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Ring formation from the direct floating catalytic chemical vapor deposition
ARTICLE IN PRESS
Physica E 33 (2006) 24–27 www.elsevier.com/locate/physe
Ring formation from the direct floating catalytic chemical vapor deposition Zhenping Zhoua,,1, Dongyun Wanb, Ying Baic, Xinyuan Doua, Li Songa, Weiya Zhoua, Yujun Moc, Sishen Xiea, a Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, China c Department of Physics, Henan University, Kaifeng 475001, PR China
b
Received 16 August 2005; received in revised form 7 October 2005; accepted 7 October 2005 Available online 31 March 2006
Abstract Rings of single-walled carbon nanotubes (SWNTs) with a high yield of 30–50% have been fabricated through a floating catalytic chemical vapor deposition (FCCVD) method. The SWNT rings, which were characterized as the self-looping nanotube coils, feature a relative small diameter of 100–300 nm and a thin thickness of 1–8 nm.The high yield of the SWNT rings has been ascribed to the unique experimental configuration which could favor the as-synthesized straight SWNTs to bend freely and easily to form the coil-shaped structures. The technique presented here may advance the new understanding to bulk-prepare the nanotube rings. r 2006 Elsevier B.V. All rights reserved. PACS: 61.48.+c; 81.16.Hc Keywords: Single-walled carbon nanotube; Rings; Chemical vapor deposition
1. Introduction Since their discovery, carbon nanotubes (CNTs) have been intensively studied because of their unique properties and potential applications [1]. CNTs can be found both as single walled carbon nanotubes (SWNTs) generally forming ropes or bunched together, and as multiwalled carbon nanotubes (MWNTs) composed of some concentric graphene layers. They also adopt various complex shapes such as the helical nanotubes [2] or the ring-shaped ones [3]. However, for the future various practical applications, effective methods have to be developed to controllably fabricate and shape CNTs. Recently, several research groups have reported the observations of ring-shaped Corresponding author. Tel.: +86 01 82649081; fax: +86 01 82640215. Also to be corresponded.
E-mail addresses: [email protected] (Z. Zhou), [email protected] (S. Xie). 1 Current address: CEMES - UPR A-8011 CNRS, Groupe NanoMat, BP 94347, France. Tel.: +33 5 62 25 78 83; fax.: +33 5 62 25 79 99. 1386-9477/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2005.10.016
nanotubes during the preparation process [3–6]. Unfortunately, there are only trace quantities of nanotube rings existing in their CNT products [6]. To overcome the above accidental occurrence of nanotube rings in the directly synthesized CNTs, other efforts have been devoted to form the nanotube rings in a post-treatment manner [7–9]. However, the production of nanotube rings in this way popularly involve the chemical process which might modulate the essential characteristic of the nanotubes. Generally, few reports so far have been concerned about this research field. In this paper, we reported the observation of a sizable number nanotube rings formed in a floating catalyst chemical vapor deposition (FCCVD). From a theoretical standpoint, it is most likely to induce the ring-shaped structures of CNTs in a free space based on the high aspect ratio of CNTs [6]. With our unique experimental setup, we have validated the above assumption with a high yield of SWNT rings. The circular structures of CNTs exhibit interesting transport properties [10,11] and have been arousing a wide range of research interests [12–14].
ARTICLE IN PRESS Z. Zhou et al. / Physica E 33 (2006) 24–27
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2. Experimental details Our FCCVD for preparing high rate of SWNT rings is schematically shown in Fig. 1, and also similar as in Ref. [15]. Generally, ferrocene and sulfur (molar ratio 16:1), acting as the catalyst source, was mixed uniformly and placed in the first furnace. A gas mixture of argon and acetylene carried the sublimed catalyst through a narrow connection tube into the roomy reaction zone in the second furnace. The reaction temperature was 1100 1C and the system pressure was held at 1 atm. Nanotube rings formed in the reaction zone were carried to their deposition position and dropped on the Si wafers pre-placed in the outer-end section of the quartz tube reactor. High resolution transmission electron micrograph (HRTEM) and atomic force micrograph (AFM) have confirmed that the obtained tube-like objects are mostly SWNTs [15]. For obtaining the most nanotube rings rather than only isolated nanotubes just as Ref. [15], finely tuning the diameter and configuration of the quartz reactor is crucial. For example, a high yield of rings generally can be obtained when the diameter ratio of the small connection tube to the reaction tube is about 1:8.
