dynamical behavior of pt clusters on (5,5) and (9,0) single wall carbon nanotubes

SHORT COMMUNICATION

Dynamical behavior of Pt clusters on (5,5) and (9,0)single wall carbon nanotubesYao-Chun Wang1, Hui-Lung Chen2, Shin-Pon Ju3,*,†, Jin-Yuan Hsieh4 and Chen-Yin Tai3

1Daxin Materials Corporation, Taichung City, 40763, Taiwan, R.O.C.2Department of Chemistry and Institute of Applied Chemistry, Chinese Culture University, Taipei, 111, Taiwan, R.O.C.3Department of Mechanical and Electro-Mechanical Engineering, Center for Nanoscience and Nanotechnology, National Sun Yat-senUniversity, Kaohsiung, 804, Taiwan, R.O.C.4Department of Mechanical Engineering, No.1, Xinxing Rd., Xinfeng Hsinchu, 30401, Taiwan, R.O.C.

SUMMARY

Density functional theory (DFT) was employed to obtain configurations and corresponding interaction energies for Ptn(n = 4–13) clusters on a single wall carbon nanotube (SWCNT). The force-matching method (FMM) was applied to fitthe potential parameters for Ptn and the SWCNT by reference data obtained from these DFT calculations. To elucidatethe dynamical behavior of Pt clusters on (5,5) and (9,0) SWCNT types, molecular dynamics was applied using the fittedpotential parameters from FMM. We then we investigated the size effect of the Pt clusters at different temperatures. In ad-dition, the square displacement was utilized to analyze their movement on the nanotube. Copyright © 2013 John Wiley &Sons, Ltd.

KEY WORDS

carbon nanotube; molecular dynamics; Pt; cluster; density functional theory; force-matching method; size effect; temperature

Correspondence

* Shin-Pon Ju, Department of Mechanical and Electro-Mechanical Engineering, Center for Nanoscience and Nanotechnology, NationalSun Yat-sen University, Kaohsiung, 804, Taiwan, R.O.C.†E-mail: [email protected]

Received 4 October 2012; Revised 2 June 2013; Accepted 14 June 2013

1. INTRODUCTION

Carbon nanotubes (CNTs) were discovered by SumioIijima in 1993 and display numerous beneficial propertiessuch as high stiffness, high Young's modulus, andelectronic properties.[1–3] Because of these properties,CNTs have attracted considerable attention and have manypotential applications, such as gas sensors, field emissiondisplays, hydrogen storage and fuel cells[4–6]. Amongthese applications, hydrogen storage in fuel cells is themost promising for renewable energy. For suchapplications, according to the U.S. Department of Energy's2010 target, the gravimetric capacity and volumetricdensity must be 6.0wt% and 45 g/L, respectively, with aprocess temperature of about 250K–330K and systempressure lower than 100 atm [7]. Chen et al. mention thatmany materials which can be applied in the hydrogen stor-age and CNT has great potential in those materials [8].CNTs can be used to store the hydrogen molecules up to8.5wt%, but the system emperature and pressure must be

80K and 100 bar [9]. Maintaining such low-temperatureand high-pressure hydrogen storage environments,however, is expensive. Recently, Wu stated that Li atomsadsorbed on boron nitride nanotubes can improve hydro-gen storage capacity [10]. Different metal clusters on thenanotube have been widely reported for design of newhigh capacity hydrogen storage devices [11–15]. Theoreti-cally, Kim et al. found that the structure of Pt atoms on thesingle wall CNT (SWCNT) can act as the fuel cellelectrode to decrease the energy barrier necessary for thecombination of oxygen and hydrogen. They also comparedthe adsorption energy of Pt clusters on pure and defectCNTs [16]. Cuong found that the binding energy betweenPt clusters and CNTs and the charge transfer from the Ptcluster toward the CNT both increase with an increase inPt cluster size [17–19]. Park found that the Pt atom bondto the vacancy site of CNT is stronger than on the Stone–Wales defect. In addition, the Pt atom adsorbed on the pureCNT was found to be the weakest when compared to thoseadsorbed on the defect CNTs [20]. Experimentally, Mu

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2014; 38:1053–1059

Published online 27 August 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.3088

