8/13/2019 1-s2.0-S0927025613005855-main

1/6

Structural and electronic properties of armchair (7, 7) carbon nanotubes

using DFT

K. Gharbavi, H. Badehian

Department of Physics, Shahid Chamran University, Ahvaz, Iran

a r t i c l e i n f o

Article history:

Received 6 August 2013Received in revised form 19 September2013Accepted 22 September 2013Available online 20 October 2013

Keywords:

Carbon nanotubesDensity functional theoryElectronic propertiesStructural properties

a b s t r a c t

The density functional theory full-potential linearized augmented plane wave method with the General-ized Gradient Approximation (PBE-GGA & WC-GGA) and Local Density Approximation for the exchangecorrelation potential were applied to calculate the structural and electronic properties of armchair (7, 7)carbon nanotubes. Structural properties such as lattice constants, bulk modules, Youngs modulus, com-pressibility, bond lengths, muffin-tin radius and effective atomic charge were calculated. According toPBE-GGA, CAC bond lengths are equal to 1.429 and Youngs modulus is equal to 0.930 tetra Pascal beingin good agreement with other studies. Band structure, density of states and electronic charge densitywere calculated. CNTs (7, 7) show a metallic behavior and the electron charge densities of CNTs (7, 7) con-firm a covalent bond between two carbon atoms. Moreover, the effects of armchair CNTs chirality on theband gaps and Youngs modulus are illustrated which confirm the calculations.

2013 Elsevier B.V. All rights reserved.

1. Introduction

The use of carbon nanotubes in nanotechnology applications re-quires an understanding of their electronic and structural proper-ties. Modeling and simulation are powerful methods to study thecharacteristics of nanomaterials and has a prominent place in thecourse of initial study of nanostructures properties. Since the dis-covery of carbon nanotubes (CNTs) in 1991[1], because of the un-ique cylinder structure consisting of a graphene sheet, itselectronic and structural properties have attracted many atten-tions[26]. The properties of CNTs are extremely dependent ontube geometry and knowing the structural properties of CNTs areparticularly useful keys to determine their nature. Translationalsymmetry (with a screw axis) could affect the electronic structureand related properties in 1D systems on a cylindrical surface[7,8].In the SWNTs, covalent functionalization breaks some C@C double

bonds and leaving holes in the structure of the nanotube will altersome properties[9]. Many studies have revealed that CNTs haveYoungs modulus on the order of tetra Pascal, with potential appli-cations in ultrastrong composite materials and nanomechanicaldevices[1015]. Although many experimental[6,1627]and sev-eral theoretical studies[2833]have been conducted on both arm-chair and zigzag nanotubes to obtain their characteristicparameters with various methods, in this paper we calculate thestructural and electronic properties of armchair (7, 7) carbonnanotubes by using a FP-LAPW approach based on first-principles

density functional theory, which to our knowledge has not beenachieved, yet.

2. Carbon nanotubes

Carbon nanotubes (CNTs) are from the fullerene structural fam-ily and Single Walled Nanotubes (SWNTs) can be supposed as longwrapped graphene sheets. Having a length to diameter ratio ofabout 1000, carbon nanotubes can be considered as one-dimen-sional structures[34]. A pair of integer indices (n, m) which calledthe chirality, represents the way the graphene sheet is wrapped.Then and m refer the number of unit vectors along two directionsin the crystal lattice of graphene. Ifm= 0, the nanotubes are calledzigzag, ifn =m, the nanotubes are called armchair otherwise,they are called chiral [7]. Depending on the chirality of SWNTs,their band gap can vary and their electrical conductivity can showsemiconducting or metallic behavior[35]. Basically, all armchairtubes are metallic. For an armchair tube, there always exist elec-tronic states that cross the corner points of the first Brillouin Zone(BZ), and therefore these nanotubes always show a metallic behav-ior[36]. Orbital hybridization can denote the nature of the bondingof a nanotube. Chemical bonding of each nanotube is composed ofsp2 bonds. This bonding structure is stronger than the sp3 bondsand causes the molecules to have the unique strength. Nanotubesgenerally align themselves into ropes and held together by Vander Waals forces. Nanotubes can merge together under high pres-sure and changing some sp2 bonds to sp3 bonds[34]. Techniqueshave been utilized to produce nanotubes in sizeable quantities,are arc discharge[37], chemical vapor deposition (CVD)[38,39],

0927-0256/$ - see front matter 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.commatsci.2013.09.050

Corresponding author. Tel.: +98 9177314414.

E-mail address:hojatbadehian@gmail.com(H. Badehian).

Computational Materials Science 82 (2014) 159164

Contents lists available at ScienceDirect

Computational Materials Science

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m m a t s c i

http://dx.doi.org/10.1016/j.commatsci.2013.09.050mailto:hojatbadehian@gmail.comhttp://dx.doi.org/10.1016/j.commatsci.2013.09.050http://www.sciencedirect.com/science/journal/09270256http://www.elsevier.com/locate/commatscihttp://www.elsevier.com/locate/commatscihttp://www.sciencedirect.com/science/journal/09270256http://dx.doi.org/10.1016/j.commatsci.2013.09.050mailto:hojatbadehian@gmail.comhttp://dx.doi.org/10.1016/j.commatsci.2013.09.050http://-/?-http://-/?-http://-/?-http://-/?-http://crossmark.crossref.org/dialog/?doi=10.1016/j.commatsci.2013.09.050&domain=pdfhttp://-/?-

8/13/2019 1-s2.0-S0927025613005855-main

2/6

laser ablation [40] and high pressure carbon monoxide (HiPCO)[41]. Atomic force microscopy (AFM) image of nanotube dispersionis shown inFig. 1[42]. There is no lattice constant to consider asCNT lattice parameters, so theoretically the model of super cell lat-tice constants should be enough to avoid artificial tubetube inter-action. Schematic view of electron orbitals (regions within theatom with highest probability of electrons existence) inside anarmchair (7, 7) carbon nanotube is shown inFig. 2[18].

