, respectively.
the z-axis. The simulation box is 49 nm × 49 nm × 8.44 nm (9.83 nm) for zigzag CNTs (armchair CNTs), and the periodic boundary condition is applied only along the z-direction. To reduce the computational cost, we fixed the CNT to the initial position. First, we prepared 100-atom Au and Pt clusters supported on an (8,0) CNT and then optimized the clusters with a simulated annealing procedure. The (8,0) CNT with a radius of 0.63 nm has been chosen because this size of CNT is one of the smallest CNTs experimentally produced44 and has large curvature compared with graphite. Because the physical and chemical properties of the Au cluster are different from those of the Pt cluster,45,46 we can investigate the effect caused by their different properties on the diffusion. In addition, because Au and Pt clusters are the most promising materials in many practical applications, it is worthy to investigate these CNTsupported nanoclusters. The Au (Pt) cluster was heated to 800 K (1200 K), equilibrated for 100 ps, and then cooled down to 300 K in increments of 100 K. The nanoclusters were held at each temperature for 100 ps. Finally, each nanocluster was equilibrated at 298 K for 400 ps. By studying the diffusion of Au and Pt clusters on the (8,0) CNT, we can highlight the different effects of the CNT and graphite and compare the results with our previous report on a graphite-supported Pt cluster. The mechanism of cluster diffusion is suggested on the basis of the (8,0) CNT. We also tested the effect of CNT chirality and curvature for (5,5) and (24,0), (43,0), (15,15), and (25,25) CNTs. To analyze the movement of the clusters, we calculated the diffusion rate (D) from a square displacement as follows:
D)
1 〈|(r(t + s) - r(s)2 |〉 2n∆t
(1)
where r(t + s) and r(s) are the vector positions of the nanocluster center of mass (COM) at times t + s and s, 〈|r(t + s) - r(s)|2〉 is the mean-square displacement, and n is the number of dimensions in which the nanocluster undergoes diffusion. In contrast to flat graphite, CNTs have a large length-to-diameter ratio. To rationalize the directional movement of nanoclusters, we therefore separate the diffusion rate of the cluster COM (DCOM) into the diffusion rates of the translation (Dt) and the revolution (Dr) (see Figure 1). The parameter Dr includes x and y components of the diffusion and represents the diffusion rate along the circumferential direction of the CNT, whereas Dt represents the diffusion rate along the CNT axis. The value of n is 2 for Dr and 1 for Dt. For more reliable D values, we performed five independent MD simulations for each system. Each run was maintained for 6 ns and divided into three sections for a simulation time of 2 ns. The D value was calculated for each section, and a total of 15 D values were averaged for a representative value of the system.
Figure 2. Diffusion trajectory of the center of mass of clusters on CNTs: (a and b) trajectories of the Au clusters on the (8,0) CNT in a linear direction and helical direction; (c and d) trajectories of the Pt clusters on the (8,0) CNT in a helical direction and circumferential direction. The red dashed circles indicate trajectories of irregularly and rapidly changing directions of diffusion.
TABLE 1: Diffusion Rates of Au and Pt Clusters Supported on Various CNTsa
Au/(8,0) Pt/(8,0) Au/(5,5) Pt/(5,5) Au/(24,0) Au/(43,0) Pt/(24,0) Pt/(43,0) Au/(15,15) Au/(25,25) Pt/(15,15) Pt/(25,25)
DCOM (10-5 cm2/s)
Dr (10-5 cm2/s)
Dt (10-5 cm2/s)
DR
3.10 2.66 1.38 2.24 0.40 0.12 2.07 1.82 1.24 0.72 1.17 1.52
2.27 3.32 1.85 2.93 0.29 0.08 1.75 0.74 1.36 0.25 0.99 0.74
4.79 1.33 0.44 0.85 0.60 0.19 2.69 3.99 1.01 1.67 1.54 3.09
0.46 2.49 4.20 3.44 0.47 0.42 0.65 0.19 1.35 0.15 0.64 0.24
a DCOM, Dr, and Dt represent the diffusion rate of the center of mass of the cluster, along the circumferential direction of the CNT (revolution) and along the axis of the CNT (translation), respectively. DR is the ratio of Dr to Dt.
