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Carbon 103 (2016) 242e254

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Carbon

journal homepage: www.elsevier .com/locate /carbon

Energy dissipation capability and impact response of carbon nanotubebuckypaper: A coarse-grained molecular dynamics study

Heng Chen a, b, Liuyang Zhang b, Jinbao Chen a, Matthew Becton b, Xianqiao Wang b, *,Hong Nie a, **

a College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, 210016, Chinab College of Engineering, University of Georgia, Athens, GA, 30602, USA

a r t i c l e i n f o

Article history:Received 14 November 2015Received in revised form2 March 2016Accepted 7 March 2016Available online 10 March 2016

* Corresponding author.** Corresponding author.

E-mail addresses: xqwang@uga.edu (X. Wang), hn

http://dx.doi.org/10.1016/j.carbon.2016.03.0200008-6223/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

Carbon nanotube (CNT) buckypaper, a randomly non-woven fibrous film structure, has enjoyed itspopularity in the sensor, actuator, filtration, and distillation devices owing to its exceptional mechanicaland electrical properties. However, there is no report aimed at unraveling the fundamental mechanism ofits energy-absorption capability under high-velocity impact despite its extraordinary frequency- andtemperature-invariant viscoelastic properties. To bridge this gap, here coarse-grained molecular dy-namics simulations are implemented to investigate effects of the external impact energy, the density ofthe buckypaper, and the length of individual CNTs on energy dissipation capability and dynamicresponse of the buckypaper under high-velocity impacts. Simulation results indicate that within itsdeformation limit the buckypaper possesses extremely high kinetic energy dissipation efficiency. Thecritical impact energy related to the deformation limit of the buckypaper tightly depends on the impactvelocity since the same impact energy with a larger impact velocity yields less compression. The energydissipation capability and impact response of the buckypaper are demonstrated to be independent of thelength of individual SWCNTs. Overall, owing to the remarkable energy dissipation capability and flexi-bility of the buckypaper, it can be regarded as a promising candidate for energy dissipation.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Energy dissipation materials and structures play a vital role inthe safety of structures and humans subjected to a crash event [1].Traditionally metals have been widely used for the energy ab-sorption devices, relying on its structural failure and plastic defor-mation to mitigate impact energy [2,3]. Cellular forms includingfoams, honeycombs, and sandwich structures also perform excel-lently in mitigating dynamic loadings due to bulking and collapsemechanisms [4e11]. In addition, internal damping caused by theunique internal structure of composites exhibits favorable perfor-mance for the control of vibration due to impact [12,13].

In order to meet the ever-increasing high-demand on light-weight, small volume, and high energy dissipation efficiency sys-tems, nanostructured materials have begun attracting researchers'interest for their excellent mechanical properties such as enhanced

ie@nuaa.edu.cn (H. Nie).

strength-to-weight, surface-to-volume, and stiffness-to-weightratios. For example, nanocomposites with reinforcement fibers orparticles possess significantly enhanced property such as volumefraction compared with the corresponding composites with macro-scale fibers or particles [14,15]. Especially, well-designed polymer-based nanomaterials have superior impact behavior and muchhigher energy dissipation density than conventional materials dueto their high impact toughness [16]. Nanoporous materials alsohave been proven to possess fantastic energy dissipation capabil-ities owing to their small pore size, high porosity, and high networkstrength [17e19]. Han at el. found that nanoporous silica had en-ergy dissipation density on the order of 300 J/g, much larger thanthat of conventional materials, and the dissipation mechanism isthe non-uniform collapse of nanopores and subsequent yielding viapermanent plastic deformations [20]. Nanoporous systems con-sisting of non-wetting liquid and nanoporous particles show en-ergy dissipation density as high as ~ 18 J/cm3 [21e25].

Fullerenes such as carbon nanotubes (CNTs) and buckyballs havebeen demonstrated to have unprecedented mechanical propertiesand energy absorption capability owing to significantly high

Table 1Potential parameters for the coarse-grained model of (5,5) SWCNT.

Parameters (5,5) SWCNT

Equilibrium bead distance, r0 (Å) 10Stretching constant, kb (kcal/(mol Å2)) 1,000Equilibrium angle, q0 (�) 180Bending constant, ka (kcal/(mol rad2)) 14,300vdW distance, s (Å) 9.35vdW energy, ε (kcal/mol) 15.10

H. Chen et al. / Carbon 103 (2016) 242e254 243

strength and stiffness, large surface area, and light weight [26e33].For example, CNTs can exhibit a Young's modulus of over 1 TPa andtensile strength above 100 GPa [34,35]. Xu et al. [36e38] found thatbuckyballs with larger size tend to yield non-recoverable defor-mation which assists energy dissipation thanks to the uniquedeformation characteristic dependent on the buckyball size underdynamic loadings. An energy absorption system of buckyballsconfined by a CNT was put forward and found to have remarkableenergy absorption density of 2000 J/g [39]. CNT-based nano-composites, such as aligned CNT/epoxy nanocomposites, haveimproved properties beneficial for energy dissipation by increasingCNT volume fraction and CNT aspect ratio [40e43]. AssembledCNTs with controlled orientation and configurations, such as CNTfoams and three-dimensional sponge-array architectures, haveexhibited unprecedented mechanical properties and energy dissi-pation capability [44e46].

Recently, both experimental and computational results revealthat the long-ranged van der Waals interactions between CNTsenable them to aggregate and thus form CNT networks [47e49]called ‘buckypaper’. Buckypaper has been verified to showintriguing mechanical and thermal properties attributed to theexcellent properties of individual CNTs, enabling it to be one of themost promising nanomaterials [50e53]. Experimental resultsindicate that the Young's modulus of buckypapers with differentdensities and CNT diameters can be tuned from 0.2 GPa to 3.1 GPa[54,55]. Li [56] found that entanglement and bundling mechanismsplay an important role in the mechanical properties of bucky-papers. Xie [57] found that the microstructures of buckypapersundergo a remarkable evolution under mechanical loadings. Bothexperimental and computational results reveal that buckypapersexhibit frequency- and temperature-invariant viscoelastic proper-ties from �196 to 1000 �C [58,59] and a zipping-unzipping mech-anism is observed under cyclic loadings [60]. Buckypapers usuallyfeature low densities of 0.05�0.4 g/cm3 and high porosities of0.8�0.9 [61], and the pore size of SWCNT (diameter 0.8�1.2 nmwith length 100�1000 nm) buckypaper was reported around10 nm [62]. All these results indicate that buckypapers may possessfavorable properties for energy dissipation, but few studies havefocused on this application. Therefore, this paper will investigatethe impact behavior and energy dissipation capability of bucky-papers by utilizing coarse-grained molecular dynamics simula-tions, in terms of effects of impact energy, density of buckypapers,and length of individual SWCNTs as well as the evolution of thedeformation. The results enable a holistic picture of impact per-formance of buckypapers and highlight a promising candidate forenergy dissipation under extreme conditions.