3. Results and discussion Figs. 2(a) and (b), show the typical scanning electron micrograph (SEM) images of the as-prepared SWNT rings on the silicon substrates. As is shown, plenty of nanotube rings exist on the Si wafers and mostly are attached to the ordinary tubes (Fig. 2(b)). Approximately, 30–50% nanotubes are of this type of circular structures. To our best knowledge, this is so far the highest ring concentration (comparing the previous largest values about 10%) [6] obtained through a direct nanotube syntheses process and close to that acquired through a post-treatment manner [8]. Compared to the previous reports [3–6], these rings typically have a relatively small diameter of 100–300 nm, but are still larger than the thermodynamically stable critical radius ring of 0.03 mm [8]. Though there mostly exist small diameters of nanotube rings in our samples, the rings with a big diameter can also be often found. When the big rings are present, they generally show the elliptical shape. In Fig. 2(c), we show an elliptical ring with its long diameter of about 1.8 mm and short diameter about 1 mm.
2nd furnace Gas outlet
Diameter: 40mm
Fig. 2. (a) and (b) Typical SEM images of the as-prepared SWNT rings with a high yield of 30–50%. (c) Several interesting nanotube rings. The big elliptical SWNT ring in the upper part of the figure has a long diameter of about 1.8 mm and short diameter about 1 mm.
Cooling air 1st furnace Gas inlet
Connection tube (diameter: 5mm) Diameter: 40mm
Fig. 1. Schematic diagram of the floating catalytic CVD apparatus for preparing the SWNT rings.
AFM were further adopted to characterize the assynthesized nanotube rings. We thus obtained the ring heights typically ranging between 1 and 8 nm. This value is equal to or a bit bigger than that of the ordinary nanotubes, suggesting that there generally are only a few
ARTICLE IN PRESS 26
Z. Zhou et al. / Physica E 33 (2006) 24–27
Fig. 3. AFM image of an oblate SWNT ring whose long diameter is about 1.7 mm and short diameter 1.1 mm. AFM analysis revealed its inhomogenous height along the circumference with a maximum value of 5.7 nm and a minimum 4.3 nm (not including the super inhomogeneity in the upper right and left sections). The scale bar in the image is 500 nm.
turns involved to form the nanotube ring. Fig. 3 shows the AFM image of an oblate SWNT ring, whose long diameter reaches about 1.7 mm and short diameter about 1.1 mm. AFM analysis on its topography revealed that it has an inhomogenous thickness and width along the circumference with a maximum height of 5.7 nm and a minimum 4.3 nm. An important issue about the ring is whether it is a toroid or a coil? According to our observations, the ring formation can be deduced basically as nanotube-looping coils based on the following facts. First, AFM measurements revealed significant inhomogeneity (partially induced by the amorphous carbon) along the circumference of the rings in all cases. This is consistent with the step formed when two sections of one single nanotube or two nanotubes collide with each other. Second, when we slightly ultrasonicated the rings on the substrates in the acetone solution and deposited them again onto the Si substrate, no rings were found. This suggests that the rings can be easily taken apart and thus argues against the formation of the perfect toroids. Finally, most rings have been observed to branch off the ordinary straight nanotubes as shown in Fig. 2 and the lower section of the ring in Fig. 3. However, how the SWNT coils have been formed? Considering that all the observed diameters of the rings are greater than the critical dimension to form thermodynamically stable rings, the ring formation must be a kinetically controlled process [7,8]. In our case, we have