Diffusion of Au and Pt Clusters on an (8,0) CNT: Effect of the Cluster-CNT Interface Figure 2 and Table 1 show the diffusion trajectories of the Au and Pt clusters supported on the (8,0) CNT as well as the corresponding D values. The parameters DCOM, Dr, and Dt of the Au and Pt clusters are on the order of 10-5 cm2/s. The DCOM value is 3.10 × 10-5 cm2/s for the Au cluster and 2.66 × 10-5 cm2/s for the Pt cluster. These values are comparable with other theoretical values reported for Pt, Cu, Ni, and Au nanoclusters on a graphite surface and on CNTs.27,30,34,36,42 The DCOM value of the Au cluster is slightly higher than that of the Pt cluster on the (8,0) CNT. This difference, however, is not large enough to affect aggregations of nanoclusters remarkably. Figure 2 also shows that the Au cluster glides smoothly along the CNT axis with a linear or helical trajectory of a longer pitch than that of the Pt cluster. In contrast, the Pt cluster mainly revolves around the CNT axis. The Pt cluster often changes its direction of diffusion by tilting right and left and rotating itself. We can intuitively expect that, if nanoclusters translate along the CNT axis, a nanocluster is likely to meet other clusters and form a larger aggregated cluster. If, however, nanoclusters revolve around the CNT axis, they have little chance of meeting other clusters and forming a larger aggregated cluster. We speculate, therefore, that the aggregative natures of CNT-
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Figure 4. Representative atomic arrangements of the bottom layers of Au and Pt clusters. The inset shows the gap (in Å) between the atomic lines. The red solid lines (Au1 and Pt1) connect the nearest neighbors, and the blue dashed lines (Au2 and Pt2) connect the second nearest neighbors. Figure 3. Overall morphology of the (8,0) CNT-supported Au and Pt clusters and the cluster-CNT interface: (a and b) Au cluster; (c and d) Pt cluster.
supported nanoclusters are an essential aspect of the directional nature of cluster diffusion, which is represented by Dt and Dr. For a more quantitative and precise analysis, we introduced the ratio of Dr to Dt (DR ) Dr/Dt.). As DR decreases, the nanocluster tends to translate along the CNT axis. Conversely, as DR increases, the nanocluster tends to revolve on the CNT axis. The average DR is 0.46 for the Au cluster and 2.49 for the Pt cluster on the (8,0) CNT (see Table 1). These values confirm that the diffusion direction of the Au cluster is quite different from that of the Pt cluster. The Au cluster, obviously, diffuses along the CNT axis, whereas the Pt cluster diffuses along the circumferential direction of the CNT. In our previous report on the diffusion of various-sized Pt clusters on a graphite support, we proposed that the geometry of the bottom layer of the clusters is the essential factor that determines the diffusion behavior of the clusters.30 In parallel with our previous report, we analyzed the interface between the clusters and the CNT so that we could determine which factors affect the diffusion behavior of the Au and Pt clusters on the (8,0) CNT. Figure 3 shows the overall morphology of CNT-supported Au and Pt clusters and their bottom layer. The Au cluster’s bottom layer, which faces the CNT, is asymmetrically elongated along the CNT axis, and the Au cluster covers the CNT. In contrast, the bottom layer of the Pt cluster is relatively flat. Clearly, very few Pt atoms are in contact with the CNT. This overall morphology of the cluster-CNT interface is in line with the report of Zhong and Stocks.45 The differences between the Au and Pt clusters may be attributed to competition between the metal-metal interaction and the metal-support interaction.47,48 The weak Au-Au interaction may explain why the bottom layer of the cluster is freely curved and covers the CNT. Even the atoms on the edge of the bottom layer of the cluster are attracted to the CNT. On the other hand, the strong Pt-Pt interaction tends to flatten the bottom layer of the Pt cluster by lifting up the edge of the bottom layer. Although the Pt-C interaction is slightly stronger than the Au-C interaction, the difference is negligible; moreover, the metal-metal interaction is more crucial in determining the morphology of the cluster-CNT interface. Our findings are in good agreement with the report of Huang et al., who showed that the interatomic bonding strength of metal atoms governs the morphology of
