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J. Phys. Chem. C 2010, 114, 2022–2026
Immobilization of Au Nanoclusters Supported on Graphite: Molecular Dynamics Simulations Ji Hoon Ryu, Hyun You Kim, Da Hye Kim, Dong Hwa Seo, and Hyuck Mo Lee* Department of Materials Science and Engineering, KAIST, Gwahangno 335, Yuseong-gu, Daejeon, Korea 305-701 ReceiVed: September 22, 2009; ReVised Manuscript ReceiVed: December 9, 2009
We present a new approach to retard undesirable cluster aggregation. Using molecular dynamics simulations, we found that a large Au cluster that collides with a small cluster of metals other than Au has a locally distorted structure. Because of the lattice mismatch with a graphite surface, the distorted region of the Au cluster acts as a pinning center during the cluster diffusion process. Through the pivotal rotation caused by the pinning center, the Au cluster significantly reduces lateral diffusion. We also found that the most effective factor in the distortion of the structure is the difference in atomic size. The results of an AuNi system which has a large difference in atomic size confirm that a collision with a small Ni cluster reduces the diffusion of the large Au cluster. On the basis of these results, we expect that the use of cluster collision leads us to promising applications in the production of immobilized clusters. 1. Introduction In recent years, great attention has been paid to supported nanosized materials due to their technological importance in many physical and chemical areas.1 Supported Au nanoclusters, in particular, have become a topic of intensive research ever since highly dispersed Au nanoclusters were discovered to have unusual catalytic properties for various reactions.2-9 The Au clusters need to be dispersed on the support to increase their durability and catalytic activity.10 Because of weak interaction between Au clusters and the support surface, however, there is a considerable aggregation of Au clusters over time leading to a decrease in catalytic activity.11 Hence, a better understanding of the dynamics of Au clusters on a support would help us to reduce the mobilization of clusters. The physical deposition method has been generally used to produce nanoclusters pinned on graphite.12-20 Palmer’s group suggested two main techniques of producing pinned clusters by varying the kinetic energy of the clusters before they land on the graphite.13-20 With the first technique, called cluster pinning, clusters with high kinetic energy (typically 20 eV/atom) collide with the surface in order to self-pin the clusters.13-17 The cluster impact on the substrate breaks the graphite lattice and causes small defects; clusters are then trapped by these defects. The second technique is called the soft-landing method.17-20 In this method, softly deposited clusters are trapped during their diffusion by the small precreated surface defects made by in situ sputtering with an Ar+ beam. These techniques were used to make stably pinned, size-selected nanoclusters, even at high temperatures. From our point of view, it is interesting that in both cases a small defect on graphite surface can act as a pinning center of a large pinned cluster and a trapped cluster (in a manner resembling the concept of “seeds” in the work of Lidgi-Guigui et al.17). Thus, if we can make a similar small pinning center in the cluster itself, we may control the diffusion of a large cluster and eventually reduce its aggregation. * Corresponding author. Electronic mail:
[email protected]. Telephone: +82-42-350-3334. Fax: +82-42-350-3310.