assumed the activation energy of the rings arising from the strong agitation when the reaction gas rushes from the small connection tube into the roomy reaction zone (Fig. 1) since we have never got any nanotube rings when the equidiameter quartz tube reactor was used under the same process parameters. Theoretically, the straight nanotubes can find their way with the best possibility to form circular structures in a free space because under the circumstance the nanotubes might bend or turn without any disturbing from such as the substrate in a general CVD process. We therefore present a simple model to explain the sizable formation of the nanotube rings in our floating catalytic CVD. First, SWNTs formed partially or completely, and floated freely in their reaction gas under our optimal preparation conditions. Then subjected to the violent disturb of the surrounding gas, they bended up and some sections of the tube might touch or overlap each other. These partially overlapped tubes could align and slide over each other to maximize their van der Waals interaction, and simultaneously to alleviate the significant coil-induced strain energy due to the increased curvature. Subsequently, the rings could continuously grow until the balance was reached between the tube–tube van der Waals interaction and the strain energy. This process could also account for the discontinuity of the ring heights along their circumference. On the other hand, because most of the SWNTs prepared in the reaction zone are isolated or free from one another under our optimal conditions [15], each nanotube might bend or turn freely without the blocking of the adjacent nanotubes, and ultimately a high yield of nanotube rings could be obtained. The above process also explain why there seem to be a favorable diameter for the small rings in Figs. 2(a) and (b). Because under the steadystate preparation conditions, each nanotube has the similar chance to bend itself to be the ring. Finally, we cannot rule out the possibility of more than one tube participating the ring formation and this might explain the more complex configurations shown in Fig. 2. On the other hand, one nanotube sometimes has several rings (Fig. 2(b)), and the reason may be that there are several ‘‘active’’ points when it bends up to form rings. 4. Conclusions In conclusion, we have observed a sizable number of SWNT rings in the nanotube samples prepared with a floating catalytic CVD. It has been revealed by the AFM and SEM that the formed SWNT rings are principally coiled-structures though we cannot completely rule out the existence of the toroidal ones. The technique presented here paves the way for effectively fabricating SWNT rings with a direct synthesis method, and the thus prepared nanotubes rings would be interesting in fundamental researches and in developing the new molecular electronics. The further research is under process to investigate the possibility of controlling the size distribution and quality of the CNTs rings.
ARTICLE IN PRESS Z. Zhou et al. / Physica E 33 (2006) 24–27
Acknowledgements The authors acknowledge financial support from the National Natural Science Foundation of China and ‘‘973’’ National Key Basic Research. References [1] C. Dekker, Phys. Today 52 (1999) 22. [2] L.P. Biro, S. Lazarescu, Ph. Lambin, P.A. Thiry, A. Fonseca, J.B. Nagy, A.A. Lucas, Phys. Rev. B 56 (1997) 12490. [3] J. Liu, H.J. Dai, J.H. Hafner, D.T. Colbert, R.E. Smalley, S.J. Tans, C. Dekker, Nature 385 (1997) 780. [4] M. Ahlskog, E. Seynaeve, R.J.M. Vullers, C. Van Haesendonck, A. Fonseca, K. Hernadi, J.B. Nagy, Chem. Phys. Lett. 300 (1999) 202.
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[5] J.-F. Colomer, L. Henrard, E. Flahaut, G. Van Tendeloo, A.A. Lucas, Ph. Lambin, Nano Lett. 3 (2003) 685. [6] W. Kim, H.C. Choi, M. Shim, H.J. Dai, Nano Lett. 2 (2002) 703. [7] R. Martel, H.R. Shea, P. Avouris, Nature 398 (1999) 299. [8] R. Martel, H.R. Shea, P.J. Avouris, Phys. Chem. B 103 (1999) 7551. [9] M. Sano, A. Kamino, J.D. Shinkai, Science 293 (2001) 1299. [10] R.C. Haddon, Nature 388 (1997) 31. [11] A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C.H. Xu, Y.H. Lee, S.G. Kim, A.G. Rinzler, D.T. Colbert, G.E. Scuseria, D. Tomanek, J.E. Fisher, R.E. Smalley, Science 273 (1996) 483. [12] M. Huhtala, A. Kuronen, K. Kaski, Comput. Phys. Commun. 148 (2002) 30. [13] O. Hod, E. Rabani, Phys. Rev. B 67 (2003) 195408. [14] S. Zhang, S. Zhao, M. Xia, E. Zhang, T. Xu, Phys. Rev. B 68 (2003) 245419. [15] Z. Zhou, L. Ci, L. Song, X. Yan, D. Liu, H. Yuan, Y. Gao, J. Wang, L. Liu, W. Zhou, G. Wang, S. Xie, J. Phys. Chem. B 108 (2004) 10751.