3. The calculation method

We have investigated the structural and electronic properties ofarmchair (7, 7) carbon nanotubes using density functional theoryas implemented in the WIEN2k code. The calculations were donewithin the density functional theory (DFT) framework with Gener-alized Gradient Approximation (PBE-GGA & WC-GGA) and LocalDensity Approximation (LDA) for solving a KohnSham equation[4345]. In the FP-LAPW method, space is divided into two regions,spherical muffin-tins around the nuclei in which radial solutionsof Schrodinger equation and their energy derivatives are used asbasis functions, and an interstitial region between the muffin-

tins (MT) in which the basis set consists of plane waves. The

calculations are fully self-consistent and there are no shapeapproximations for the charge density or potential. Core statesare treated fully relativistically and valence and semi-core statesare treated semi-relativistically (i.e. ignoring spinorbit coupling).In this method valence and core states origin energy have beenseparated, and the energy separating the valance state from thecore state has been considered 10.0 Ry in order to reach energyEigen values convergence. The wave functions in the interstitial re-gion were expanded in plane waves with a cut-offKmax= 5.5/RMT,where RMT indicates the smallest atomic muffin-tin sphere radiusand Kmax provides the magnitude of the largest K vector in theplane wave expansion. The value of the parameterRKmax controlsthe size of the basis sets in these calculations. The otherparameters are: Gmax= 12 and RMT(C) = 1.3 a.u. For partial wavesin atomic spheres, maximum Lvalue is 10 and for partial wavesin non-muffin-tin calculations, maximum value ofL is equal to 4.

4. Results

4.1. Structural properties

Tetragonal unit cell was chosen for a CNT (7, 7) structure and z-direction was considered as the tube axis (Fig. 3). The total numberofk-point in the first Brillouin Zone (BZ) was taken to be equal to200, and thek-point set mesh was 1 1 200. By the optimizationof the lattice constants, with respect to the total energy, we found9 vacuum for nanotube separation in the lateral directions beingenough to avoid artificial tubetube interaction. The calculationswere performed for the tube arranged in array as shown in2 2 2 repeated of single nanotube (Fig. 3).

4.1.1. Lattice constant and bulk modulus

Avoiding artificial tubetube interaction, carbon nanotube ar-rays have nanoscale dimensions. In this work, the structuralparameters of a CNT (7, 7) were simulated calculating the total en-

ergy by modifying the lattice parameters. The energy vs. volumecurve is shown inFig. 4. The theoretical lattice constant and bulkmodulus were calculated using Murnaghan equation of state tofit the theoretical electronic ground state energy[46]:

EV E0 B0V0

B0

V

V0

V

V0

1B0 B0

B0 1

264

375 1

whereE(V) is the ground state energy with the unit cell volume V,V0is the equilibrium volume at zero pressure, B is the bulk modulus,B0 @B=@P(at P= 0 and constant temperature) is the first derivationofBrespect to the pressure. The bulk modulus denotes the hardnessof the structure and the inverse of bulk module considered as the

compressibility of the structure. As the bulk modulus increases(decreases), the crystal hardness will increase (decreases).

Condensation of volume is defined by equation[46]:

KV 1

V0

dV

dP 2

V0is the unit cell volume at zero pressure. The bulk modulus,B, andthe first derivation ofB respect to the pressure, B 0, were calculatedby fitting the Murnaghan equation of state respect to the total ener-gies vs. lattice constant (a) and results are compared with other the-oretical and experimental studies of a CNT (7, 7) in Table 1.

Comparatively, the lattice constant of a CNT (7, 7) using PBE-GGA approximation illustrates the excellence of this approxima-

tion. There are no experimental results to compare with, andobviously, there is no experimental lattice constant to discuss.

Fig. 1. AFM image of the nanotube dispersion [42].

Fig. 2. Schematic view of electron orbitals inside an armchair (7, 7) carbonnanotube[18].

160 K. Gharbavi, H. Badehian/ Computational Materials Science 82 (2014) 159164

8/13/2019 1-s2.0-S0927025613005855-main

3/6

4.1.2. CAC bond lengths

Consequently, CAC bond length is the only parameter to calcu-late errors percentage in present simulation and noticeably, thenanotubes chirality have significant effects on these parameter[47,48]. The bonds direction along the nanotube axis is differentfrom those of along the nanotube circumference. Nanotubes withsmaller indices have larger bond elongation but it does not exceed0.008 [47]. CAC bond lengths of a CNT (7, 7) structure are giveninTable 2.

Calculated values show that PBE-GGA approximation results inbond lengths of a CNT (7, 7) with least percentage of relative error.

According to this approximation, a CAC bond length calculatedequal to 1.429 .