2. Model and computational methods

2.1. Coarse-grained model for CNT

As full atomistic molecular dynamics simulations are compu-tationally expensive for long interacted CNT networks, in order toenhance computational efficiency it calls for mesoscale modeling[60,63]. Here a coarse-grained molecular dynamics model isapplied to effectively express the mechanical properties of CNTs[55] over relatively large length scales. Our coarse-grained molec-ular dynamics (CGMD) simulations are performed on the opensource platform LAMMPS [64]. In CGMD model of CNT network,each CNT is simplified as a multi-bead chain. For a certain chain,stretching and bending properties are reflected through bondsbetween two adjacent beads and angles formed by three successivebeads, respectively. Long-ranged van der Waals (vdW) interactionbetween pairs of beads accounts for the inter-tube interaction.CNTs' twisting behavior, usually neglected in current papers about

computational model of buckypaper, can make marginal effect onthe absolute value of our results. And the corrugation effect resul-ted from the nature of the bead-spring model when CNTs slideagainst each other is regardless in this paper. Since this CG modeland its relevant force field regardless of the corrugation effect havebeen proved by many researchers to successfully describe differentmechanical properties of the buckypaper, such as the entanglementand bundling phenomenon, the structural and mechanical prop-erties, the visco-elastic properties of the buckypaper and so on[56,58,60,65,66], the corrugated effect is assumed to be marginal.Thus, the total energy of the coarse-grained system is given by:

Etot ¼ Ebond þ Eangle þ EvdW (1)

where Ebond ¼ Pbonds

12 kbðr � r0Þ2 denotes the inter-chain stretching

energy along the axial direction, kb is the stretching constant, r isthe current bond length and r0 is the equilibrium bond length.

Eangle ¼P

angles

12 kaðq� q0Þ2 represents the bending energy, where ka

is the bending constant, and q and q0 express the current angle and

the equilibrium angle respectively. EvdW ¼ Ppairs

4ε½ðs=rÞ12 � ðs=rÞ6�,

a pairwise 12-6 Lennard-Jones potential, depicts the van der Waalsinteraction with ε describing the depth of the potential well and s

describing the equilibrium distance where the inter-bead potentialis zero. These six parameters kb, r0, ka, q0, ε and s can be derivedfrom a full atomistic computational experiments using the Tersoffpotential or ReaxFF potential [67,68]. According to Buehler andCranford's research [69,70], r0, q0, and s can be determined byequilibrium conditions while kb, ka and ε can be obtained by energyconservation calculations. In detail, uniaxial tension tests of a singleCNT can be applied to describe the stretching behavior of CNTs andcalculate the Young's modulus E and then the equivalent kb equal toEA/r0 (A is the cross-section area of the CNT) can be obtained.Bending tests can determine the bending behavior and bendingstiffness EI (I is the bending moment of inertia) of the CNT and thuska ¼ 3EI/2b0 can be gained. Simulations of an atomistic assembly oftwo CNTs can calculate the equilibrium distance D between themand the adhesive strength b, and thereby ε and s can be acquired viaε ¼ br0 and s ¼ D/26 respectively.

In this work, a buckypaper is modeled as if formed by (5, 5)SWCNTs and the potential parameters of the coarse-grained modelare depicted in Table 1. The parameters obtained from the fullatomistic simulation have been validated by tensile test, self-folding of CNTs, self-assembly process, and behavior of CNT bun-dles [55,69,70]. The tensile stressestrain relationship reported byBuehler is found to agree well with the experimental results re-ported by Peng [35]. The cutoff distance of the long-ranged van derWaals interactions is set to be 9.35 nm. Based on the mass per unitlength of SWCNT and the equilibrium bead distance, the mass ofeach bead is given by 1,953.23 g/mol. For all the simulations results,the total length of all the SWCNTs in the buckypaper is fixed to be51,200 nm. In terms of effects of impact energy and density, thebuckypaper consists of 512 SWCNTs with individual length of

H. Chen et al. / Carbon 103 (2016) 242e254244

100 nm. In order to investigate the effects of SWCNT length,SWCNTs with different lengths 100 nm, 149 nm, 237 nm, 410 nm,and 800 nm are used to construct five types of buckypapersrespectively, keeping the density and total SWCNTs lengthunchanged.

2.2. Configurations of buckypaper

In order to ensure the randomness and isotropy, the randomwalk method is adopted to generate the buckypaper. Toward thisend, a series of points with the number denoted as np are uniformlydistributed in an orthogonal cell by setting a certain number ofseeds (nx,ny, nz) along the three axes respectively. Taking each pointas the initial bead, a SWCNT grows to the next bead via a randombond vector with the length as the equilibrium bead distance 10 Å.Then an overlap check is conducted to avoid the overlap of beads.That is, if the distance between this bead and its nearest bead is lessthan a specific distance (2 Å), the new generated position isconsidered to be occupied by another bead and therefore thisSWCNT will return one step to the last position and then proceedvia a new random vector. This check process is repeated until thenew position is not occupied and then the new bead is generated.Once the distance of the random walk equals the SWCNT lengthrequired for investigation, the walk stops and the current bead isthe terminal bead of the SWCNT. It can be seen that the number ofpoints (np¼ nx� ny � nz) and the walk steps determine the numberof SWCNTs and the length of each SWCNT, respectively. In thiswork, all the SWCNTs in a single cell have the same length. In termsof density effects, the density of buckypaper is changed by tuningthe distance between the adjacent seeds along each axis and thustuning the density of distributed points. After the structure isequilibrated, the density varies from 40.67 kg/m3 to 107.60 kg/m3

which closely matches the value obtained from experiments [59]and simulations [58].

