Compressive and tensile properties of Ar filled carbon nano-peapods

Materials Letters 61 (2007) 527 – 530 www.elsevier.com/locate/matlet

Compressive and tensile properties of Ar filled carbon nano-peapods Haijun Shen School of Aeronautics and Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing, China, 210016 Received 1 December 2005; accepted 4 May 2006 Available online 30 May 2006

Abstract In order to investigate the compressive and tensile mechanical properties of the carbon nano-peapods filled with Ar atoms outside, inside, or both outside and inside their C60 fullerenes, the MD (molecular dynamics) method was used to simulate the compression and tension of the carbon peapods. According to the calculated results the effects of the filled pattern and amount of Ar atom on the mechanical properties of the carbon peapods were discussed systematically. It is shown that (1) the Ar filled nano-peapods have better compressive properties than the unfilled one, and the more Ar atoms are filled, the better the compressive properties are, (2) when the same amount of Ar atoms are filled, the carbon peapod with Ar atoms both outside and inside its C60 fullerenes has the best compressive properties and the one with Ar atoms only outside has the worst compressive properties, and (3) the filled pattern and amount of Ar atom seem to have little effect on the tensile properties of the carbon peapods. © 2006 Elsevier B.V. All rights reserved. Keywords: Ar filled; Carbon nano-peapod; Molecular dynamics; Compression; Tension

1. Introduction Due to their unusual electronic, mechanical and optical properties, carbon nanotubes and fullerenes have been attracting people's attention from the fields of physics, chemistry and material [1–3]. Recently a novel functional material so-called carbon nano-peapod, i.e. the carbon nanotube filled with C60 fullerenes, is also found [4,5]. It is shown that, in the carbon peapod, the C60 fullerenes are dispersed and have only nonbonded interaction to each other [5,6]. Generally carbon tube and peapod form in the experimental environment of inert gas, therefore it is very possible that the carbon tube and peapod are filled with some inert gas atoms [7]. Up to now the mechanical properties of carbon peapod as well as inert gas filled carbon tube have been reported [8]. However, studies on the mechanical properties of the inert gas filled carbon peapod are not yet found as far as this author knows. Considering the above reason, in the present paper the classical MD (molecular dynamics) method is used to simulate the compression and tension of the carbon peapods filled with Ar atoms outside, inside, or both outside and inside their C60 E-mail address: [email protected]. 0167-577X/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2006.05.003

fullerenes. Further, according to the computed results, the compressive and tensile properties of the carbon peapods are compared and analyzed. Some conclusions in this paper are valuable for people to further understand the mechanical properties of carbon nano-peapods. 2. Models and method Fig. 1 presents six carbon nano-peapods to be investigated. They all have four C60 fullerenes and Ar atoms are filled in the peapods with different patterns and amounts. In Fig. 1 the homocentric circles are used to indicate the Ar atoms. All the external walls of the peapods are the (10,10) carbon tube with the initial length l0 about 3.68 nm and the diameter about 1.50 nm. The C60 fullerenes have a diameter about 0.73 nm and a space about 1.05 nm. The gap between the carbon tube and the C60 is about 0.37 nm. The (10,10) carbon tube is generated by our “nanotube generator”, a software module developed in Reference [9]. All the modeling of the C60 fullerenes, the “assembling” of the Ar filled carbon peapod, and the geometry optimization are accomplished in the quantum-chemical software of HyperChem7® [10]. The optimization uses the MM+ force field as well as the Fletcher's conjugate gradient method

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H. Shen / Materials Letters 61 (2007) 527–530

Fig. 1. The carbon nano-peapods. (a) Unfilled, (b) filled with 2 Ar atoms between any adjacent C60 fullerenes, (c) filled with 4 Ar atoms between any adjacent C60, (d) filled with 1 Ar atom inside each C60, (e) filled with 2 Ar atoms inside each C60, and (f) filled with 1 Ar atom inside each C60 and 1 atom between any adjacent C60.