4.1.3. Charge decomposition analysis of C atom in a CNT (7, 7)Electronic charges inside and outside the muffin-tin spheres of

carbon atoms in this nanostructure are presented in Table 3. Theresults demonstrate the suitable selection of the muffin-tinspheres radius.

4.1.4. Effective atomic charge

The effective atomic charge is an important parameter to bestudied[49]. The chemical bonds between the atoms in a structurecan be determined comparing the effective atomic charge and theamount of inequality from an atoms nominal charge. Calculatedeffective charge of CNTs (7, 7) atoms using three approximationsis presented inTable 4and also results are compared with nominalcharge. Results show that there are 2.049 electrons for each C atom

and there are covalent or metallic bonds between C atoms in CNTs(7, 7).

4.1.5. Youngs modulus

CNTs have very strong and resilient structures and they can eas-ily be straightened out without any damage to its physical struc-ture. The Youngs modulus is defined as the ratio of the uniaxialstress over the uniaxial strain in the range of stress in whichHookes law holds[50].

Youngs modulus (Y) is a measure of how a material would reactwhen bent or stretched and is one of the several elastic moduli; forexample, bulk modulus for volume deformation, and shear modu-lus for surface deformation. The Youngs modulus of CNTs rangesfrom 1.281.8 TPa (teraPascals) [51,52]. One teraPascal is equal

to a pressure of about seven orders of magnitude greater thanatmospheric pressure. The Youngs modulus of steel is 0.21 TPa,meaning that the Youngs moduli of CNTs are typically ten timesgreater than that of steel. Youngs modulus, Y, is the applied tensilestress over the strain[51]:

Yr

e3

where r is the stress (the amount of applied force per cross-sectional area) and e is the strain (the deformation, or change in

Fig. 3. 2 2 2 Periodicity, repeated of a CNT (7, 7) single nanotube with tetragonal unit cell.

Fig. 4. Energy vs. volume curve for CNT (7, 7) using Generalized GradientApproximation (PBE-GGA).

Table 1

Structural parameters of a CNT (7, 7) (this work) and other results.

Quantity WC-GGA LDA PBE-GGA Theoretical results

A() 17.554 17.310 17.525 19.45[27]B(GPa) 88.254 89.465 88.353 B0 3.242 3.396 3.255 Kv(m

2/N) 0.01133 0.01117 0.01131

Table 2

Bond lengths of a CNT (7, 7) structure and comparison with experimental result.

Quantity PBE-GGA LDA WC-GGA Experimental results

acAc () 1.429 1.409 1.411 1.421[48]

Percentage of relative error 0.556 0.873 0.690

K. Gharbavi, H. Badehian/ Computational Materials Science 82 (2014) 159164 161

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

8/13/2019 1-s2.0-S0927025613005855-main

4/6

length, caused by applied stress). The sp2 bonds can rehybridize asthey are strained making the CNTs more apt to resist breaking[51,52]. A great deal of theoretical studies on CNTs dynamics prop-erties have been based on molecular dynamics (MD) simulations. Inthe classical MD simulations, due to the electrons, all degrees offreedom as well as quantum effects, are ignored, but in DFT ap-proach potentials between electronelectron, electronion as wellas ionion interactions are also considered[5,53].

Beside this, the CarParrinello molecular dynamics (CPMD) isused to calculate Youngs modulus of carbon nanotubes. WithinCPMD, for the first time, it was allowed to combine moleculardynamics (MD) simulations of atomic and molecular systems withelectronic structure calculations. Since then, molecular dynamics

simulations of systems comprising up to a few hundred atoms ispossible by using the density functional theory[54,55].

DFT calculation, which is known as a time consuming methodand considering more details about the electrons and the ions,can give more interactions and corrections about electronelec-tron, electronion and ionion, which are disregarded in classicalMD. Considering these corrections, the simulated Youngs moduliof CNTs would be more credible. But it can only simulate the staticstate[44,55].

In this paper we use DFT to estimate The Youngs modulus of aCNT (7, 7). The Generalized Gradient Approximation (PBE-GGA)were used for the exchange correlation term[44,56].

There are 28 atoms in each cell and the nanotube diameter is9.418 , Thus, the nanotube area is 69.651 1020 m2 (equilibriumcondition). The deformation energy would be used to calculateYoungs modulus in DFT simulation. Initial length of the SWCNTcell was 2.474 and the initial potential energy was 4.452 Ry(equilibrium condition). The energy vs. volume curve for a CNT(7, 7) was shown in Fig. 4 (the energyvolume diagram). Thenself-consistent field (SCF) for super cell being 16 times greater thanequilibrium volume, was run. In this case, the area of cross sectionis still equal to A. In this case the length of the SWCNT cell was2.475 and the potential energy was 4.471 Ry. Using DFT theYoungs modulus can be calculated by the formula[52]:

Y E

A:ll

e4

where DE is the increment of the potential energy (0.02 Ry,

1Ry = 2.179 1018

J), A is the cross sectional area of SWCNT

Table 3

Charge decomposition of C atom in a CNT (7, 7).

Approximation PBE-GGA LDA WC-GGA

Nominal charge 6.000 e 6.000 e 6.000 eCharge inside the muffin-tin sphere 3.596 e 3.591 e 3.588 eCharge outside the muffin-tin sphere 2.404 e 2.409 e 2.412 eSummation of charge inside and outside muffin-tin sphere charge 6.000 e 6.000 e 6.000 e

Table 4

Effective atomic charge of C atom in CNTs (7, 7).