Physica E 33 (2006) 24–27 www.elsevier.com/locate/physe
Ring formation from the direct floating catalytic chemical vapor deposition Zhenping Zhoua,,1, Dongyun Wanb, Ying Baic, Xinyuan Doua, Li Songa, Weiya Zhoua, Yujun Moc, Sishen Xiea, a Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, China c Department of Physics, Henan University, Kaifeng 475001, PR China
b
Received 16 August 2005; received in revised form 7 October 2005; accepted 7 October 2005 Available online 31 March 2006
Abstract Rings of single-walled carbon nanotubes (SWNTs) with a high yield of 30–50% have been fabricated through a floating catalytic chemical vapor deposition (FCCVD) method. The SWNT rings, which were characterized as the self-looping nanotube coils, feature a relative small diameter of 100–300 nm and a thin thickness of 1–8 nm.The high yield of the SWNT rings has been ascribed to the unique experimental configuration which could favor the as-synthesized straight SWNTs to bend freely and easily to form the coil-shaped structures. The technique presented here may advance the new understanding to bulk-prepare the nanotube rings. r 2006 Elsevier B.V. All rights reserved. PACS: 61.48.+c; 81.16.Hc Keywords: Single-walled carbon nanotube; Rings; Chemical vapor deposition
1. Introduction Since their discovery, carbon nanotubes (CNTs) have been intensively studied because of their unique properties and potential applications [1]. CNTs can be found both as single walled carbon nanotubes (SWNTs) generally forming ropes or bunched together, and as multiwalled carbon nanotubes (MWNTs) composed of some concentric graphene layers. They also adopt various complex shapes such as the helical nanotubes [2] or the ring-shaped ones [3]. However, for the future various practical applications, effective methods have to be developed to controllably fabricate and shape CNTs. Recently, several research groups have reported the observations of ring-shaped Corresponding author. Tel.: +86 01 82649081; fax: +86 01 82640215. Also to be corresponded.
E-mail addresses: [email protected] (Z. Zhou), [email protected] (S. Xie). 1 Current address: CEMES - UPR A-8011 CNRS, Groupe NanoMat, BP 94347, France. Tel.: +33 5 62 25 78 83; fax.: +33 5 62 25 79 99. 1386-9477/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2005.10.016
nanotubes during the preparation process [3–6]. Unfortunately, there are only trace quantities of nanotube rings existing in their CNT products [6]. To overcome the above accidental occurrence of nanotube rings in the directly synthesized CNTs, other efforts have been devoted to form the nanotube rings in a post-treatment manner [7–9]. However, the production of nanotube rings in this way popularly involve the chemical process which might modulate the essential characteristic of the nanotubes. Generally, few reports so far have been concerned about this research field. In this paper, we reported the observation of a sizable number nanotube rings formed in a floating catalyst chemical vapor deposition (FCCVD). From a theoretical standpoint, it is most likely to induce the ring-shaped structures of CNTs in a free space based on the high aspect ratio of CNTs [6]. With our unique experimental setup, we have validated the above assumption with a high yield of SWNT rings. The circular structures of CNTs exhibit interesting transport properties [10,11] and have been arousing a wide range of research interests [12–14].
ARTICLE IN PRESS Z. Zhou et al. / Physica E 33 (2006) 24–27
25
2. Experimental details Our FCCVD for preparing high rate of SWNT rings is schematically shown in Fig. 1, and also similar as in Ref. [15]. Generally, ferrocene and sulfur (molar ratio 16:1), acting as the catalyst source, was mixed uniformly and placed in the first furnace. A gas mixture of argon and acetylene carried the sublimed catalyst through a narrow connection tube into the roomy reaction zone in the second furnace. The reaction temperature was 1100 1C and the system pressure was held at 1 atm. Nanotube rings formed in the reaction zone were carried to their deposition position and dropped on the Si wafers pre-placed in the outer-end section of the quartz tube reactor. High resolution transmission electron micrograph (HRTEM) and atomic force micrograph (AFM) have confirmed that the obtained tube-like objects are mostly SWNTs [15]. For obtaining the most nanotube rings rather than only isolated nanotubes just as Ref. [15], finely tuning the diameter and configuration of the quartz reactor is crucial. For example, a high yield of rings generally can be obtained when the diameter ratio of the small connection tube to the reaction tube is about 1:8.