Afterwards the initial buckypaper (Fig. 1(a)) is relaxed based onan isothermal-isobaric (NPT) ensemble to perform the free energyminimization. During the equilibrium process (Fig. 1(a) e (b)), thetemperature and the pressure are driven to a constant 300 K and1 atm respectively. The SWCNTs appear to be entangled andaggregated due to the van der Waals interactions. Two dynamicstandard 12-6 L-J walls are added outside both the upper and lowersurfaces and always keep 10 Å away from the buckypaper, for theconvenience of adding two rigid plates needed for the followingimpact simulations. During the relaxation, certain SWCNTs begin toattach each other and zip together (Fig. 1(d)e(e)), which is alsoobserved in Refs. [58,60]. The total energy of the buckypaper dropsrapidly in the first 3 ns and then achieves an equilibrium valueslowly in the subsequent 4 ns. For validation of the buckypapermodel, MD simulations for static compression and shear tests areperformed and it is found that both the stressestrain curve and theelastic modulus (Figs. S3eS5) agree well with that provided in Liet al. [56]. The Young's modulus obtained in our simulations isaround 0.01�0.1 GPa, slightly lower than that reported by experi-ments [71,72] around 0.2�12 GPa because of the lower density ofbuckypaper. Hence, the model of buckypaper used in this paper canbe considered to be reasonable.

As mentioned before, after the fully relaxation of buckypaperthe L-J walls are removed and two rigid plates with the same lengthand width are added to the system. As is depicted in Fig. 1(c), oneplate (impactor) is right above the buckypaper and 20 Å from itsupper surface while the other one (receiver) is fixed under thebuckypaper and 20 Å from its lower surface. Impact energy (Eimpact)is achieved by endowing thewhole impactor with an initial velocity(v0) along the z direction. A microcanonical ensemble (NVE) isemployed so that the total energy of the system remains

unchanged. Periodic boundary conditions are remained in both xand y dimensions while aperiodic conditions are applied to the zdimension. Timestep for all the simulations is 10 fs.

3. Results and discussions

3.1. Effects of impact energy

In order to understand the effect of impact energy on the energydissipation capability and impact response of the buckypaper, aseries of impact energies ranging from E0 to 10E0 (E0 ¼ 1.5 fJ) areapplied to impact the buckypaper. The impact energy can be variedby either tuning the initial velocity or the mass of the impactor. Forbetter investigation of their effects, two methods, noted as FM(fixing mass and changing velocity) and FV (fixing velocity andchanging mass), respectively, are both adopted. For FV cases, theinitial velocity of the impactor is fixed as 200 m/s while the mass(m) varies from 7.5� 10�17 g to 7.5� 10�16 g. For FM cases, themassof the impactor is fixed as 3.7 � 10�17g while the initial velocityvaries from 282.8 m/s to 894.4 m/s. This velocity regime isconventionally considered as high impact speed domain, mainlyaiming at the ballistic impact related problem. By observing theanimation of the impact process in the visualization softwareOVITO [73], it is found that as the impactor goes downwards theSWCNTs in the upper irregular region start to be compressed, andthus a narrow densified region appears on top of the buckypapersystem as shown in Fig. 2(b). Due to the continuation of thecompression and the propagation of the stress wave induced by theimpactor, it causes the extension of the densification region in theupper part of the buckypaper, as shown in Fig. 2(c). It is also noticedthat SWCNTs in the lower part of the buckypaper are not affected bythe loading at the early stage of impact. Afterwards the densifica-tion region moves downwards and transfers the straining to therest of the buckypaper structure gradually, thus more SWCNTs getinvolved into densification. Finally those SWCNTs in the lowest partare exposed to impact and a flat surface is formed as a result of thefixed receiver. As is demonstrated in Fig. 2(d), the region near theupper and lower surfaces is denser than the middle part of thebuckypaper. It is noted that in the densifying procedure SWCNTsare detached and attached cyclically through the unzipping-zipping mechanism at these entanglement sites. As is depicted inFig. 3, the two partially attached (violet) SWCNTs in Fig. 3(a) detachin Fig. 3(b) and then combine with another (violet) CNT forming anew attachment of longer length in Fig. 3(c). Then they detach inFig. 3(d) but attach with each other again rapidly in Fig. 3(e); thisprocess is repeated frequently during the rest of the impact process.The reason is probably that the nonlinear dynamic impact behaviorof buckypaper results in the fluctuation of individual SWCNTs. Thisdetachment-attachment process enables energy dissipation,because energy is consumed when SWCNTs overcome the van derWaals interactions during the detachment process. When theimpactor velocity is damped to zero, the impactor has the largestdisplacement and the buckypaper goes to the deformationextreme. Afterwards the impactor rebounds slightly, seen inFig. 2(e) and (f). Herein, we define the rebound distance of thebuckypaper to be the displacement of the upper surface of thebuckypaper from the impactor, reaching the maximum displace-ment upon detaching from the buckypaper. It is noticed that duringthe impact process individual CNTs hardly have very large defor-mation and thus it's reasonable to make an elastic assumption ofindividual CNTs while the collective behaviors from many indi-vidual CNTs can be plastic deformation. During the impact process,the kinetic energy of the impactor is transferred to potential energy(strain energy) and thermal energy of the buckypaper resulting in atemperature increase of the buckypaper. Potential energy includes

Fig. 1. Computational cell of buckypaper for impact simulations and snapshots during the equilibrium process: (a) The initial configuration of random walk. (b) Side view of therelaxed model after equilibrium process. (c) Computation cell of buckypaper with receiver and impactor. (d) and (e) Zipping and attachment behavior of some typical SWCNTsextracted from the whole model during the equilibrium process. (A colour version of this figure can be viewed online.)

Fig. 2. Deformation evolution of the buckypaper with density of 78.97 kg/m3, SWCNT length of 100 nm, impact velocity of 200 m/s, and impact energy of 15 J. (a) Initialconfiguration of the buckypaper. (b) Initial narrow densification region. (c) Straining arrives at the receiver. (d) Straining is transferred to the whole buckypaper. (e) The maximumcompression distance. (f) Rebound of the impactor. (A colour version of this figure can be viewed online.)

H. Chen et al. / Carbon 103 (2016) 242e254 245

Fig. 3. Detachment-attachment behavior of several selected SWCNTs from the (5,5) SWCNT buckypaper during the impact process, while other SWCNTs remain hidden. (a) Theoriginal state of the buckypaper. (b) Detachment. (c)New attachment. (d)Detachment. (e)Attachment again. (d)e(e) happens recurrently. (A colour version of this figure can beviewed online.)