graphite-supported nanoclusters.46 They found that a graphitesupported Au cluster is better wetted than a graphite-supported Pt cluster because the interatomic bonding of the Au cluster is weaker than that of the Pt cluster. As shown in Figure 3, the bottom layer of both the Au and Pt clusters has a hexagonal lattice with a (111) facet. The vertically elongated nanocluster morphology along the CNT axis of the Au cluster is energetically favored due to the tendency of minimization of the directional tension on the bottom layer of the cluster by reducing the number of atoms along the circumferential direction of the CNT. Representative atomic lines of the cluster bottom layers are presented in Figure 4. Each Au and Pt cluster has two different directional atomic arrangements, Au1 and Au2 and Pt1 and Pt2, respectively. There is a gap of 2.406 Å between the Au1 lines, 1.389 Å between the Au2 lines, 2.343 Å between the Pt1 lines, and 1.353 Å between the Pt2 lines. The overall structure and the atomic arrangement of the bottom layer of the clusters are maintained during the diffusion. Very few atoms interact with the CNT; hence, in comparing with the Au cluster, the Pt cluster shows a greater tendency of tilting to the right and left and rotating itself during MD simulation. Note that we previously reported this type of tilting and self-rotation of the cluster in a previous study on the diffusion of a graphite-supported Pt cluster.30 On a graphite support, adatoms generally migrate from stable β sites, the center of the hexagonal ring of graphite, to adjacent sites across one of the six bridge sites that connect the first nearest neighbors of the carbon atoms.49 In the case of CNTs, however, the potential energy surface (PES) varies with the curvature and chirality,49 which means that adatoms experience a different PES. Furthermore, we can intuitively expect the diffusion pathways of a CNT-supported nanocluster to differ from those of adatoms because the interface of the cluster and the CNT is no longer a one-dimensional point for a single adatom but rather a two-dimensional face. We hypothesize therefore that the favorable diffusion pathways of nanoclusters are determined by the cluster-CNT interface. The diffusion pathways that closely match the lattice of the bottom layer of the cluster are favorable because the cluster tends to diffuse along the direction with smaller diffusion barriers. Whenever the atomic arrangement of the bottom layer of the cluster closely matches the diffusion pathways of the CNT, the cluster avoids high-energy barriers. Figure 5a shows the potential low-energy barrier pathways on the (8,0) CNT surface. The ABA1 and ABA2 pathways
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J. Phys. Chem. C, Vol. 113, No. 24, 2009 10419 TABLE 2: Gaps (in Å) in the Diffusion Pathways Constructed on the PES of CNTs and Graphitea
Figure 5. Potential diffusion pathways on the surface of (a) the (8,0) CNT, (b) the extended (8,0) CNT based on the actual location of the β sites, and (c) the extended (5,5) CNT.
(8,0) (24,0) (43,0) (5,5) (15,15) (25,25) graphite
ABA1
ABA2
BB1
BB2
2.13 2.13 2.13 3.79 2.71 2.47 2.13
3.64 2.56 2.38 2.36 2.24 2.20 2.13
2.28 1.60 1.44 1.23 1.23 1.23 1.23
1.51 1.30 1.27 1.77 1.45 1.37 1.23
β sites 4.55 3.19 2.87 4.03 2.98 2.77 2.45
3.15 2.66 2.57 2.45 2.45 2.45 2.45
a The relative locations of each diffusion pathway are depicted in Figure 5b and c. Because of the directional nature of the PES of CNTs, two different β sites can be defined (see Figure 5b and c): the former is perpendicular to the CNT axis; the latter is along the helical direction (right). All of these values are averaged with Au and Pt.
Figure 6. The most stable β sites on the surface of (a) graphite and (b) the (8,0) CNT. The height of the β site is 2.85 Å for Au and 2.78 Å for Pt. The gap in β sites perpendicular to the (8,0) CNT axis is 4.58 Å for Au and 4.53 Å for Pt. The averaged values are presented.
connect with the adjacent stable β sites (A) and bridge sites (B), and the BB1 and BB2 pathways connect the bridge sites without β sites. Because the energy difference between the bridge sites and the β sites is quite small,30,49 diffusion pathways that connect the bridge sites, namely BB1 and BB2, may be activated along with the conventional pathways (ABA1 and ABA2). Figure 6 shows the most stable β sites on the surface of graphite and the (8,0) CNT. The gaps between the β sites for Au and Pt adatoms are further on the CNT surface compared with those on graphite because of the curvature of the CNT. We therefore constructed a new and extended imaginary CNT surface at the actual location of the β sites (see Figure 5b and Figure 6) and analyzed the cluster-CNT interface based on such an imaginary surface, the PES that the cluster actually experiences. The potential diffusion pathways on the imaginary CNT surface are presented in Figure 5b. A close look at the cluster diffusion in Figure 2 reveals that the cluster tends to follow the specific pathways. Because the atoms of the bottom layer of the cluster are arranged linearly, we were able to estimate the relation between the atomic lines of the bottom layer of the cluster (Au1, Au2, Pt1, and Pt2) and the possible diffusion pathways on the imaginary CNT surface (ABA1, ABA2, BB1, and BB2). The gaps between the diffusion pathways and the neighboring pathways are presented in Table 2. The gaps of the (8,0) CNT, except for the ABA1 pathway, are larger than those of the
Figure 7. Matching between atomic lines of the bottom layer of the cluster and the diffusion pathways: (a) BB1 of (8,0) CNT with line Au1, (b) ABA1 of (8,0) CNT with line Pt1, (c) BB1 of (5,5) CNT with line Au2, and (d) BB1 of (5,5) CNT with line Pt1.