[11]. The optimizations show that, despite the gap of 0.37 nm between the carbon tube and the C60 fullerenes, due to high potential wall at the gap the Ar atoms outside the C60 are tightly imprisoned between the adjacent C60 fullerenes. The classical MD method is used to simulate the compression and tension of the Ar filled carbon peapods. In the simulations, the carbon atoms in the left frames of Fig. 1 are fixed, and the ones in the right frames are compressed or tensioned horizontally. The interaction between the bonded carbon atoms in the (10,10) carbon and the C60 fullerenes uses the bond-order concept based Tersoff potential [12,13]: XX U¼ f c ½aij d Er ðrij Þ−bij d Ea ðrij Þ ð1Þ i

jNi

with

many-body function of the positions of the atoms i, j and k. It has the form of bij ¼ vij ð1 þ bni i d nniji Þ

mi

2

ni

ð3Þ

with nij ¼

X

fc ðrik Þxik d gðhijk Þ

kpi; j

gðhijk Þ ¼ 1 þ

c2i c2i − 2 2 di di þ ðhi þ coshijk Þ2 −1

aij ¼ eij ð1 þ bni i d sniji Þ2ni X sij ¼ f c ðrij Þdik d gðhijk Þ kpi; j

Er ðrij Þ ¼ Aij d exp ð−kij d rij Þ kij ¼ Ea ðrij Þ ¼ Bij d exp ð−lij d rij Þ 8 1 > > <1



rij −Rij fc ðrij Þ ¼ 1 þ cos p > 2 Sij −Rij > : 0

ki þ kj 2

li þ lj 2 pffiffiffiffiffiffiffiffiffi Aij ¼ Ai Aj

lij ¼ 

rij bRij Rij brij bSij

ð2Þ

Sij brij

bij is the many-body order parameter describing how the bondformation energy is affected by the local atomic arrangement due to the presence of other neighbouring atoms (the k atoms). It is a

Bij ¼

pffiffiffiffiffiffiffiffiffi Bi Bj

ð4Þ ð5Þ ð6Þ ð7Þ

where, rij is the distance of the ith and jth carbon atom, θijk is the angle between rij and rjk, fc(rij) is a truncation function. The correlative constants with the i–j–k atomic system Ai = 1393.60 eV,

H. Shen / Materials Letters 61 (2007) 527–530

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Fig. 4. The compressive F–ε curves of the nano-peapods with different filled amounts of Ar atom inside each C60.

Fig. 2. The carbon nano-peapod under compressive strain ε. (a) ε = 3.2%, (b) ε = 4.2%, and (c) ε = 6.4%.

Bi = 346.74 eV, λi = 3.4879 Å− 1, μi = 2.2119 Å− 1, εij = 0, χij = 1.00, βi = 1.5724E−7, ni = 0.72751, mi = 1, δik = 0, ωik = 1, ci = 38,049.0, di = 4.3840, hi = −0.57058, Rij = 1.8 Å, and Sij = 2.1 Å [12]. The non-bonded Van der Waals interaction between the C60 fullerenes, between the C60 fullerenes and carbon tube, between the Ar atoms, and between the Ar and carbon atoms uses the L– J pair-potential [14]:

All the MD simulations take the time step of Δt = 1 fs, the Verlet Leapfrog integration algorithm [16], and the constant temperature T = 300 K. 3. Results and discussion 3.1. The compressive properties of the Ar filled peapods

where, rij is the distance between the corresponding atoms, the constants of εxy, and σxy take the values in References [14,15], i.e. εC–C = 0.440 kJ, σC–C = 0.385 nm, εAr–Ar = 1.030 kJ, σAr–Ar = 0.336 nm, εC–Ar = 0.735 kJ, and σC–Ar = 0.3616 nm.