H. Chen et al. / Carbon 103 (2016) 242e254246

vdW pairwise energy, bond energy, and angle energy. As shown inFig. S1, the vdW pairwise energy decreases during the impactprocess, resulting in a stronger vdW interactions than the initialone. However, both bond energy and angle energy increase duringthe impact process due to the compression deformation.

To better understand the deformation mechanism of thebuckypaper in the impact process, the upper contact force (Fi) be-tween the impactor and the buckypaper and the lower contactforce (Fr) between the buckypaper and the receiver are monitored.

Fig. 4. Contact forces between the impactor and buckypaper (Fi) and between thebuckypaper and the receiver (Fr) versus time under impact energy 3E0 and 6E0 for FVand FM cases, respectively. (A colour version of this figure can be viewed online.)

According to the comparison between them depicted in Fig. 4, it isfound that the upper contact force increases quickly at the earlystage of compression since more and more SWCNTs are involved inresisting the compression, and then the upper contact force reachesa local peak with the buckypaper morphology in Fig. 2(b). Duringthis procedure the buckypaper remains relaxed and unaffected,except for a small portion on the top. As the impactor goes down,the densification region forms to resist further compression and astress wave is introduced to its neighboring part under theimpactor. The densification region is not being compressed to itslimit and the upper contact force decreases until the bottom part ofthe buckypaper receives the compression signal (seen in Fig. 2(c)).Supported by the receiver, the lower surface of the buckypaperstarts flat and the interaction between the buckypaper and thereceiver becomes apparent. As the region near the lower surface ofthe buckypaper becomes more and more densified, the lowercontact force increases and then surpasses the upper contact force.It has to be noted that the first peak value of the lower contact forceis greatly less than that of the upper contact force, which is becausethat the power of the stress wave is attenuated considerably duringthe propagation process. When the impactor reaches its maximumdisplacement with apparent pores still left in the buckypaper fromthe side view, the buckypaper is regarded to still have sufficientroom for deformation, as illustrated in the snapshot of Fig. 5(D).Both contact forces fluctuate slightly until the rebound of theimpactor, such as the case of FV at 3E0 and FM at both 3E0 and 6E0 inFig. 4. Otherwise if the buckypaper is so tight that no pore isobserved in the buckypaper from the side view, the buckypaper isregarded to reach its effective deformation limitation as depicted inthe snapshot of Fig. 5(C), resulting in a significant increase of thecompression stiffness. As the buckypaper becomes denser, thecompression stiffness gets larger. Therefore, as the compressioncontinues both contact forces increase and tend to reach the peaksat the maximum compression followed by the rebound of theimpactor. Accompanied with the rebound of the impactor bothcontact forces in all cases keep decreasing and become zero uponthe detachment of the impactor from the buckypaper. By compar-ison of the contact forces in FV and FM cases under the same impactenergy, at the early stage the upper force in FM case grows more

Fig. 5. Contact force between the impactor and buckypaper versus displacement of theimpactor at 3E0, 6E0, and 8E0 for FV and FM cases respectively. Inserts show themorphologies under impact energy 8E0 at the displacement of 60 nm and maximumdisplacement respectively. The labels of the inserts have the same color as the corre-sponding curves. (A colour version of this figure can be viewed online.)

0 2 4 6 8 10 12 14 160

0.5

1

1.5

2

2.5

Impact energy (fJ)

Max

imum

con

tact

forc

e (

N)

Fixed v, FiFixed v, FrFixed m, FiFixed m, Fr

Fig. 6. Maximum upper and lower contact forces versus impact energy for both FV andFM cases. (A colour version of this figure can be viewed online.)

0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Impact energy (fJ)

Dis

plac

emen

t of t

he im

pact

or (n

m)

Fixed v, rebound distanceFixed v, maximum displacementFixed m, rebound distanceFixed m, maximum displacement

Fig. 7. Maximum displacement of the impactor and rebound distance versus impactenergy for FV and FM cases. Inserts show the morphologies of the buckypaper at the

H. Chen et al. / Carbon 103 (2016) 242e254 247

rapidly to a larger peak than that in FV case, because the largerinitial velocity of the impactor in FM case results in a shorterpropagation distance of the straining and thus a larger resistantstiffness. As follows, this force in FM case decreases more rapidly toa smaller value than that in FV case. In addition, the amplitude ofthe lower contact force in FM case is lower than that in FV casesince more energy is dissipated before the straining arrives at thereceiver.

Based on the work-kinetic energy relationship, the work doneby the impactor equals to the transferred kinetic energy of theimpactor and can be represented by the area surrounded by theupper contact force curve and the horizontal axis in Fig. 5.Comparing Fig. 4 with Fig. 5, we notice that at the same displace-ment of the impactor, more impact energy is attenuated in the FMcase than that in the FV casewith the same impact energy, resultingin a shorter compression distance in the FM cases than in the FVcases. Also in the FM cases, with the increment of the impact energyfrom 3E0 to 8E0, more energy dissipation arises at the samedisplacement of the impactor, whereas in the FV cases the energydissipation has no significant difference. The reason is that theimpact velocity of the impactor plays a dominant role in thedeformation evolution of the buckypaper. For a larger velocity, theimpactor takes a shorter time to reach the same displacement andthe propagation distance of the straining is shorter, leading to asmaller yet more compact densification region. For example, thesnapshots (A) and (B) in Fig. 5 show the morphologies of thebuckypaper under the impact energy 8E0 for the FV and FM casesrespectively when the displacement of the impactor is 60 nm. It canbe seen that the region near the lower surface of the buckypaper in(A) has been compressed while that of (B) is not. Additionally, thetop region (B) is more densified than that in (A). Snapshots (C) and(D) represent their morphologies at the maximum compressiondistance. The buckypaper in (C) has completely deformed, inresponse to the rapid increment of the contact force as it ap-proaches the maximum compression. Yet, the buckypaper in (D)has superior deformation ability, and thus at this stage the forceremains small.