graphite surface. Such elongated gaps of the diffusion pathways were compared with gaps of the linear atomic arrangement of the Au and Pt clusters presented in Figure 4. The directions as well as gaps were taken into account when diffusion pathways were compared with the atomic lines of the bottom layer of the cluster. For the Au cluster, the number of possible combinations of matching is eight (ABA1-Au1, ABA1-Au2, ABA2-Au1, ABA2-Au2, BB1-Au1, BB1-Au2, BB2-Au1, and BB2-Au2) and the three potential diffusion pathways are ABA1-Au1, BB1Au1, and BB2-Au2 with well matched gaps. Of the three pathways, ABA1 is unsuitable because the Au1 line is difficult to arrange along the ABA1 pathway. BB2-Au2 is, however, possible, if the Au cluster is slightly tilted. The most probable diffusion pathway that matches the atomic line of the bottom layers of the cluster is BB1 for the Au cluster because the gap and direction of the Au1 line closely match those of BB1, as shown in Figure 7a. The same procedure for the Pt cluster indicated that the three potential diffusion pathways are ABA1Pt1, BB2-Pt1, and BB1-Pt2. The most probable diffusion pathway is ABA1-Pt1, as shown in Figure 7b, and BB2-Pt1 and BB1-Pt2 are also probable if the Pt cluster is tilted or rotated. From Figure 2, which shows the diffusion behavior of the clusters on the (8,0) CNT, we can see that the clusters sometimes
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Figure 8. Bottom layer of an Au cluster supported on various CNTs: (a) (8,0) CNT, (b) (5,5) CNT, and (c) (43,0) CNT.
move obliquely. If the BB1-Au1 and ABA1-Pt1 pathways were the only pathways responsible for the cluster diffusion, the oblique movement would not be observable. We postulate therefore that, because of the tilting of the cluster, the BB2 pathway contributes to the cluster diffusion in conjunction with the Au2 and Pt2 lines. Figure 2c and d shows that the Pt cluster sometimes vibrates at saddle points or rapidly changes its diffusion path, whereas the Au cluster diffused smoothly. A likely reason for this difference is the fact that the Pt cluster tends to undergo more severe tilting and self-rotation than the Au cluster. Because of this movement, the Pt cluster tends to be repeatedly diffused along the ABA1 or BB2 pathways. In spite of the severe tilting and self-rotation of the Pt cluster, the diffusion trajectories of the Pt cluster are limited to ABA1 and BB2. We can therefore clearly speculate that the matching between the railway that connects the low barrier points on the PES of the CNT and the wheel track produced by the atomic arrangement of the bottom layer of the cluster determines the diffusive behavior of the cluster. The somewhat stylized diffusive behavior of the Pt cluster gives credence to our hypothesis on cluster diffusion. Effect of the Chirality and Curvature of the CNT on the Diffusive Behavior of the Au and Pt Clusters We introduced the (5,5), (15,15), (25,25), (24,0), and (43,0) CNTs to provide insight into how the chirality and curvature of the CNT affect the diffusive behavior of the Au and Pt clusters and to generalize our hypothesis on the diffusion of CNT-supported clusters. Surprisingly, the morphology of the CNT-cluster interface is independent of the chirality (see Figure 8a and b). To explain the effect of chirality, we used the (5,5) CNT, the radius of which is close to the radius of the (8,0) CNT. Table 1 shows that the DR value of the Au cluster supported on the (5,5) CNT is 4.20, which is about nine times greater than the DR value of the Au cluster supported on the (8,0) CNT. From our model of cluster diffusion on the CNT, we can attribute the remarkable effect of chirality on the diffusive behavior of the Au cluster to changes in the diffusion pathways of the CNT. Table 2 and Figure 5c show that the direction and gap of the diffusion pathways of the (5,5) CNT differ from the corresponding values of the (8,0) CNT. In the (5,5) CNT, the vertically aligned ABA1 pathway cannot be the preferred diffusion pathway because the elongated gap of the ABA1 line does not match the gap of the Au1 line. Rather,
Figure 9. Diffusion rate as a function of the CNT radius: (a) DCOM and (b) DR.