By MD simulation, Fig. 2 presents the compressive deformation of the peapod with 2 Ar atoms between any adjacent C60. The configurations of the other peapods under compression are similar to the case of Fig. 2, and are not shown here. Fig. 3 presents the compressive force–strain curves (the F–ε curves) of the peapods with zero, 2 or 4 Ar atoms between any adjacent C60. Fig. 4 shows the compressive F–ε curves of the ones with zero, 1 or 2 Ar atoms inside each C60. Fig. 5 shows the compressive F–ε curves of three peapods with the same filled amount but different filled patterns of Ar atoms. They are the peapod with 2 Ar atoms between any adjacent C60 shown in Fig. 1 (b), with 2 Ar atoms inside each C60 shown in Fig. 1 (e), and with 1 Ar atom inside each C60 and 1 Ar atom between any adjacent C60 shown in Fig. 1 (f), respectively.

Fig. 3. The compressive F–ε curves of the nano-peapods with different filled amounts of Ar atom between any adjacent C60.

Fig. 5. The compressive F–ε curves of the nano-peapods with the same filled amount but different filled patterns of Ar atom.

U ðrij Þ ¼ 4exy ½ðrxy =rij Þ12 −ðrxy =rij Þ6 

ð8Þ

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H. Shen / Materials Letters 61 (2007) 527–530

4. Conclusions By the MD method, the compression and tension of six Ar filled carbon peapods with different filled amounts and filled patterns are simulated. Further, according to the calculated results, their compressive and tensile mechanical properties are compared and discussed. The results show that the peapod filled with more Ar atoms has better compressive properties, that, among the three peapods with different Ar filled patterns but same filled amount, the one filled both inside and outside the C60 has the best compressive properties, and the one filled only outside has the worst, and that the filled pattern and amount of Ar atom have only little effect on the tensile properties of the carbon peapods. Acknowledgment Fig. 6. The tensile F–ε curves of the carbon nano-peapods.

From Fig. 2, it can be found that: (1) When the compressive strain is small, for example at ε = 3.2%, the C60 fullerenes can still retain the axis of the (10,10) carbon tube. (2) When the compressive strain increases to about 4.2%, the two middle C60 fullerenes begin to obviously depart the axis, which is the sign for local buckling of the carbon peapod. However, the Ar atoms imprisoned between the C60 fullerenes can not traverse the gap between the C60 and carbon tube yet. (3) When the strain ε further increases to about 6.4%, the local buckling appears on the carbon-tube wall. At the same time, the local gap between the C60 and carbon tube increases markedly and the Ar atoms are able to cross the gap easily. From Figs. 3–5, it is found that: (1) With the increase of the strain ε, the compressive force F of all the peapods increases. But the F increases very slightly after ε N 4.5%. In fact, the MD simulations show that after ε N 4.5% all the peapods begin to locally cave in on their tube wall. This implies that the peapods have the flexure strain about 4.5%. (2) Under the same strain ε, the more the Ar atoms are filled, the larger the compressive force F of the peapods with Ar atoms inside or outside the C60 is, i.e. the more the Ar atoms are, the better the compressive properties of the peapods are. (3) In spite of the same filled amount, under the same strain ε the peapod with Ar atoms both inside and outside the C60 has the largest F and the peapod with Ar atoms only outside has the smallest. That is, the peapod with Ar atoms both inside and outside the C60 has the best compressive mechanical properties and the one only outside has the worst. 3.2. The tensile properties of the Ar filled carbon peapods Fig. 6 presents the tensile F–ε curves of all the peapods in Fig. 1. From Fig. 6, it can be found that the F–ε curves of all the peapods have only little difference at the range of ε b 20%. This means that the carbon peapods don't have obvious difference in the tensile properties. In fact, after ε N 20%, all the peapods have begun to fracture. In addition, from Fig. 6 as well as Figs. 3 and 4, it can also be seen that the tensile limit of the peapods is about 150 nN, much larger than their compressive limit of 40–45 nN.

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