Therefore, as depicted in Fig. 6, for a lower impact energy thatenables the buckypaper to have adequate deformation capability,the maximum upper contact force appears at the early stage of theimpact and increases slowly along with the impact energy. Inaddition, the upper contact force for the FM case is higher than thatfor the FV case. For a large impact energy that causes the bucky-paper to compress beyond its deformation limit, the maximumforce occurs at the maximum compression. With the growth of theimpact energy, the force increases rapidly because of the abruptincrement of the compression stiffness, and after a certain impactenergy it exceeds that of the FM casewhich increases steadily. Fig. 6also shows that both contact forces in the FV case are very close toeach other while the lower contact force is noticeably smaller thanthe upper contact force in the FM case. The difference for bothforces in the FM cases becomes pronounced with the growth of the

maximum compression distance. (A colour version of this figure can be viewed online.)

H. Chen et al. / Carbon 103 (2016) 242e254248

impact energy. The results indicate that a larger impact velocitymeans that more energy is attenuated before being transmitted tothe receiver.

The relationship between the maximum displacement of theimpactor and the impact energy is described in Fig. 7. With theincrement of the impact energy, the rebound distance of thebuckypaper stays approximately constant in both FM and FV cases,and is always in the range of 15 nm to 20 nm. The maximumdisplacement of the impactor varies widely with different impactenergies. For FV cases, it increases from 43 nm to 117 nmwhile theimpact energy rises from E0 to 6E0. Then it increases steadilybecause of the deformation limit of the buckypaper. For FM cases,with the impact energy varying from E0 to 10E0, it keeps increasingfrom 33 nm to 101 nm. The pattern of the curve indicates that itcontinues to increase if larger impact energy is applied due to thebuckypaper's superior deformation capability. With the growth ofthe impact energy the difference of the initial impactor velocitybetween FV and FM cases under the same impact energy becomesapparent. Since less compression is needed for a larger initialimpactor velocity under the same impact energy, the maximumdisplacement of the impactor for FV case is always larger than thatfor FM case and the difference increases with the growth of theimpact energy from E0 to 6E0. Then with the continued incrementof the impact energy this difference narrows because the bucky-paper in FV case reaches its deformation limit whereas thebuckypaper in FM cases still has deformation capability left.

The difference between the initial kinetic energy of the impactor(Einitial) and the final kinetic energy after detachment (Efinal) isdefined as energy dissipation of the impactor. Based on the prin-ciple of energy conservation, the energy dissipation of the impactorequals to the energy absorption by the buckypaper. That is, thedissipated kinetic energy of the impactor is transformed into thestrain energy induced by the deformation and thermal energyinduced by the frictional sliding between CNTs and plastic defor-mation. A larger impact velocity is favorable to introduce moresliding between CNTs thus creating more thermal energy, whichexplains the phenomenon that less compression distance is neededfor the FM cases under the same impact energy from the energeticstandpoint. According to Fig. 8, the increase of the linear center-of-mass kinetic energy of the buckypaper due to the impact is very

0 2 4 6 8 10 12 14 1680

85

90

95

100

Impact energy (fJ)

Ener

gy d

issi

patio

n ef

ficie

ncy

(%)

0 2 4 6 8 10 12 14 160

4

8

12

16

Ener

gy d

issi

patio

n (fJ

)

Energy dissipation efficiency, FVEnergy dissipation efficiency, FMEnergy dissipation, FVEnergy dissipation, FMIncreased mass-of-center kinetic energy, FVIncreased mass-of-center kinetic energy, FM

Fig. 8. Energy dissipation efficiency and energy dissipation versus impact energy forFV and FM cases. (A colour version of this figure can be viewed online.)

tiny in both FM and FV cases so that the increased kinetic energy ofthe buckypaper can be regarded as almost completely transformedinto thermal energy. In the FM cases the energy dissipation keepsincreasing nearly linearly as the impact energy rises from E0 to 10E0.Whereas in the FV cases this linear trend remains only from E0 to6E0 because the buckypaper deformation becomes saturated at theimpact energy 6E0. Slight squeezing deformation and sliding be-tween CNTs still exist in a saturated buckypaper subjected toimpact, therefore for impact energy larger than 6E0 the energyabsorption still increases with a larger impact energy, but the rateof increase lessens at a higher impact energy since the stiffeningbuckypaper at the final stage of impact attenuates energy absorp-tion capability. It is worthwhile to mention that the slope of thelinear increment stage in the FM curve is higher than that in the FVcurve. That means, more impact energy is absorbed by the bucky-paper in the FM case than in the FV case even under the sameimpact energy, owing to the less recoverable deformation of thebuckypaper in the FM cases. Based on the ratio of the energydissipation to the initial impact energy, the energy dissipation ef-ficiency as interpreted in Fig. 8 can be acquired by theformula (Einitial�Efinal)/Einitial. It is found that the buckypaper showsremarkable energy dissipation efficiency for a specific range ofimpact energy. For the FV cases, with the growth of the impactenergy the energy dissipation efficiency is always up to about 96.5%before the deformation of the buckypaper is oversaturated, fol-lowed by a fast decline of the efficiency corresponding to thenonlinear increase of the energy absorption. For the FM cases, theenergy dissipation efficiency at the impact energy E0 is similar tothat of the FV case because of the similar impact velocities. As theimpact energy increases to 3E0, the efficiency improves to 99.52%and then with successive growth of the impact energy the effi-ciency remains rising slowly to 100%. This finding indicates that theincrease of the energy absorption for FM cases is not strictly linear.In fact, the increased rate of energy absorption is improved slightlywith the increment of the impact energy. The reason is that a largerimpact velocity causes more sliding between CNTs and thus gen-erates a higher ratio of thermal energy to the total dissipation en-ergy, leading to a relatively lower ratio of recoverable impactenergy to the initial impact energy.