the helically aligned ABA2 pathway and the horizontally aligned BB1 pathway closely match the Au1 and Au2 line, respectively (see Figures 5c and 7c and d). As a result, although the morphology of the cluster-CNT interface of the Au cluster supported on the (5,5) CNT is almost the same as that supported on the (8,0) CNT, the Au cluster on the (5,5) CNT just revolves on the CNT axis. The chirality-dependent diffusive behavior strongly supports our speculation on the mechanism of the cluster-CNT diffusion. Table 1 and Figure 9 show that DCOM and DR are quite dependent on the radius of the CNT. When DCOM is high, the cluster diffused well and DR affects the direction of the diffusion. As the radius of the CNT increases, the CNT becomes closer to a graphite surface and the effect of the CNT curvature is lessened. Thus, the bottom layer of the Au cluster is rather symmetrical when the CNT radius is large (see Figure 8). Note, however, that as the radius of the CNT increases, the value of DCOM generally decreases. The DCOM value of the Au cluster supported on the (43,0) CNT is 0.12 × 10-5 cm2/s, which is less than that of the Au cluster on both the (8,0) and the (5,5) CNT by one order of magnitude (Table 1 and Figure 9). Also, this value is smaller by one or two orders of magnitude than that of the clusters supported on graphite.27,30,34,36 Whenever DCOM is considerably small, DR no longer has any effect on the cluster diffusion and the cluster is almost fixed and rarely diffuses. This result is most likely due to the very small lattice parameter mismatch between the CNT β sites and the Au atoms in the bottom layer of the cluster, as reported in Deltour’s results.32 As the radius of the CNT varies, there would be a certain CNT size range where the gap of the CNT β sites closely fits with the atomic distances of the bottom layer of the cluster. Whenever the radius of the CNT is in this range, the cluster is fixed. The bond length of the Au atoms in the bottom layer of the cluster is 2.79 Å. The gap of the β sites of the (43,0) CNT is 2.87 Å in the direction perpendicular to the axis
Diffusion of Au and Pt Nanoclusters on Carbon Nanotubes of the CNT and 2.57 Å in the helical direction (see Table 2 and Figure 8c). The β sites closely match each atom of the bottom layer of the Au cluster, and consequently, the Au cluster almost sticks to the CNT. Summary In summary, we studied the diffusive nature of the Au and the Pt clusters on various CNTs and found that the cluster-CNT interface is crucial. The Au cluster, which has a weak interatomic interaction, wraps around the CNT and has a curved bottom layer. In contrast, the Pt cluster, which has a relatively strong interatomic interaction, has a flattened bottom layer. The Au cluster with the curved bottom layer grabs the CNT in a relatively strong manner and weakly tilts and rotates itself. When the atomic arrangements of the bottom layer of the cluster match the low-energy barrier diffusion pathways constructed on the PES of a CNT, the cluster diffuses along the preferred direction. Because the distribution of the low-energy pathways on the CNT depends on the chirality and radius of the CNT, the characteristics of the cluster diffusion depend on the nature of the CNT. As the radius of the CNT increases, the gap of the CNT β sites decreases and approximates (become closer to) the interatomic distance of the Au and Pt clusters. The cluster is consequently fixed on the CNT that has a DCOM value that is smaller by one or two orders of magnitude than those supported on graphite or small CNTs. With careful investigation of the diffusion mechanism of Pt and the Au clusters on various CNTs, we propose a strategy for minimizing the aggregation of CNT-supported nanoclusters without any chemical treatments such as vacancy formation or CNT doping. The diffusive nature of nanoclusters can be controlled by careful modification of the chirality and size of the CNT. This strategy helps prevent undesirable aggregation of CNT-supported clusters and improves the durability of these composite nanostructures in practical applications. Acknowledgment. This work was supported by the Korean Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MEST) (No. R01-2008-000-109860). References and Notes (1) Serp, P.; Corrias, M.; Kalck, P. Appl. Catal., A 2003, 253, 337. (2) Georgakilas, V.; Gournis, D.; Tzitzios, V.; Pasquato, L.; Guldi, D. M.; Prato, M. J. Mater. Chem. 2007, 17, 2679. (3) Baletto, F.; Ferrando, R. ReV. Mod. Phys. 2005, 77, 371. (4) Kim, H. Y.; Kim, H. G.; Ryu, J. H.; Lee, H. M. Phys. ReV. B 2007, 75, 4. (5) Kim, D. H.; Kim, H. Y.; Kim, H. G.; Ryu, J. H.; Lee, H. M. J. Phys.: Condens. Matter 2008, 20, 5. (6) Kim, H. G.; Choi, S. K.; Lee, H. M. J. Chem. Phys. 2008, 128, 144602. (7) Ferrando, R.; Jellinek, J.; Johnston, R. L. Chem. ReV. 2008, 108, 844. (8) Kim, H. Y.; Kim, H. G.; Kim, D. H.; Lee, H. M. J. Phys. Chem. C 2008, 112, 17138.
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