Copyright © 2013 John Wiley & Sons, Ltd. 1053

showed that coverage ratio of Pt clusters on the CNT isaffected by the Pt particle size and the efficiency of the fuelcell when they are adsorbed on the CNT [21]. Park et al.investigated the adsorption site of the Pt atom on defectmultiwalled CNTs. Through XRD and TEM observations,they found that the Pt atom tends to occupy the defect partof the multiwalled CNT. In addition, they also demon-strated that the Pt clusters could be material used in afuel cell. These reviews above demonstrate thatSWCNTs with adsorbed Pt clusters could be promisinghydrogen storage devices and that it is thereforeimportant to understand the dynamical behaviors of thePt clusters adsorbed on the CNT and how they mayimprove hydrogen storage capacity. The less a Pt clustermoves on the SWCNT, the more suitable it may be forhydrogen storage due to its stability over a range oftemperatures. However, since it is computationally tooexpensive to investigate the dynamical behaviors of Ptclusters on the SWCNT by ab initio molecular dynamics(MD), classical MD simulation is used for its accuratepotential to model their interactions. Hence, we usedthe force-matching method (FMM) to obtain the potentialfunction parameters on the basis of the reference dataderived from density functional theory (DFT)

calculations. The dynamical behaviors of Pt4, Pt6, Pt9,Pt13 clusters on the SWCNT were studied.

1.1. Simulation detail

1.1.1. Fitting processBefore the FMM is utilized to fit Morse potential

parameters which accurately reflect the interaction betweenthe cluster and CNT, we need to obtain the most stablestructure of the Ptn cluster. Basin-hopping methods withbulk tight-binding potential parameters were utilized toobtain the relatively stable structures of Pt4 and Pt13. Sincethe bulk tight-binding potential parameters cannot reflectthe accurate structure of clusters, those structures wereoptimized by DFT simulation. In the DFT simulation, theoptimization was performed using Dmol3 of MaterialStudio 5.5, developed by Accelrys Software, Inc. The set-tings for the DFT calculation were the generalized gradientapproximation with Perdew-Wang-91 parameterization.Effective-core-potentials calculations were performed witha double numeric plus polarization basis setting. Theenergy tolerance in the self-consistent field calculationswas set to 2 × 10�4 eV. The k-point was set to 1 × 1 × 3for the Brillouin zone integration. After obtaining themost stable Ptn cluster structure, we placed the Ptcluster on the CNT (5, 5) and performed the DFT-MDsimulation to obtain the reference data. The cell lengthwas 35Å x 35Å x 17.246Å, and temperature was heldat 300 K. There were 140 carbon atoms comprising theCNT in the system. To accurately reflect the interaction

Table I. Morse potential parameters.

Parameters D(eV) a(1/Å) r0(Å)

Pt-C 0.0417 1.328 3.279

(a) (b)

(c) (d)

Figure 1. The most stable structures of (a) Pt4, (b) Pt6, (c) Pt9, (d) Pt13 clusters.

Dynamical behavior of Pt clusters on (5,5) and (9,0) SWCNTsY.-C. Wang, S.-P. Ju and C.-Y. Tai

1054 Int. J. Energy Res. 2014; 38:1053–1059 © 2013 John Wiley & Sons, Ltd.DOI: 10.1002/er

between Pt and carbon atoms, Morse potential, devel-oped in 1929 [a], was utilized. This potential functionhas the following form:

V rij� � ¼ De 1� e�a rij�r0ð Þ� �2

where De is the energy, and rij and r0 are the distancebetween Pt and carbon atoms in the system and anenergy-minimum state, respectively. Finally, we canobtain the new Morse potential parameters from FMM,which are listed in Table I. In addition, the error is about9.3% when compared to the DFT calculated result.

1.1.2. FMMThe FMM was used in the present study to determine

the Morse potential parameters for the CNT. The FMM isbased on fitting atomic forces obtained from a potential

function to those calculated from ab initio approaches formany atomic configurations as:

Z ¼ Zc þ ZF

ZF ¼ ∑NA

j¼1∑

α¼x;y;zWj

f jα � f 0; jα� �2

f 0; j2

ZC ¼ ∑NC

k¼1Wk

Ak � A0;k� �2

A0;k2

where Z F is the target function; when the target function isclose to the zero, it means that the parameters can reflectthe interaction more accurately. f0,jα and A0,k stand for thereference data of force and global parameters, respectively.N and W are the data number and the weight function. Inthis study, the reference data were obtained from theDFT result.