Approximate PBE-GGA LDA WC-GGA Nominal charge

C1 2.049 2.056 2.056 2C2 2.049 2.056 2.056 2Percentage of

relative error2.495 2.820 2.815

Table 5

Comparison of the Youngs modulus of three armchair CNTs using different method.

Chirality DFT (TPa) MD (TPa) Experiment (TPa)

CNT (5, 5) 1.032[59] 1[12] 1[60]CNT (7, 7) 0.930 (this work) 1.096[61] CNT (10, 10) 1[62] 0.750.9[63]

Fig. 5. The calculated electronic band structure for CNTs (7, 7) (PBE-GGA). The zeroof the energy was set at top of the valence band.

Table 6

The results for the band gap calculated by this method and others [57].

Chirality (n,m) GGA[57] LDA TB[65] QE[64]

(3, 3) 0.0 (7, 0) 0.47 0.09[66] 1 0.48(15, 0) 0.09 0.0 0 .041(17, 0) 0.52 0.53(7,7) 0.000 (this work) 0.000 (this work)

Fig. 6. Total DOS of CNT (7, 7) (PBE-GGA).

162 K. Gharbavi, H. Badehian/ Computational Materials Science 82 (2014) 159164

8/13/2019 1-s2.0-S0927025613005855-main

5/6

(69.65 10

20 m2), Dl is the increment of the length(0.001 1010 m), and e = Dl/l0is the strain of this carbon nanotube(4.042 104). Hence, the Youngs modulus of an armchair (7, 7)SWCNT is equal to 0.930 TPa.

The comparison between the Bulk modulus (=88.353 GPa) andYoungs modulus (=0.930 TPa) of this armchair carbon nanotubedemonstrate the reaction of CNTs (7, 7) under volume deformationand length deformation respectively (PBE-GGA). Results show thatthe hardness of the simulated carbon nanotube in three dimen-sions is less than the uniaxial hardness which is logical and ex-pected. The comparison of the Youngs modulus of threearmchair CNTs using different approaches are given in Table 5.

4.2. Electronic properties

4.2.1. Band structure

The structure of a carbon nanotube strongly affects its elec-tronic properties and the main reason is the symmetry and uniqueelectronic structure of graphene[7,57]. The calculated electronicband structure of the CNTs (7, 7) carbon nanotube in the high-symmetry directions in the Brillouin zone (BZ) is shown in Fig. 5.The Fermi energy level is set to zero. The energy unit was consid-ered in eV and the origin of energy was arbitrarily set to be at themaximum valence band (zero of energy). The energy band gaps ob-tained from different SWCNTs are given inTable 6.

4.2.2. Density of states

The electron distribution in an energy spectrum is described by

the density of states (DOS) and it can be measured in photoemis-sion experiments. The total DOS spectrum of armchair (7, 7) nano-tubes from 6 eV to 22 eV is shown in Fig. 6. The Fermi energylevel is set to zero. The electronic band structure and DOS showthat an armchair (7, 7) carbon nanotube is a metallic nanotubewith zero band gap and the valence and conduction bands crosseach other at the Fermi level which is in agreement with the otherstudies[21,22].

4.2.3. Electron density

The electron density of the nanotube is an important parameterto be studied. The charge density is derived from a high-convergedwave function, so the result is valid and it can be used to study theelectronegativity of C atoms in above mentioned carbon nanotube

[58]. Contour plots of electron density show that the chemicalbonding of this structure is mainly covalent (Fig. 7).

5. Conclusions

The structural and electronic properties of armchair (7, 7) car-bon nanotubes using density functional theory as implementedin the WIEN2k code was investigated. The lattice constant of CNT(7, 7) were calculated using three approximations and PBE-GGAapproximation showed better results than previous approaches.According to PBE-GGA approximation, CAC bond lengths are equalto 1.429 . Moreover, result shows that the hardness of the simu-lated carbon nanotubes in three dimensional axes is less than theuniaxial hardness which is logical and expected. The results ofeffective atomic charge predict 2.049 electrons per each carbonatom and there are covalent or metallic bonds between C atomsin CNTs (7, 7). Contour plot of electron density shows that chemical

bonding of CAC is mainly covalent. The results showed that thenanotubes have a metallic behavior which confirms the predic-tions. Moreover, The Youngs modulus of CNTs (7, 7) was calculated(=0.930 TP) and was compared with others. The results given bythese methods are in consistent with the MD method.

References

[1] S. Iijima, Nature 354 (1991) 5658.[2] G. Bertoni, L. Calmels, Micron 37 (2006) 486491.[3] R. Nizam, S. Mahdi, A. Rizvi, A. Azam, International Journal of Science and

Technology 1 (2011) 153162.[4] R.S. Ruoff, D. Qian, W.K. Liu, Comptes Rendus Physique 4 (2003) 9931008.[5] B.I. Yakobson, P. Avouris, Topics in Applied Physics 80 (2001) 287327.[6] J. Zhao, H. Park, J. Han, J.P. Lu, Physical Chemistry B 108 (2004) 42274230 .[7] M.S. Dresselhaus, G. Dresselhaus, R. Saito, Carbon 33 (1995) 883891 .