3. Results and discussion Figs. 2(a) and (b), show the typical scanning electron micrograph (SEM) images of the as-prepared SWNT rings on the silicon substrates. As is shown, plenty of nanotube rings exist on the Si wafers and mostly are attached to the ordinary tubes (Fig. 2(b)). Approximately, 30–50% nanotubes are of this type of circular structures. To our best knowledge, this is so far the highest ring concentration (comparing the previous largest values about 10%) [6] obtained through a direct nanotube syntheses process and close to that acquired through a post-treatment manner [8]. Compared to the previous reports [3–6], these rings typically have a relatively small diameter of 100–300 nm, but are still larger than the thermodynamically stable critical radius ring of 0.03 mm [8]. Though there mostly exist small diameters of nanotube rings in our samples, the rings with a big diameter can also be often found. When the big rings are present, they generally show the elliptical shape. In Fig. 2(c), we show an elliptical ring with its long diameter of about 1.8 mm and short diameter about 1 mm.
2nd furnace Gas outlet
Diameter: 40mm
Fig. 2. (a) and (b) Typical SEM images of the as-prepared SWNT rings with a high yield of 30–50%. (c) Several interesting nanotube rings. The big elliptical SWNT ring in the upper part of the figure has a long diameter of about 1.8 mm and short diameter about 1 mm.
Cooling air 1st furnace Gas inlet
Connection tube (diameter: 5mm) Diameter: 40mm
Fig. 1. Schematic diagram of the floating catalytic CVD apparatus for preparing the SWNT rings.
AFM were further adopted to characterize the assynthesized nanotube rings. We thus obtained the ring heights typically ranging between 1 and 8 nm. This value is equal to or a bit bigger than that of the ordinary nanotubes, suggesting that there generally are only a few
ARTICLE IN PRESS 26
Z. Zhou et al. / Physica E 33 (2006) 24–27
Fig. 3. AFM image of an oblate SWNT ring whose long diameter is about 1.7 mm and short diameter 1.1 mm. AFM analysis revealed its inhomogenous height along the circumference with a maximum value of 5.7 nm and a minimum 4.3 nm (not including the super inhomogeneity in the upper right and left sections). The scale bar in the image is 500 nm.
turns involved to form the nanotube ring. Fig. 3 shows the AFM image of an oblate SWNT ring, whose long diameter reaches about 1.7 mm and short diameter about 1.1 mm. AFM analysis on its topography revealed that it has an inhomogenous thickness and width along the circumference with a maximum height of 5.7 nm and a minimum 4.3 nm. An important issue about the ring is whether it is a toroid or a coil? According to our observations, the ring formation can be deduced basically as nanotube-looping coils based on the following facts. First, AFM measurements revealed significant inhomogeneity (partially induced by the amorphous carbon) along the circumference of the rings in all cases. This is consistent with the step formed when two sections of one single nanotube or two nanotubes collide with each other. Second, when we slightly ultrasonicated the rings on the substrates in the acetone solution and deposited them again onto the Si substrate, no rings were found. This suggests that the rings can be easily taken apart and thus argues against the formation of the perfect toroids. Finally, most rings have been observed to branch off the ordinary straight nanotubes as shown in Fig. 2 and the lower section of the ring in Fig. 3. However, how the SWNT coils have been formed? Considering that all the observed diameters of the rings are greater than the critical dimension to form thermodynamically stable rings, the ring formation must be a kinetically controlled process [7,8]. In our case, we have