In our previous study, we found that the shape of the bottom layer of nanoclusters mainly depends on the overall structure of clusters supported on graphite.21 Clusters with an ordered structure have a symmetric bottom layer called a hexagonal lattice, whereas some clusters with a closed shell or disordered structure have an asymmetric bottom layer called a rectangular lattice. In the case of a hexagonal lattice, the Pt atoms in the bottom layer are periodically well matched with stable sites on the graphite, and this matching process expedites the diffusion of a Pt cluster. In contrast, a Pt cluster with a rectangular lattice cannot move as fast as a cluster with a hexagonal lattice because of the asymmetry of the rectangular lattice. For a mixed lattice that simultaneously has two types of the bottom lattice, the portion of the bottom layer that is an asymmetric lattice acts as a pinning center. Hence, a Pt cluster with a mixed lattice rotates pivotally during the diffusion process, and the rotational motion makes the cluster move less. With the aid of our previous studies on the statistics and dynamics of nanoclusters,21-24 we aim to provide a method of immobility for the large Au cluster. By cluster collision with a small cluster other than Au, we can make a locally distorted structure in the large Au cluster which leads to a pinning center in the Au cluster itself. We found that this pinning center makes the Au cluster rotate pivotally rather than diffuse itself laterally, and it significantly reduces the cluster movement. The results confirm that our new approach has potential with regard to the production of durable nanoclusters. 2. Computational Details We conducted classical molecular dynamics simulations in canonical ensemble conditions (NVT). The quantum SuttonChen (Q_SC) potential25 was used to describe the interaction between all kinds of metal atoms used in this study. Because the interaction between the metal clusters and graphite is mainly dominated by a weak van der Waals force, we used the 12-6 Lennard-Jones (LJ) potential, where the well-depth and size parameters are 0.033 244 eV and 0.295 8 nm for Au-C, 0.029 103 eV and 0.296 05 nm for Ag-C, 0.040 922 eV and
10.1021/jp909113u 2010 American Chemical Society Published on Web 01/20/2010
Immobilization of Au Nanoclusters on Graphite 0.293 6 nm for Pt-C, 0.023 049 eV and 0.285 2 nm for Ni-C, and 0.019 996 eV and 0.322 5 nm for Cu-C, respectively.26 All MD simulations were conducted in a slab-structured system (7.368 × 6.381 × 30 nm), where periodic boundary conditions are applied along the graphite layers (of the x and y axes). The graphite, which consists of two graphite layers arranged in an AB stack with an interlayer spacing of 0.34 nm, is set to the bottom of the simulation box, and nanoclusters are located on the graphite surface. For the initial cluster structure, we prepared various stabilized Mn clusters (where M ) Au, Ag, Pt, Ni, and Cu elements and n ) 10, 15, 20, 90, 100, 135, 150, 180, and 200 atoms). Because the object of this study is not to produce an Au-based bimetallic nanocluster but to reduce the diffusion and aggregation of an Au cluster, we used small clusters which collide with a large Au cluster, with 10% of the atoms of the whole system. In this study, a whole system consists of 100, 150, or 200 atoms and is represented by Au100, Au150, Au200, Au90X10, Au135X15, and Au180X20, respectively (where X ) Ag, Pt, Ni, and Cu). To create the necessary conditions for a physical collision, we placed two clusters on a graphite surface at a distance of 0.3 nm from each other and optimized the collided clusters with a simulated annealing process. Each cluster was heated to 700 K for 50 ps and then allowed to cool to 600, 500, and 400 K with simulated periods of 50 ps, respectively. Finally, each cluster was equilibrated at 298 K for 2 ns. All final structures used in this study are from the final step of equilibration. In the case of pure Au systems, single Au cluster was placed on the surface. The detailed potentials and other simulation conditions used in this study were the same as in our previous study.21 To investigate the amount of cluster movement, we observed the diffusion rates (Dcm) of the cluster’s center of mass. We also observed the rotational rates (Drotation) so that we could examine the cluster’s rotational motion. All diffusion rates and rotational rates in this study are calculated during the equilibration process at 298 K. The dynamic analysis methods are described in detail in our previous study.21 3. Results and Discussion On the basis of the experimental concept, we considered using a cluster collision between two different clusters to make the pinning center in the cluster itself. When a large Au cluster collides with small clusters that have different properties from Au, we can locally change the ordered structure of the large Au cluster. If the changed structure is disordered and has an asymmetric bottom layer, it can act as a pinning center and retard the cluster diffusion. Our study of influences on structural change considered factors such as the alloying, cohesive energy, and atomic size of Ag, Pt, and Ni elements. Table 1 shows the cohesive energy and covalent radius for Au, Ag, Pt, Ni, and Cu. The values in parentheses are absolute percent differences from Au. The effects expected from the addition of each element are as follows: • In the AuAg system, we considered the alloying effect after a cluster collision. Because Ag has the most similar properties to Au, we can examine the type of structural change that can occur from simply mixing the atoms. • In the AgPt system, the difference in cohesive energy is examined if effective in structural change. Because the cohesive energy is related to the strength of an atomic bond, we supposed that significant difference of up to 53% in the cohesive energy between Au and Pt would affect the structural change after the cluster collision.