[8] A. Javey, J. Kong, Carbon Nanotube Electronics (2009).[9] E. Flahaut, R. Bacsa, A. Peigney, C. Laurent, Chemical Communications 12(2003) 14421443.

[10] B.G. Demczyk, Y.M. Wang, J. Cumings, M. Hetman, W. Han, A. Zettl, R.O.Ritchie, Materials Science and Engineering A 334 (2002) 173178.

[11] H. Jiang, P. Zhang, B. Liu, Y. Huang, P.H. Geubelle, H. Gao, K.C. Hwang,Computational Materials Science 28 (2003) 429442.

[12] A.L. Kalamkarov, A.V. Georgiades, S.K. Rokkam, V.P. Veedu, M.N. Ghasemi-Nejhad, International Journal of Solids and Structures 43 (2006) 68326854.

[13] A. Krishnan, E. Dujardin, T.W. Ebbesen, P.N. Yianilos, M.M.J. Treacy, PhysicalReview B 58 (1998) 1401314019.

[14] D. Srivastava, C. Wei, K. Cho, Applied Mechanics Reviews 56 (2003) 215230.[15] Z. Wang, M. Devel, B. Dulmet, S. Stuart, Nanotubes and Carbon Nanostructures

17 (2009) 110.[16] J.R.A. Collado, International Journal of Quantum Chemistry 108 (2008) 257

264.[17] A.N. Kolmogorov, V.H. Crespi, Physical Review Letters 85 (2000) 47274730.[18] H. Kuzmany, A. Kukovecz, F. Simona, M. Holzweber, C. Kramberger, T. Pichler,

Synthetic Metals 141 (2004) 113122.

[19] B. Liu, H. Jiang, Y. Huang, S. Qu, M.-F. Yu, Physical Review B 72 (2005). 035435-035431035435-035438.

Fig. 7. CNT (7, 7) electron density distribution in the (001) plane (a) in two dimensions and (b) in three dimensions (PBE-GGA).

K. Gharbavi, H. Badehian/ Computational Materials Science 82 (2014) 159164 163

http://refhub.elsevier.com/S0927-0256(13)00585-5/h0005http://refhub.elsevier.com/S0927-0256(13)00585-5/h0010http://refhub.elsevier.com/S0927-0256(13)00585-5/h0010http://refhub.elsevier.com/S0927-0256(13)00585-5/h0015http://refhub.elsevier.com/S0927-0256(13)00585-5/h0015http://refhub.elsevier.com/S0927-0256(13)00585-5/h0015http://refhub.elsevier.com/S0927-0256(13)00585-5/h0020http://refhub.elsevier.com/S0927-0256(13)00585-5/h0025http://refhub.elsevier.com/S0927-0256(13)00585-5/h0030http://refhub.elsevier.com/S0927-0256(13)00585-5/h0035http://refhub.elsevier.com/S0927-0256(13)00585-5/h0040http://refhub.elsevier.com/S0927-0256(13)00585-5/h0040http://refhub.elsevier.com/S0927-0256(13)00585-5/h0045http://refhub.elsevier.com/S0927-0256(13)00585-5/h0045http://refhub.elsevier.com/S0927-0256(13)00585-5/h0050http://refhub.elsevier.com/S0927-0256(13)00585-5/h0050http://refhub.elsevier.com/S0927-0256(13)00585-5/h0050http://refhub.elsevier.com/S0927-0256(13)00585-5/h0055http://refhub.elsevier.com/S0927-0256(13)00585-5/h0055http://refhub.elsevier.com/S0927-0256(13)00585-5/h0060http://refhub.elsevier.com/S0927-0256(13)00585-5/h0060http://refhub.elsevier.com/S0927-0256(13)00585-5/h0060http://refhub.elsevier.com/S0927-0256(13)00585-5/h0065http://refhub.elsevier.com/S0927-0256(13)00585-5/h0065http://refhub.elsevier.com/S0927-0256(13)00585-5/h0065http://refhub.elsevier.com/S0927-0256(13)00585-5/h0070http://refhub.elsevier.com/S0927-0256(13)00585-5/h0075http://refhub.elsevier.com/S0927-0256(13)00585-5/h0075http://refhub.elsevier.com/S0927-0256(13)00585-5/h0075http://refhub.elsevier.com/S0927-0256(13)00585-5/h0080http://refhub.elsevier.com/S0927-0256(13)00585-5/h0080http://refhub.elsevier.com/S0927-0256(13)00585-5/h0085http://refhub.elsevier.com/S0927-0256(13)00585-5/h0090http://refhub.elsevier.com/S0927-0256(13)00585-5/h0090http://refhub.elsevier.com/S0927-0256(13)00585-5/h0095http://refhub.elsevier.com/S0927-0256(13)00585-5/h0095http://refhub.elsevier.com/S0927-0256(13)00585-5/h0095http://-/?-http://refhub.elsevier.com/S0927-0256(13)00585-5/h0095http://refhub.elsevier.com/S0927-0256(13)00585-5/h0095http://refhub.elsevier.com/S0927-0256(13)00585-5/h0090http://refhub.elsevier.com/S0927-0256(13)00585-5/h0090http://refhub.elsevier.com/S0927-0256(13)00585-5/h0085http://refhub.elsevier.com/S0927-0256(13)00585-5/h0080http://refhub.elsevier.com/S0927-0256(13)00585-5/h0080http://refhub.elsevier.com/S0927-0256(13)00585-5/h0075http://refhub.elsevier.com/S0927-0256(13)00585-5/h0075http://refhub.elsevier.com/S0927-0256(13)00585-5/h0070http://refhub.elsevier.com/S0927-0256(13)00585-5/h0065http://refhub.elsevier.com/S0927-0256(13)00585-5/h0065http://refhub.elsevier.com/S0927-0256(13)00585-5/h0060http://refhub.elsevier.com/S0927-0256(13)00585-5/h0060http://refhub.elsevier.com/S0927-0256(13)00585-5/h0055http://refhub.elsevier.com/S0927-0256(13)00585-5/h0055http://refhub.elsevier.com/S0927-0256(13)00585-5/h0050http://refhub.elsevier.com/S0927-0256(13)00585-5/h0050http://refhub.elsevier.com/S0927-0256(13)00585-5/h0045http://refhub.elsevier.com/S0927-0256(13)00585-5/h0045http://refhub.elsevier.com/S0927-0256(13)00585-5/h0040http://refhub.elsevier.com/S0927-0256(13)00585-5/h0035http://refhub.elsevier.com/S0927-0256(13)00585-5/h0030http://refhub.elsevier.com/S0927-0256(13)00585-5/h0025http://refhub.elsevier.com/S0927-0256(13)00585-5/h0020http://refhub.elsevier.com/S0927-0256(13)00585-5/h0015http://refhub.elsevier.com/S0927-0256(13)00585-5/h0015http://refhub.elsevier.com/S0927-0256(13)00585-5/h0010http://refhub.elsevier.com/S0927-0256(13)00585-5/h0005http://-/?-http://-/?-http://-/?-http://-/?-