(a) (b)

(d)(c)

Figure 2. Distribution of (a)(b) axial and (c)(d) tangent SD for the Pt4 cluster on the different CNTs. (a)(c) are the (5,5) CNT, and (b)(d) arethe (9,0) CNT.

Dynamical behavior of Pt clusters on (5,5) and (9,0) SWCNTs Y.-C. Wang, S.-P. Ju and C.-Y. Tai

1055Int. J. Energy Res. 2014; 38:1053–1059 © 2013 John Wiley & Sons, Ltd.DOI: 10.1002/er

1.1.3. MD simulationWe performed the MD simulation with modified param-

eters in the NVT ensemble. The time step of 1 fs was set forthe time integration, and Nose–Hoover thermostat is usedin the system. The periodic boundary condition was ap-plied. Four different Pt clusters (Pt4, Pt6, Pt9, and Pt13) wereplaced individually in a supercell of 300 carbon atoms forthe (5,5) SWCNT with a volume of 30 × 30 × 36.8927Å3,and in a supercell of 540 carbon atoms for the (9,0)SWCNT with a volume of 30 × 30 × 63.9Å3. The potentialfunctions of the CNT and cluster are the Tersoff and tight-binding potentials, respectively. In order to obtain the moststable structures on the CNTs, the annealing method wasused from 2000K to 1K. These most stable structures wereused to perform the MD simulation and investigate the in-creasing temperature effect. The temperature was increasedfrom 1K to 750K at 0.001K/fs.

2. RESULTS AND DISCUSSION

Figure 1(a)–(d) shows the most stable structures for the Pt4,Pt6, Pt9, and Pt13 clusters, respectively. Those structures aresimilar to Li's results [22]. The bond lengths and bindingenergy are similar to those of the reference. In order toobtain the dynamical behaviors of Pt clusters on the two dif-ferent CNTs, the square displacement (SD) was utilized as:

SD ¼ r tð Þ � r 0ð Þj j2

where r(t) and r(0) stand for the position at t and reference.In this study, the positions of center of mass for all clusterswere calculated to obtain the SD. When the SD valueremains the same, this means that the material is locatedat the same position. Figure 2(a) and (b) shows the axialSD distributions for the Pt4 cluster on the (5,5) and the

(a) (b)

(d)(c)

Figure 3. Distribution of (a)(b) axial and (c)(d) tangent SD for the Pt6 cluster on the different CNTs. (a)(c) and (b)(d) are the SD on the(5,5) and (9,0) CNTs, respectively.



(9,0) CNTs, respectively, while (c) and (d) show tangentdistributions for (5,5) and (9,0) CNTs. From Figure 2(a),it can be seen that the Pt4 cluster moves only relativelyslightly when the temperature is lower than 300K. Thiscan be more clearly observed in the inset of Figure 2(a),which shows SD values lower than 100Å2. Moreover, theaxial SD value periodically rises, then consistently returnsto near 5Å2. This phenomenon occurs several times at 90,125, 171, 208, and 250K. This implies that the Pt4 clustermoves a small distance but returns to its original positionat lower temperatures (<300K). In addition, the largestvalue of SD is 80Å2, which indicates that the Pt4 clusterdoes not move significantly at lower temperatures. Whenthe temperature is higher than 300K, however, the Pt4cluster moves relatively fast and over a longer distance.The SD value increases quite clearly, with its highest valuehigher than 4000Å2. This axial SD distribution shows thatwhen temperature is higher than 300K, the Pt4 cluster willnot return to its original position. Note that the Pt4 cluster