J. Phys. Chem. C, Vol. 114, No. 5, 2010 2023 TABLE 1: Cohesive Energy and Covalent Radius of Au, Ag, Pt, Ni, and Cua element
cohesive energy (eV)
covalent radius (Å)
Au Ag Pt Ni Cu
3.81 (0%) 2.95 (22.6%) 5.84 (53.3%) 4.44 (16.5%) 3.49 (8.4%)
1.44 (0%) 1.45 (0.7%) 1.39 (3.5%) 1.25 (13.2%) 1.28 (11.1%)
a
The values in parentheses refer to absolute percent differences from the Au values.
• In the AuNi system, the atomic size difference is regarded as a key factor in structural change. Using the covalent radius, we compare the atomic size as to the metal elements. Table 1 shows that the covalent radius of Ni, the smallest radius, is 13.2% smaller that that of Au. Thus, structural change can be caused by size differences in a collision with a Ni cluster. 3.1. Pure Au System. Before examining how the collision works in practice, we need to consider the static and dynamic properties of the pure Au system as a reference. Table 2 presents the overall structure of clusters, the bottom layers, the diffusion rates (Dcm), the rotation rates (100 × Drotation), the average movements of all atoms in clusters, and the average bond length in the bottom layers with various systems. As summarized in Table 2, Au100 and Au200 clusters have an ordered structure with a hexagonal bottom lattice. These two clusters therefore have high Dcm values and move faster and further than other clusters. However, due to the icosahedral structure (Ih) with a mixed bottom lattice (where two types of hexagonal and asymmetric lattice exist simultaneously), the Au150 cluster has a relatively low Dcm value and leads to slow diffusion. The relation between the bottom lattice and the diffusion rate in this system corresponds well with the results of our previous study.21 In these results, all the diffusion rates in the pure Au system are somewhere on the order of 10-5 cm2/s, which matched the value obtained in other theoretical studies for Pt, Cu, Ni, and Au clusters on a graphite surface.26-29 In addition to the diffusion rates, we determined the average movements of all atoms in the cluster throughout the entire diffusion process. Table 2 shows that all the Au clusters moved a distance of over 3.6 × 103 nm during their diffusion time. This value of movement was used in this study as a criterion of undesirable cluster diffusion, and our aim is to reduce this distance for practical use of Au clusters. 3.2. Overall Structure and Bottom Structure of Collided Clusters. To clarify which factors affect the structural change of Au clusters, we analyzed the static properties of clusters formed by a collision between Au and other clusters. Figure 1 shows the overall structure (first and second rows) and the bottom layers (third row) of Au180Ag20, Au180Pt20, Au180Ni20, and Au180Cu20 clusters. The first row shows the top view of the clusters, and the second shows the cross section. All the clusters are locally alloyed at their collision region, which is indicated in a green and red dotted circle. In the Au180Ag20 and Au180Pt20 clusters, the Ag and Pt atoms harmonize well with the Au atoms at pure Au sites as represented in the green dotted circle (see the second row). Accordingly, these clusters have a perfectly ordered structure with a hexagonal bottom lattice such as pure Au clusters (see the third row). Table 2 shows that the structures of other clusters with different size in AuAg and AuPt systems are also equivalent to the structures of Au180Ag20 and Au180Pt20 clusters. It means that the collision with Ag and Pt clusters cannot affect the structural change even if the collision yields locally alloyed clusters. We can deduce therefore that the
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TABLE 2: Static and Dynamic Properties of Pure Au, AuAg, AuPt, AuNi, and AuCu Systems with Cluster Size, N (Number of Atoms)a
Au AuAg AuPt AuNi AuCu
a
system size (N)
structure
bottom layer
Dcm (10-5 cm2/s)
100 × Drotation (10-5 cm2/s)
average movement (nm)
bond length (Å)
100 150 200 100 150 200 100 150 200 100 150 200 100 150 200
fcc + hcp fcc + Ih fcc fcc + hcp fcc + hcp fcc + hcp fcc + hcp fcc fcc + hcp fcc + am fcc + am fcc + am hcp + am fcc + am fcc + am
hexa. mixed hexa. hexa. hexa. hexa. hexa. hexa. hexa. mixed mixed mixed mixed mixed mixed
9.54 2.77 4.50 18.73 8.36 12.29 10.63 7.65 7.63 0.38 0.35 0.14 2.39 0.17 0.16
1.54 7.25 2.59 0.19 1.06 0.21 0.25 0.33 0.53 11.15 11.61 15.32 9.15 15.05 15.01
6.01 × 103 3.57 × 103 4.13 × 103 8.25 × 103 5.39 × 103 6.65 × 103 6.24 × 103 5.25 × 103 5.14 × 103 1.49 × 103 1.43 × 103 1.12 × 103 3.48 × 103 1.17 × 103 1.14 × 103
2.76 2.77 2.77 2.68 2.72 2.66 2.48 2.43 2.42 2.73 2.58 2.53
The disordered amorphous structure is represented as “am”.