8/13/2019 1-s2.0-S0927025613005855-main

6/6

[20] J. Lu, S. Nagase, Y. Maeda, T. Wakahara, T. Nakahodo, A.T.D. Yu, Z. Gao, R. Han,H. Ye, Chemical Physics Letters 405 (2005) 9092.

[21] Y. Maeda, S. Kimura, M. Kanda, Y. Hirashima, T. Hasegawa, T. Wakahara, Y.Lian, T. Nakahodo, T. Tsuchiya, T. Akasaka, J. Lu, X. Zhang, Z. Gao, Y. Yu, S.Nagase, S. Kazaoui, N. Minami, T. Shimizu, H. Tokumoto, R. Saito, AmericanChemical Society 127 (2005) 1028710290.

[22] D.J. Mowbray, C. Morgan, K.S. Thygesen, Physical Review B 79 (2009). 195431-195431195431-195436.

[23] W. Nicholls, M. Borg, D. Lockerby, J. Reese, Microfluidics and Nanofluidics 12(2012) 257264.

[24] W.H. Noon, K.D. Ausman, R.E. Smalley, J. Ma, Chemical Physics Letters 355(2002) 445448.

[25] Y. Shim, Y.J. Jung, H.J. Kim, Physical Chemistry Chemical Physics 13 (2011)39693978.

[26] J. Wang, Z. Jin, J. Cheng, Y. Li, Physical Chemistry C 113 (2009) 81328135 .[27] W. Zhu, X. Yan, Y. Xiao, Physics Letters A 372 (2008) 13081312 .[28] H. Zeng, H. Hu, J.P. Leburton, ACS Nano 4 (2009) 292296.[29] J.E. Knox, M.D. Halls, H.B. Schlegel, Journal of Computational and Theoretical

Nanoscience 3 (2006) 17.[30] Y. Liu, R.O. Jones, X. Zhao, Y. Ando, Physical Review B 68 (2003) 125413

125420.[31] A.A. Rafati, S.M. Hashemianzadeh, Z.B. Nojini, Physical Chemistry C 112 (2008)

35973604.[32] S.S. Razavi, S.M. Hashemianzadeh, H. Karimi, Journal of Molecular Modeling 17

(2011) 11631172.[33] H. Zeng, J. Zhao, H. Hu, J.-P. Leburton, Journal of Applied Physics 109 (2011)

083716.[34] D. Gerke, NASA 2009 Body of Knowledge (BoK) Carbon Nanotube Technology,

National Aeronautics and Space Administration, 2010.[35] M.S. Dresselhaus, G. Dresselhaus, J.C. Charlier, E.H. Andez, Philosophical

Transactions of the Royal Society of London Series A 362 (2004) 20652098.[36] R. Nizam, S. Mahdi, A. Rizvi, A. Azam, International Journal of Science and

Technology 1 (2011) 22243577.[37] C. Journet, P. Bernier, Applied Physics A-Materials Science & Processing 67

(1998) 19.[38] A. Eftekhari, P. Jafarkhani, F. Moztarzadeh, Carbon 44 (2006) 13431345.[39] Z.F. Ren, Z.P. Huang, J.W. Xu, J.H. Wang, P. Bush, M.P. Siegal, P.N. Provencio,

Science 282 (1998) 11051107.[40] T. Guo, P. Nikolaev, A. Thess, D.T. Colbert, R.E. Smalley, Chemical Physics

Letters 243 (1995) 4954.[41] P. Nikolaev, M.J. Bronikowski, R.K. Bradley, F. Rohmund, D.T. Colbert, K.A.