movement is not rotational when the temperature is lowerthan 600K. That is, the cluster ‘slides’ rather than ‘rolls’across the CNT, and its surface area remains the same.Figure 2(c) shows the tangent SD distribution for the Pt4cluster. Its low values indicate that the Pt4 cluster prefersto move in the axial direction even at temperatures higherthan 300K. When the temperature is higher than 650K,however, the value of SD increases dramatically as the Pt4cluster starts to rotate or ‘roll’ at 650K. Whenever move-ment is rotational, the tangent SD distribution will spikeobviously and can be easily identified. Figure 2(b) showsthe axial distribution of SD of Pt4 cluster on the (9,0)CNT. Here, it is clear that the Pt4 cluster moves only rela-tively slightly at temperatures lower than 350K, resultingin the lower values for SD (<25Å2). The Pt4 cluster onthe (9,0) CNT also usually returns to its original positionwhen temperature is lower than 350K, similar to the (5,5)CNT. Also similar is that at higher temperatures, the valueof tangent SD increases dramatically for the (9,0) CNT.

(c)

(a) (b)

(d)




Figure 3(a)–(b) and (c)–(d) shows the SD distributionsfor the Pt6 cluster on the (5,5) and (9,0) CNTs, respectively,as in Figure 2. For the (5,5) CNT, the SD distributionillustrates that the Pt6 cluster does not prefer to move inthe tangential direction in the process of increasingtemperature, and that most movement is axial in nature.At temperatures lower than 600K, the distribution of axialSD is relatively smaller than higher than 600K. Note thatthe Pt6 cluster changes its shape at 500K. After this change,the value of axial SD becomes clearly larger. From Figure 3(b) and (d) for the (9,0) CNT, it is clear that when thetemperature is lower than 300K, the Pt6 cluster moves onlyslightly. Higher than 300K, both axial and tangent SDshow an obvious increase. In addition, although the Pt6cluster also changes its shape at 500K, it does not moveas clearly as when on the (5,5) CNT. Figure 4(a)–(b) and(c)–(d) shows the SD distributions for the Pt9 cluster onthe (5,5) and (9,0) CNTs, respectively. For the (5,5) CNT,though both the axial and tangent SD distributions are

small, the axial shown in Figure 4(a) is larger than thetangent shown in Figure 4(c). The low tangent and axialSD values (<50Å2) in Figure 4(a)–(d) indicate that thePt9 cluster does not move significantly on either the (5,5)or (9,0) CNT due to its shape. The Pt9 cluster is a tent-likestructure with a broad base, resulting in a stronger interac-tion between the Pt9 cluster and the CNTs.

Figure 5(a)–(b) and (c)–(d) shows the SD distributions forthe Pt13 cluster on the (5,5) and (9,0) CNTs, respectively.The shape of the Pt13 cluster is spherical. All of the axialand tangential values in Figure 5(a)–(d) are lower than50Å2, which means that the Pt13 cluster only changes its po-sition very slightly and remains near its original position. Ageneral comparison of the dynamical behaviors of Pt clusterson the (5,5) and (9,0) CNTs shows that at temperatures lowerthan 300K, their movements are smaller, as demonstrated bylower axial and tangent SD values. At higher temperaturesthan 300K, Pt clusters move more significantly. In addition,Pt clusters on the (5,5) CNT greatly prefer to move in the

(a) (b)

(d)(c)




axial direction. In contrast, Pt clusters prefer to move alongthe tangent direction on the (9,0) CNT when compared tothe (5,5) CNT, but it is not possible to determine the directionof their tangent movement.

3. CONCLUSIONS

This study investigates the dynamical behavior of differentsize Pt clusters on different CNTs and finds that the clustersshow different movement behaviors on (5,5) and (9,0) CNTs.At temperatures lower than 300K, Pt cluster movement is notsignificant. Higher than 300K, the SD distribution shows anobvious increase in movement. In addition, the Pt4 and Pt6clusters show that they can easily diffuse along the tangentdirection of the zigzag CNT. With an increase in cluster size,it is difficult for the Pt cluster to diffuse on the CNT. Thissuggests that Pt13 is the critical cluster size for the stableadsorption of a Pt cluster on the CNT.

ACKNOWLEDGEMENTS

The authors would like to thank the National ScienceCouncil of Taiwan, under Grant No. NSC101-2628-E-110-003-MY3, and National Center for High-performanceComputing for supporting this study.

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dynamical behavior of pt clusters on (5,5) and (9,0) single wall carbon nanotubes

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