3.2. Effects of density of buckypaper

In terms of the effects of the buckypaper density on the dynamicbehavior and energy dissipation capability of the buckypaper,computational specimens consisting of 512 SWCNTs with the samelength of 100 nm occupy different volumes of simulation boxes.Impact energy is changed by FM method. According to Goldsmith[74], the mechanism involving permanent deformation can nolonger be described by the equations of the elastic domain, butmust be interpreted by relations capable of including the largestrains and permanent deformations encountered in the impactprocess. The theory of plastic wave propagation or plastic flow al-ways postulates incompressibility of the material in the plasticdomain which requires invariance of the bulk modulus, while hy-drodynamic theory can be used to describe this impact probleminvolving compressible medium. The hydrodynamic theory of wavepropagation treats the medium buckypaper as a compressible fluidwithout shear resistance and, to a first approximation, withoutviscosity. By neglecting the shear modulus of the material, allpermanent deformations are considered to occur as the result ofchanges in the bulk modulus or, equivalently, in the density of thebody. The hydrodynamic theory consider that the motion of theparticles behind the shock front to be steady, however, in ourresearch the impact behavior between the impactor and thebuckypaper keeps for an extended period. That is, behind the shock

0.08

0.12

0.16

0.2

onta

ct fo

rce

(N

)

H. Chen et al. / Carbon 103 (2016) 242e254 249

front the continuous compression keeps going until the impactordeparts from the buckypaper, which causes the impact problem tobe more complicated. And neglecting the effects of the porosity ofthe buckypaper, here we just focus on the initial shock stage tocalculate the velocity of the shock front for a rough estimation.Once the impactor strikes the upper surface of the buckypaper, theconstituent particles of the upper surface instantaneously have thesame velocity as the impactor does, creating a violent shock waveethe Hugoniot shock e that travels along the thickness of bucky-paper and brings the adjacent particles to have the same velocity.The shocked region behind the wave is subject to a transientHugoniot pressure of high magnitude, which explains the rapidincrease of the contact force at the initial stage in Fig. 4. Based onthe laws of conservation of mass, momentum, and energy, thegoverning equation for this shock process can be expresses as:r1(U�v1) ¼ r0(U�v0), p1�p0 ¼ r0(U�v0)(v1�v0), and

p1v1 � p0v0 ¼ r0ðU � v0Þ�I1 � I0 þ 1

2 ðv21 � v20Þ�, where subscripts

0 and 1 denote the undisturbed and compressed state of thebuckypaper, r is the density of the buckypaper, p is the shockpressure and gives the maximum possible value for the impact atits very beginning, v is the particle velocity, U is the shock wavevelocity and I represents the internal energy per unit mass. Becausethe buckypaper is initially at rest and free, v0 ¼ 0 and p0 ¼ 0. Thusthe shock wave velocity can be expressed as U ¼ p1

r0v1, where v1 and

p1 can be derived from the impactor velocity and the impac-torebuckypaper interaction respectively. The shock wave velocitiesin buckypapers with different buckypapers derived from hydro-dynamic theory and tracked from the simulations are presented inFig. S2. Since the sound speed in the uncompressed state is identicalto the velocity of the propagation of elastic compressional waves inthe medium, the elastic compressional wave velocity can bederived based on the NewtoneLaplace equation

c ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�K þ 4

3G��

r

s, where K and G denoting the bulk modulus and

shear modulus of the buckypaper respectively are obtained fromMD simulations of compression and shear tests (shown in Fig. S5).The speed sound is also shown in Fig. S2. It is found that the realcompressional wave velocity is much higher than the elastic onebecause of the compressibility of the buckypaper, which agrees

0 2 4 6 8 10 12 14 1675

80

85

90

95

100

Impact energy (fJ)

Ener

gy d

issi

patio

n ef

ficie

ncy

(%)

107.60 kg/m3

91.01 kg/m3

78.97 kg/m3

71.73 kg/m3

52.81 kg/m3

44.38 kg/m3

40.67 kg/m3

Fig. 9. Energy dissipation efficiency of buckypapers with different densities versusimpact energy. (A colour version of this figure can be viewed online.)

well with the results in Ref. [74]. Since the receiver is fixed andrigid, enforcing zero-displacement normal to the boundary, thewave is reflected completely without energy loss.

Fig. 9 presents the energy dissipation efficiency of the bucky-paper with different densities versus impact energy. For low impactenergy, energy dissipation efficiencies for all cases are extremelyhigh, about 95% to 98%, due to its sufficient deformation capability.On this occasion the buckypaper with a lower density seems tohave slightly higher energy dissipation efficiency owing to thelower stiffness of the buckypaper. As the impact energy rises, theefficiency declines first for the lowest-density buckypaper, fol-lowed by higher-density buckypapers in turn. That is, buckypaperswith a higher density are capable of bearing higher impact energieswithin the deformation limit. Thus in the case that the buckypaperhas oversaturated deformation, a higher-density buckypaper has ahigher energy dissipation efficiency under the same impact energy.For densities 40.67 kg/m3, 44.38 kg/m3 and 52.81 kg/m3, it can beinferred that the decline of energy dissipation efficiency beginsunder impact energies between 4E0 to 5E0 in order and the effi-ciencies under the same impact energy are close to each other dueto their similar densities. The buckypaper with the largest densitycan sustain the impact energy up to 8E0 within the deformationlimit. It is because that a larger density means more slidingoccurred and thus more thermal energy dissipated.

Fig. 10 traces the upper contact force versus the compressiondistance at the impact energy 4E0 and 7E0 respectively. It can befound that the maximum compression distance declines with thegrowth of the density. Because at the same compression distance alarger density means more CNTs are deformed and more slidingoccurs between CNTs to produce more strain energy and more

0 30 60 90 120 1500

0.4

0.8

1.2

1.6

Displacement of impactor (nm)

Con

tact

forc

e (

N)

40.67 kg/m3

50.02 kg/m3

62.05 kg/m3

78.97 kg/m3

0

0.04

C

Fig. 10. The upper contact force versus displacement of the impactor in the case ofbuckypapers with different densities. Inserts show the morphologies at the maximumcompression distance. The labels of the inserts have the same color as the corre-sponding curves. (A colour version of this figure can be viewed online.)

Fig. 12. A fitting surface of the compression ratio as a function of the density of thebuckypaper and the impact energy based on cubic spline interpolation. df (A colourversion of this figure can be viewed online.)