Smith, R.E. Smalley, Chemical Physics Letters 313 (1999) 9197.

[42] M.E.G. Lyons, G.P. Keeley, Electrochemical Science 3 (2008) 819853.[43] P. Blaha, K. Schwarz, in: Vienna University of Technology, Austria, 2008.[44] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C.

Fiolhais, Physical Review B 46 (1992) 66716687.[45] M. Petersen, F. Wanger, L. Hufnagel, M. Scheffler, P. Blaha, K. Schwarz,

Computer Physics Communications 126 (2000) 294309.[46] F.D. Murnaghan, Sciences of the United State America 30 (1944) 244.[47] M.F. Budyka, T.S. Zyubina, A.G. Ryabenko, S.H. Lin, A.M. Mebel, Chemical

Physics Letters 407 (2005) 266271.[48] V.K. Jindal, A.N. Imtani, Computational Materials Science 44 (2008) 156162.

[49] T. Ragab, C. Basaran, Carbon 49 (2011) 425434.[50]X. Zhou, J. Zhou, Z.O. Yang, Physical Review B 62 (2000) 1369213696 .[51] C.P. Poole, F.J. Owens, Introduction to Nanotechnology, Wiley, 2003.[52] P.A.G. Sankar, K.U. Kumar, European Journal of Scientific Research 60 (2011)

324340.[53] C.W. Fan, J.H. Huang, C. Hwu, Y.Y. Liu, In: The Third Taiwan-Japan Workshop

on Mechanical and Aerospace Engineering, Hualian, Taiwan, 2005.[54] P. Tangney, Journal of Chemical Physics 124 (2006) 044111044114.[55] J.L. Zang, Q. Yuan, F.C. Wang, Y.P. Zhao, Computational Materials Science 46

(2009) 621625.[56] W. Koch, M.C. Holthausen, A Chemists Guide to Density Functional Theory,

Wiley, New York, 2001.[57] T. Movlarooy, A. Kompany, S.M. Hosseini, N. Shahtahmasebi, Computational

Materials Science 49 (2010) 450456.[58] J. Guo, in: Electrical engineering, Purdue University, Ann Arbor, 2004 pp. 123 .[59] H. Mori, Y. Hirai, S. Ogata, S. Akita, Y. Nakayama, Japanese Journal of Applied

Physics 44 (2005) 13071309.[60]M.F. Yu, B.S. Files, S. Arepalli, R.S. Ruoff, Physical Review Letters 84 (2000)

55525555.[61] S.H. Yang, S.H. Ming, Z.G. Xiang, International Academic Publishers 45 (2006)

741744.[62] A. Jorio, G. Dresselhaus, M.S. Dresselhaus, Carbon Nanotubes: Advanced Topics

in the Synthesis, Structure Properties and Applications, Springer, 2008.[63] Y. Ji, Y.J. Lin, A. Buldum, An investigation of buckypapers Youngs modulus

utilizing nanoscale modeling and molecular dynamics simulation, in: 4th IEEEInternational Conference on Nano/Micro Engineered and Molecular Systems,China, 2009.

[64] B. Kozinsky, N. Marzari, Physical Review Letters 96 (2006) 166801166805.[65] N. Hamada, S.-i. Sawada, A. Oshiyama, Physical Review Letters 68 (1992)

15791581.[66] X. Blase, L.X. Benedict, E.L. Shirley, S.G. Louie, Physical Review Letters 72

(1994) 18781881.