Figure 1. Overall structures (first and second rows) and bottom layers (third row) of the Au180Ag20, Au180Pt20, Au180Ni20, and Au180Cu20 cluster, from left to right. The first row shows the top view of the clusters, and the second shows the cross-sectional atomic configuration.
alloying effect and the differences in cohesive energies are not influential on structural change. In contrast, Ni atoms are not in harmony with Au atoms at the collision region though the Au180Ni20 cluster also has a locally alloyed structure. As indicated in the red dotted circle in Figure 1 (see the second row), the Ni atoms penetrate into the large Au cluster and distort the ordered structure of the Au cluster. As a result, this part of the Au cluster has a disordered structure. Partially disordered structures are also found in Au90Ni10 and Au135Ni15 clusters. Different from the six-folded bonds in a hexagonal lattice, some five-folded bonds are observed around the Ni atoms due to the structural distortion (see the third row). The presence of these asymmetric five-folded bonds can obviously be attributed to the small atomic size of Ni. To clarify the size effect of Ni in more detail, we examined the average bond length between the Au and other element atoms (Ag, Pt, Ni, and Cu) of each bottom layer. In all the systems, including pure Au, the bond length of the Au-Au bond is about 2.79 Å. Although a little shorter than Au-Au bonds, AuAg and AuPt clusters have a similar bond length to those of pure Au clusters, as shown in Table 2. In the case of AuNi systems, however, the average bond length between Au and Ni
atoms is 2.44 Å. This bond length is insufficient for the production of a perfectly ordered structure with a hexagonal lattice in AuNi clusters. As a result, the AuNi cluster has a disordered structure with an asymmetric bottom lattice in the collision region. Because of the mismatch with the graphite surface, the asymmetric bottom lattices have low diffusion rates. The collision region finally can act as a pinning center of an AuNi cluster as we assumed previously. Similar results are observed in AuCu systems except the Au90Cu10 cluster. 3.3. Diffusion and Pinning of Collided Clusters. In addition to analyzing the static properties of collided clusters, we also considered the dynamic properties, particularly with regard to Dcm and Drotation. In AuAg and AuPt systems, all clusters have a hexagonal lattice in their bottom layers. As a result, they tend to laterally diffuse rather than rotate. The values of high Dcm and low Drotation in Table 2 confirm the preferred lateral diffusion of the clusters. Due to the fast lateral diffusion, all clusters in the AuAg and AuPt systems move a long distance during the diffusion process. In the period of 3 ns, all the clusters in these systems move over 5 × 103 nm. This distance is similar or longer than that of pure Au clusters. We infer, therefore, as shown in Figure 2, that a collision with small Ag and Pt clusters has no effect on the immobility of a large Au cluster. These
Immobilization of Au Nanoclusters on Graphite
Figure 2. Variation of diffusion rates of pure Au, AuAg, AuPt, AuNi, and AuCu systems with cluster size.
J. Phys. Chem. C, Vol. 114, No. 5, 2010 2025 AuPt clusters. Note especially that the Au90Ni10 cluster moves a distance that is about four times shorter than that of the Au200 cluster. Given that the cluster aggregation is directly dependent on the cluster movements, it is apparent that a collision with a small Ni cluster is highly effective in reducing the undesirable diffusion and aggregation of the Au cluster. On the basis of our findings, we postulated the following: if a small Cu cluster collides with a large Au cluster, the Cu cluster also reduces the cluster diffusion because Cu is as small as Ni. As shown in Figure 1, Figure 2, and Table 2, the AuCu clusters have a locally disordered structure with a relatively small bond length, which leads to a low Dcm value and a high Drotation value. As with AuNi clusters, the AuCu clusters rotate rather than laterally diffuse themselves. On account of the fact that the moving distance is as short as 1.1 × 103 nm except for the Au90Cu10 cluster, it is clear that the collision with a small Cu cluster tends to make a large Au cluster move less as the small Ni cluster did. All of these results provide conclusive evidence to our approach for an immobilization of clusters. In addition, we considered the structural change after cluster collision, because AuNi presents a tendency toward phase separation, while AuCu is a system with a strong tendency for intermixing, making also ordered phases even though Ni and Cu have similar atomic sizes.30-32 However, we confirmed that solute atoms are still separated, and thus their initial collided structure is maintained in a host cluster during longer simulation time due to low temperature and the supporter effect.26,33 As a result, the distorted structure of Au clusters can still affect the diffusion process of the Au cluster even after longer time. 4. Conclusions
Figure 3. Total trajectory of three atoms, with bottom and side views of the Au180Ni20 cluster.