H. Chen et al. / Carbon 103 (2016) 242e254250

thermal energy. Snapshots (a) and (b) in Fig. 10 which show themorphology of buckypapers with density 78.97 kg/m3 and40.67 kg/m3 respectively at the maximum compression distanceunder impact energy 4E0 show that at the current impact energythe buckypapers with four different densities possess sufficientdeformation capability at the largest compression. At the initialstage the peak force for the higher-density buckypaper is larger dueto the increased stiffness of the deformed region. However, thesecond peaks nearby the maximum compression distance for theabove four cases are approximately the same due to the similarstiffness resulting from the combination of compression distanceand density. Snapshots (c), (d) and (e) show the morphologies ofthe buckypaper with densities of 78.97 kg/m3, 62.05 kg/m3 and40.67 kg/m3 respectively at the maximum compression distanceunder impact energy 7E0. They indicate that impact energy 7E0enables the buckypaper with density 78.97 kg/m3 to just achievethe deformation limit but the buckypaper with a lower densityexperiences oversaturated deformation in accordance with theresults in Fig. 9. Therefore, the force increases suddenly when theimpactor approaches the maximum compression and the peakascends sharply with the decline of the density. Fig. 11 presents themaximum upper contact force versus the density under differentimpact energies. For the impact energy varying from E0 to 4E0, allthe buckypapers with different densities possess adequate energydeformation capability. As a result, as the density grows themaximum contact forces have no obvious difference and as theimpact energy grows the force shows a slight increment. As theimpact energy increases from 5E0 to 8E0, oversaturated deforma-tion first appears in a lower-density buckypaper resulting in theabrupt increase of the force, whereas for the higher-densitybuckypaper the force remains steady. For the impact energy overa critical value, oversaturated deformation appears in all thebuckypapers and thus the force declines with the growth of thedensity.

As discussed earlier, the compression distance of the bucky-paper is influenced by the contact force and the energy dissipation.Since a larger density typically corresponds to a smaller specimensize of the buckypaper, the compression ratio is defined as thepercentage of the maximum compression distance to the height ofthe buckypaper. The relationship among the compression ratio,

40 50 60 70 80 90 100 1100

0.5

1

1.5

2

2.5

3

3.5

4

Density (kg/m3)

Max

imum

con

tact

forc

e (

N)

E02E03E04E05E06E07E08E09E010E0

Fig. 11. Maximum upper contact force versus density under impact energies varyingfrom E0 to 10E0. (A colour version of this figure can be viewed online.)

density and impact energy is given in Fig. 12. For a certain density,as the impact energy grows the compression ratio increases with adeclining rate and eventually tends to be constant due to theoversaturated deformation. For certain impact energy, with theincrement of the density both the compression ratio and themaximum compression distance decline. It means that under thesame compression ratio more energy is absorbed by the bucky-paper with a larger density mainly due to more sliding betweenCNTs dissipating more kinetic energy into thermal energy. At thelowest impact energy, the decline of the compression ratio versusthe density is slight. As impact energy raises, the decline rate in-creases first and then decreases with the appearance of the over-saturated deformation of the buckypaper. In addition, since thebuckypaper with a low density reaches the deformation limit at thelow impact energy, the compression ratio also reaches stable. It canbe found that at the largest impact energy only the buckypaperwith the largest density 107.6 kg/m3 still has slight room for

40 50 60 70 80 90 100 1100

1

2

3

4

5

6

7

8

9

Density (kg/m3)

Ener

gy a

bsor

ptio

n pe

r uni

t vol

ume

(MJ/

m3 )

E03E05E07E010E0

Fig. 13. Energy absorption per unit volume of the buckypaper versus density underdifferent impact energies. (A colour version of this figure can be viewed online.)

H. Chen et al. / Carbon 103 (2016) 242e254 251

compression and the compression ratios for different densities arevery close.

Fig. 13 depicts the energy absorption per unit volume (EAUV) ofthe buckypaper. With the increment of the density, the EAUV in-creases linearly with the impact energy until oversaturated defor-mation, such as E0 and 3E0. This can be probably explained as thenumber of beads per unit volume is proportional to the density ofthe buckypaper. The slope can be calculated byðDEh � DElÞ=ðdh � dlÞ where dh and dl are the higher and lowerdensity respectively and DEh and DEl are the energy dissipationcorresponding to dh and dl respectively. As is known from Fig. 8, forthe impact energy that does not cause the oversaturated defor-mation of the buckypaper, the energy absorption as well as EAUM isproportional to the impact energy at a certain density. As a result,the slope is also proportional to the impact energy approximately.As the impact energy rises, the lower-density buckypaper reachesits deformation limit more quickly and thus the increment of EAUVversus impact energy becomes slower, resulting in nonlinearincrement of the EAUV versus density.

3.3. Effects of length of SWCNT

Since individual length distribution of SWCNT can vary fromseveral nanometers to micrometers and even meters [69], it isnoteworthy to investigate the effect of the individual CNTs' lengthon the energy dissipation capability of the buckypaper. Due to thelimit of the computational resource, the lengths of individualSWCNTs used here are in the range of 100 nme800 nm. Fig. 14presents the energy dissipation efficiency of the buckypaper withdifferent lengths of individual SWCNTs from 100 nm, 149 nm,237 nm, 410 nme800 nm at different impact energies. Densities ofall the specimens in this section are kept at 78.97 kg/m3, the sameas that in Section 3.1. It can be found that the energy dissipationefficiency varies slightly as the length of individual SWCNTschanges. For impact energies E0 and 4E0, the efficiency always re-mains about 96%. As is discussed in Section 3.1, the buckypaperwith SWCNTs of length 100 nm does not reach its deformation limitunder both impact energies. It can be inferred that buckypapersstudies in this section are all below their deformation limits. For the

100 149 237 410 80080

84

88

92

96

100

Length of individual SWCNTs (nm)

Ener

gy d

issi

patio

n ef

ficie

ncy

(%)

E04E07E010E0

Fig. 14. Energy dissipation efficiency of buckypaper with different lengths of indi-vidual SWCNTs under different impact energies. (A colour version of this figure can beviewed online.)