assumed the activation energy of the rings arising from the strong agitation when the reaction gas rushes from the small connection tube into the roomy reaction zone (Fig. 1) since we have never got any nanotube rings when the equidiameter quartz tube reactor was used under the same process parameters. Theoretically, the straight nanotubes can find their way with the best possibility to form circular structures in a free space because under the circumstance the nanotubes might bend or turn without any disturbing from such as the substrate in a general CVD process. We therefore present a simple model to explain the sizable formation of the nanotube rings in our floating catalytic CVD. First, SWNTs formed partially or completely, and floated freely in their reaction gas under our optimal preparation conditions. Then subjected to the violent disturb of the surrounding gas, they bended up and some sections of the tube might touch or overlap each other. These partially overlapped tubes could align and slide over each other to maximize their van der Waals interaction, and simultaneously to alleviate the significant coil-induced strain energy due to the increased curvature. Subsequently, the rings could continuously grow until the balance was reached between the tube–tube van der Waals interaction and the strain energy. This process could also account for the discontinuity of the ring heights along their circumference. On the other hand, because most of the SWNTs prepared in the reaction zone are isolated or free from one another under our optimal conditions [15], each nanotube might bend or turn freely without the blocking of the adjacent nanotubes, and ultimately a high yield of nanotube rings could be obtained. The above process also explain why there seem to be a favorable diameter for the small rings in Figs. 2(a) and (b). Because under the steadystate preparation conditions, each nanotube has the similar chance to bend itself to be the ring. Finally, we cannot rule out the possibility of more than one tube participating the ring formation and this might explain the more complex configurations shown in Fig. 2. On the other hand, one nanotube sometimes has several rings (Fig. 2(b)), and the reason may be that there are several ‘‘active’’ points when it bends up to form rings. 4. Conclusions In conclusion, we have observed a sizable number of SWNT rings in the nanotube samples prepared with a floating catalytic CVD. It has been revealed by the AFM and SEM that the formed SWNT rings are principally coiled-structures though we cannot completely rule out the existence of the toroidal ones. The technique presented here paves the way for effectively fabricating SWNT rings with a direct synthesis method, and the thus prepared nanotubes rings would be interesting in fundamental researches and in developing the new molecular electronics. The further research is under process to investigate the possibility of controlling the size distribution and quality of the CNTs rings.
ARTICLE IN PRESS Z. Zhou et al. / Physica E 33 (2006) 24–27
Acknowledgements The authors acknowledge financial support from the National Natural Science Foundation of China and ‘‘973’’ National Key Basic Research. References [1] C. Dekker, Phys. Today 52 (1999) 22. [2] L.P. Biro, S. Lazarescu, Ph. Lambin, P.A. Thiry, A. Fonseca, J.B. Nagy, A.A. Lucas, Phys. Rev. B 56 (1997) 12490. [3] J. Liu, H.J. Dai, J.H. Hafner, D.T. Colbert, R.E. Smalley, S.J. Tans, C. Dekker, Nature 385 (1997) 780. [4] M. Ahlskog, E. Seynaeve, R.J.M. Vullers, C. Van Haesendonck, A. Fonseca, K. Hernadi, J.B. Nagy, Chem. Phys. Lett. 300 (1999) 202.
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[5] J.-F. Colomer, L. Henrard, E. Flahaut, G. Van Tendeloo, A.A. Lucas, Ph. Lambin, Nano Lett. 3 (2003) 685. [6] W. Kim, H.C. Choi, M. Shim, H.J. Dai, Nano Lett. 2 (2002) 703. [7] R. Martel, H.R. Shea, P. Avouris, Nature 398 (1999) 299. [8] R. Martel, H.R. Shea, P.J. Avouris, Phys. Chem. B 103 (1999) 7551. [9] M. Sano, A. Kamino, J.D. Shinkai, Science 293 (2001) 1299. [10] R.C. Haddon, Nature 388 (1997) 31. [11] A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C.H. Xu, Y.H. Lee, S.G. Kim, A.G. Rinzler, D.T. Colbert, G.E. Scuseria, D. Tomanek, J.E. Fisher, R.E. Smalley, Science 273 (1996) 483. [12] M. Huhtala, A. Kuronen, K. Kaski, Comput. Phys. Commun. 148 (2002) 30. [13] O. Hod, E. Rabani, Phys. Rev. B 67 (2003) 195408. [14] S. Zhang, S. Zhao, M. Xia, E. Zhang, T. Xu, Phys. Rev. B 68 (2003) 245419. [15] Z. Zhou, L. Ci, L. Song, X. Yan, D. Liu, H. Yuan, Y. Gao, J. Wang, L. Liu, W. Zhou, G. Wang, S. Xie, J. Phys. Chem. B 108 (2004) 10751.