results are well accordant with those of the previous chapter; that is, there were no changes both in the overall cluster and in the bottom lattice which control the diffusion rates in AuAg and AuPt systems. As already noted, all the AuNi clusters have mixed lattices which have two different types of lattices in the bottom layer: a hexagonal lattice, which is caused by the perfectly ordered Au structure, and an asymmetric lattice, which is caused by the disordered structure at the collision region. Table 2 and Figure 2 show that all the AuNi clusters have a lower Dcm value and a higher Drotation value than the pure Au, AuAg, and AuPt clusters. Thus, the AuNi clusters tend to rotate in a pivotal manner rather than diffuse themselves in a lateral manner. The results are confirmed in Figure 3, which shows the trajectory of three atoms in the Au180Ni20 cluster during the whole diffusion process. In Figure 3, the Au1, Au2, and Au3 atoms are located on the pure Au region, center region, and collided region of a cluster, in order. As shown in this figure, the Au3 atom which is located on the collided region of the cluster wandered over the smallest area during the diffusion process. That is, the Au3 atom was stuck on the graphite surface and had the vibrational motion rather than the lateral diffusion. On the contrary, the Au1 atom which is located on the pure Au region of the cluster wandered over the largest area during the same diffusion time. Hence, we deduce that the disordered region, including the Au3 atom, caused by the cluster collision can act as a pinning center during the diffusion process. All the AuNi clusters have an average movement of about 1.3 × 103 nm during the same diffusion time. These distances are quite short compared to those of the pure Au, AuAg, and
To retard undesirable cluster aggregation, we suggest an immobilization method with cluster collision. When a small cluster other than Au collides with a large Au cluster, some part of the structure of the Au cluster is distorted. Because the distorted structure acts as a pinning center, the collided Au cluster tends to pivotally rotate rather than diffuse itself in a lateral manner. That is, a cluster collision can reduce the diffusion of the Au cluster. It seems significant because of the fact that the cluster diffusion is directly related to cluster aggregation. We also found that the difference in atomic size is the most effective factor of structure distortion. Owing to the large difference in atomic size between Au and Ni, the collision of an Au cluster with a Ni cluster cannot produce a perfectly ordered structure. The collided region can also be observed to act as a pinning center and reduce the Au cluster diffusion. Hence, during the same diffusion process, AuNi clusters move a shorter distance than pure Au clusters. All of these results suggest a possibility of preventing aggregation and production of durable nanoclusters in a practical catalytic application. Acknowledgment. This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. 2009-0059348). References and Notes (1) Jensen, P. ReV. Mod. Phys. 1999, 71, 1695. (2) Fu, Q.; Saltsburg, H.; Flytzani-Stephanopoulos, M. Science 2003, 301, 935. (3) Chen, M. S.; Goodman, D. W. Science 2004, 306, 252. (4) Yoon, B.; Koskinen, P.; Huber, B.; Kostko, O.; von Issendorff, B.; Hakkinen, H.; Moseler, M.; Landman, U. Chem. Phys. Chem. 2007, 8, 157. (5) Chen, M. S.; Goodman, D. W. Chem. Soc. ReV. 2008, 37, 1860.