impact energy 7E0, the efficiency is slightly lower than that for E0and 4E0, which indicates that the buckypaper has slightly saturateddeformation under impact energy 7E0. For impact energy 10E0, theefficiency falls greatly to around 86% due to the limited energyabsorption capability of buckypaper after reaching its deformationlimit. These findings imply that the energy dissipation efficiency isindependent of the length of individual SWCNTs. Likewise, Fig. 15shows that the maximum compression distance of the bucky-paper remains almost unchanged with different lengths of indi-vidual SWCNTs under the four impact energies. The difference isthat themaximum compression distance increases greatly from theimpact energy E0 to 4E0 while it increases gently from impact en-ergy 4E0 to 7E0. The reason is that as the compression distancegrows the density of the buckypaper increases, and thus furthercompression with the same distance is able to absorb more impactenergy. Themaximum compression distance increases very slightlyfor impact energy from 7E0 to 10E0 since the buckypaper reaches itsdeformation limit. Fig. 16 illustrates that the maximum uppercontact force almost remains constant when the length of indi-vidual SWCNTs varies. The force increases slightly for impact en-ergies from E0 to 4E0 due to the maximum compression distancebeing far away from the limit. Then an obvious increment of theforce happens for impact energies from 4E0 to 7E0 due to theslightly saturated deformation corresponding to impact energy 7E0.Then the force increases tremendously for impact energy from 7E0to 10E0 as the buckypaper reaches the deformation limit. Hence, itcan be inferred that at the same impact energy the evolution of thecontact force follows the compression distance irrespective of thevariation of the length of individual SWCNTs, since the energydissipation efficiency, the maximum compression distance, and themaximum contact force are all independent of the length of indi-vidual SWCNTs. The reason is that the effects of the length on poresize can be negligible [56] and the mechanical properties of such abuckypaper mainly depend on the mass density of the buckypaper,which has been reported in both experiment and simulation [58].By tracking energy variation during the impact process (shown inTable S1), it is found that in the initial state the angle energy in-creases with the increment of the length of individual SWCNTs,since longer SWCNTs are more prevalent to buckling. However, thevariations of angle energy corresponding to different lengths due to

100 149 237 410 80030

50

70

90

110

130

150

Length of individual SWCNTs (nm)

Max

imum

dis

plac

emen

t of i

mpa

ctor

(nm

)

E04E07E010E0

Fig. 15. Maximum displacement of the impactor versus length for individual SWCNTsunder different impact energies. (A colour version of this figure can be viewed online.)

100 149 237 410 8000

0.5

1

1.5

2

2.5

Length of individual SWCNTs (nm)

Max

imum

con

tact

forc

e (

N)

E

4E7E

10E

Fig. 16. Maximum upper contact force versus length for individual SWCNTs underdifferent impact energies. (A colour version of this figure can be viewed online.)

H. Chen et al. / Carbon 103 (2016) 242e254252

the impact are almost the same. It also can be found that thethermal energy takes major part of the absorbed energy, that is, thedominant mechanism is internal sliding.

4. Conclusions

In this paper, the dynamic behavior and energy dissipationcapability of a buckypaper have been extensively investigated byperforming a series of molecular dynamics simulations with a va-riety of design parameters such as impact energy, the density ofbuckypaper, and the length of individual SWCNTs. Effects of theseparameters on energy dissipation capability of the buckypaperhave been analyzed. Simulation results indicate that the bucky-paper possesses extremely high energy dissipation efficiency, al-ways more than 95%, before reaching its deformation limit. Underthe same impact energy, a larger impact velocity yields slightlyhigher energy dissipation efficiency, even close to 100%, owing tomore sliding between SWCNTs and thus more energy dissipatedinto thermal energy.When the buckypaper exceeds its deformationlimit, the energy dissipation efficiency declines, and both the upperand lower contact forces increase abruptly. Within the deformationlimit, the buckypaper with higher density is able to sustain largerimpact energies due to the increment of more strain energy andthermal energy under the same compression but has slightly lowerenergy dissipation efficiency due to the increased compressionstiffness. Therefore, for specific impact energy it is feasible to adjustthe volume of the buckypaper by tuning the density within certainrealms to fulfill the desired requirements. It is also found that theenergy dissipation capability of a buckypaper is independent on thelength of individual SWCNTs since the contact forces follows theevolution of the compression distance while changing the length ofindividual SWCNTs. It has to be noted that the lengths used in thispaper are far below the persistence length, large systems withextremely long CNTs is likely to behave much differently. Besidesthe remarkable energy dissipation efficiency, the buckypaper alsoreveals remarkable mass density and volume density of energydissipation up to 90 J/g and 8.6 J/cm3 respectively which may befurther improved by enlarging the impact energy and/or changingits density. Thus the buckypaper is applicable for volume-

controlled and mass-controlled products essential to be protectedfrom impact. Overall, in spite that all these findings are obtained insilico, this study can shed lights on the dynamic behavior of thebuckypaper, offering a promising candidate for energy dissipationdevices and stimulating more relevant work.

No research, however, provides a perfect study, with this workbeing no exception to the rule. More endeavors should be devotedto expand the realm of the length of individual CNTs, the impactenergy, the impact velocity under the same impact energy and thedensity of buckypaper. Particularly, the buckypaper density can beobtained as large as 1.39 g/cm3, thus yielding greatly improvedtransport and mechanical properties such as Young's modulus over2 GPa [54]. Fluid component can be introduced within the poreswhich would provide a hydraulic action and viscoelastic drag [75].Besides, previous research has proved that mixture of SWCNTswithdouble-walled carbon nanotubes (DWCNTs) in a buckypaper in-fluences its ultimate mechanical property due to the strong adhe-sion energy and large bending rigidity [56]. Especially, the Poisson'sratio of the mixed buckypaper can be tuned from a positive to anegative value by increasing the DWCNT composition, which isbeneficial for the energy dissipation. Therefore, mixed buckypapershould be explored to achieve better energy dissipation capability.In addition, other forms of buckypaper could be set up, such as thatmade of aligned CNTs which has better performance on thermaland electrical conductance [76], and cross-links between CNTswhich enhances thermal stability and load transfer of buckypaper[77]. Besides the uniaxial compressive loading, there are manyother forms loading and deformation mechanisms pertinent tocollisions, impact and penetration, such as membrane response ofbuckypaper at high frequency vibration [78], the tensile and frac-ture response in the case of spall [79] and the bending response ofbuckypaper [80]. Since the reflected wave is determined by thenature of the boundary condition [81], other types of reflectingboundary are worthwhile to be invested in the future, such as freesurface boundary which has zero-stress conditions and allows forspall in the case of tension at the away-boundary as well ascompression near the impact boundary. Other types, not limited,include elastic boundary and attached dashpot, corresponding tomore complicated wave reflection. The energy dissipation anddynamic response of the buckypaper with different boundarieswould likely be much different from each other.

Competing financial interests

The authors declare no competing financial interests.

Acknowledgments

HC, JC, and HN appreciate the support from the Scholarship ofNanjing University of Aeronautics and Astronautics (China) (GrantNo: [2013]59). LZ, MB, and XWwould like to acknowledge supportsfrom the University of Georgia (UGA) Research Foundation andNational Science Foundation (Grant No. CMMI-1306065). Calcula-tions are performed at the UGA Advanced Computing ResourceCentre.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.carbon.2016.03.020.

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