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(6) Turner, M.; Golovko, V. B.; Vaughan, O. P. H.; Abdulkin, P.; Berenguer-Murcia, A.; Tikhov, M. S.; Johnson, B. F. G.; Lambert, R. M. Nature 2008, 454, 981. (7) Herzing, A. A.; Kiely, C. J.; Carley, A. F.; Landon, P.; Hutchings, G. J. Science 2008, 321, 1331. (8) Studt, F.; Abild-Pedersen, F.; Bligaard, T.; Sorensen, R. Z.; Christensen, C. H.; Norskov, J. K. Science 2008, 320, 1320. (9) Yoon, B.; Hakkinen, H.; Landman, U.; Worz, A. S.; Antonietti, J. M.; Abbet, S.; Judai, K.; Heiz, U. Science 2005, 307, 403. (10) Joo, S. H.; Choi, S. J.; Oh, I.; Kwak, J.; Liu, Z.; Terasaki, O.; Ryoo, R. Nature 2001, 412, 169. (11) Tseung, A. C. C.; Dhara, S. C. Electrochim. Acta 1975, 20, 681. (12) Bromann, K.; Felix, C.; Brune, H.; Harbich, W.; Monot, R.; Buttet, J.; Kern, K. Science 1996, 274, 956. (13) Gibilisco, S.; Di Vece, M.; Palomba, S.; Faraci, G.; Palmer, R. E. J. Chem. Phys. 2006, 125, 084704. (14) Smith, R.; Nock, C.; Kenny, S. D.; Belbruno, J. J.; Di Vece, M.; Palomba, S.; Palmer, R. E. Phys. ReV. B 2006, 73, 125429. (15) Di Vece, M.; Palomba, S.; Palmer, R. E. Phys. ReV. B 2005, 72, 073407. (16) Yin, F.; Xirouchaki, C.; Guo, Q. M.; Palmer, R. E. AdV. Mater. 2005, 17, 731. (17) Lidgi-Guigui, N.; Mulheran, P.; Palmer, R. E. Appl. Phys. Lett. 2008, 93, 123107. (18) Palmer, R. E.; Pratontep, S.; Boyen, H. G. Nat. Mater. 2003, 2, 443. (19) Li, Z. Y.; Young, N. P.; Di Vece, M.; Palomba, S.; Palmer, R. E.; Bleloch, A. L.; Curley, B. C.; Johnston, R. L.; Jiang, J.; Yuan, J. Nature 2008, 451, 46.
Ryu et al. (20) Claeyssens, F.; Pratontep, S.; Xirouchaki, C.; Palmer, R. E. Nanotechnology 2006, 17, 805. (21) Ryu, J. H.; Seo, D. H.; Kim, D. H.; Lee, H. M. Phys. Chem. Chem. Phys. 2009, 11, 503. (22) Lee, S. H.; Han, S. S.; Kang, J. K.; Ryu, J. H.; Lee, H. M. Surf. Sci. 2008, 602, 1433. (23) Kim, D. H.; Kim, H. Y.; Kim, H. G.; Ryu, J. H.; Lee, H. M. J. Phys.: Condens. Matter 2008, 20, 035208. (24) Kim, H. Y.; Kim, H. G.; Ryu, J. H.; Lee, H. M. Phy. ReV. B 2007, 75, 212105. (25) Cagin, T.; Kimura, Y.; Qi, Y.; Li, H.; Ikeda, H.; Johnson, W. L.; Goddard, W. A., III. In Proceedings of the Materials Research Society Symposia; Johnson, W. L., Liu, C. T., Inoue, A., Eds.; Materials Research Society: Pittsburgh, PA, 1999; p 43. (26) Huang, S. P.; Mainardi, D. S.; Balbuena, P. B. Surf. Sci. 2003, 545, 163. (27) Lamas, E. J.; Balbuena, P. B. J. Phys. Chem. B 2003, 107, 11682. (28) Lewis, L. J.; Jensen, P.; Combe, N.; Barrat, J. L. Phys. ReV. B 2000, 61, 16084. (29) Huang, S. P.; Balbuena, P. B. Mol. Phys. 2002, 100, 2165. (30) Ferrando, R.; Jellinek, J.; Johnston, R. L. Chem. ReV. 2008, 108, 845. (31) Ferrando, R.; Fortunelli, A.; Rossi, G. Phys. ReV. B 2005, 72, 085449. (32) Ferrando, R.; Rossi, G.; Toai, T. J. Faraday Discuss. 2008, 138, 49. (33) Huang, S. P.; Balbuena, P. B. J. Phys. Chem. B 2002, 106, 7225.
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