164 K. Gharbavi, H. Badehian/ Computational Materials Science 82 (2014) 159164

http://refhub.elsevier.com/S0927-0256(13)00585-5/h0100http://refhub.elsevier.com/S0927-0256(13)00585-5/h0100http://refhub.elsevier.com/S0927-0256(13)00585-5/h0105http://refhub.elsevier.com/S0927-0256(13)00585-5/h0105http://refhub.elsevier.com/S0927-0256(13)00585-5/h0105http://refhub.elsevier.com/S0927-0256(13)00585-5/h0105http://refhub.elsevier.com/S0927-0256(13)00585-5/h0110http://refhub.elsevier.com/S0927-0256(13)00585-5/h0110http://refhub.elsevier.com/S0927-0256(13)00585-5/h0115http://refhub.elsevier.com/S0927-0256(13)00585-5/h0115http://refhub.elsevier.com/S0927-0256(13)00585-5/h0115http://refhub.elsevier.com/S0927-0256(13)00585-5/h0120http://refhub.elsevier.com/S0927-0256(13)00585-5/h0120http://refhub.elsevier.com/S0927-0256(13)00585-5/h0120http://refhub.elsevier.com/S0927-0256(13)00585-5/h0125http://refhub.elsevier.com/S0927-0256(13)00585-5/h0125http://refhub.elsevier.com/S0927-0256(13)00585-5/h0130http://refhub.elsevier.com/S0927-0256(13)00585-5/h0130http://refhub.elsevier.com/S0927-0256(13)00585-5/h0135http://refhub.elsevier.com/S0927-0256(13)00585-5/h0140http://refhub.elsevier.com/S0927-0256(13)00585-5/h0145http://refhub.elsevier.com/S0927-0256(13)00585-5/h0145http://refhub.elsevier.com/S0927-0256(13)00585-5/h0150http://refhub.elsevier.com/S0927-0256(13)00585-5/h0150http://refhub.elsevier.com/S0927-0256(13)00585-5/h0150http://refhub.elsevier.com/S0927-0256(13)00585-5/h0155http://refhub.elsevier.com/S0927-0256(13)00585-5/h0155http://refhub.elsevier.com/S0927-0256(13)00585-5/h0160http://refhub.elsevier.com/S0927-0256(13)00585-5/h0160http://refhub.elsevier.com/S0927-0256(13)00585-5/h0165http://refhub.elsevier.com/S0927-0256(13)00585-5/h0165http://refhub.elsevier.com/S0927-0256(13)00585-5/h0165http://refhub.elsevier.com/S0927-0256(13)00585-5/h0170http://refhub.elsevier.com/S0927-0256(13)00585-5/h0170http://refhub.elsevier.com/S0927-0256(13)00585-5/h0175http://refhub.elsevier.com/S0927-0256(13)00585-5/h0175http://refhub.elsevier.com/S0927-0256(13)00585-5/h0180http://refhub.elsevier.com/S0927-0256(13)00585-5/h0180http://refhub.elsevier.com/S0927-0256(13)00585-5/h0185http://refhub.elsevier.com/S0927-0256(13)00585-5/h0190http://refhub.elsevier.com/S0927-0256(13)00585-5/h0190http://refhub.elsevier.com/S0927-0256(13)00585-5/h0195http://refhub.elsevier.com/S0927-0256(13)00585-5/h0195http://refhub.elsevier.com/S0927-0256(13)00585-5/h0200http://refhub.elsevier.com/S0927-0256(13)00585-5/h0200http://refhub.elsevier.com/S0927-0256(13)00585-5/h0200http://refhub.elsevier.com/S0927-0256(13)00585-5/h0205http://refhub.elsevier.com/S0927-0256(13)00585-5/h0210http://refhub.elsevier.com/S0927-0256(13)00585-5/h0210http://refhub.elsevier.com/S0927-0256(13)00585-5/h0215http://refhub.elsevier.com/S0927-0256(13)00585-5/h0215http://refhub.elsevier.com/S0927-0256(13)00585-5/h0220http://refhub.elsevier.com/S0927-0256(13)00585-5/h0225http://refhub.elsevier.com/S0927-0256(13)00585-5/h0225http://refhub.elsevier.com/S0927-0256(13)00585-5/h0230http://refhub.elsevier.com/S0927-0256(13)00585-5/h0235http://refhub.elsevier.com/S0927-0256(13)00585-5/h0240http://refhub.elsevier.com/S0927-0256(13)00585-5/h0245http://refhub.elsevier.com/S0927-0256(13)00585-5/h0245http://refhub.elsevier.com/S0927-0256(13)00585-5/h0250http://refhub.elsevier.com/S0927-0256(13)00585-5/h0250http://refhub.elsevier.com/S0927-0256(13)00585-5/h0255http://refhub.elsevier.com/S0927-0256(13)00585-5/h0255http://refhub.elsevier.com/S0927-0256(13)00585-5/h0260http://refhub.elsevier.com/S0927-0256(13)00585-5/h0260http://refhub.elsevier.com/S0927-0256(13)00585-5/h0260http://refhub.elsevier.com/S0927-0256(13)00585-5/h0265http://refhub.elsevier.com/S0927-0256(13)00585-5/h0265http://refhub.elsevier.com/S0927-0256(13)00585-5/h0270http://refhub.elsevier.com/S0927-0256(13)00585-5/h0270http://refhub.elsevier.com/S0927-0256(13)00585-5/h0315http://refhub.elsevier.com/S0927-0256(13)00585-5/h0315http://refhub.elsevier.com/S0927-0256(13)00585-5/h0280http://refhub.elsevier.com/S0927-0256(13)00585-5/h0280http://refhub.elsevier.com/S0927-0256(13)00585-5/h0285http://refhub.elsevier.com/S0927-0256(13)00585-5/h0285http://refhub.elsevier.com/S0927-0256(13)00585-5/h0290http://refhub.elsevier.com/S0927-0256(13)00585-5/h0290http://refhub.elsevier.com/S0927-0256(13)00585-5/h0290http://refhub.elsevier.com/S0927-0256(13)00585-5/h0295http://refhub.elsevier.com/S0927-0256(13)00585-5/h0295http://refhub.elsevier.com/S0927-0256(13)00585-5/h0300http://refhub.elsevier.com/S0927-0256(13)00585-5/h0305http://refhub.elsevier.com/S0927-0256(13)00585-5/h0305http://refhub.elsevier.com/S0927-0256(13)00585-5/h0310http://refhub.elsevier.com/S0927-0256(13)00585-5/h0310http://refhub.elsevier.com/S0927-0256(13)00585-5/h0310http://refhub.elsevier.com/S0927-0256(13)00585-5/h0310http://refhub.elsevier.com/S0927-0256(13)00585-5/h0305http://refhub.elsevier.com/S0927-0256(13)00585-5/h0305http://refhub.elsevier.com/S0927-0256(13)00585-5/h0300http://refhub.elsevier.com/S0927-0256(13)00585-5/h0295http://refhub.elsevier.com/S0927-0256(13)00585-5/h0295http://refhub.elsevier.com/S0927-0256(13)00585-5/h0295http://refhub.elsevier.com/S0927-0256(13)00585-5/h0290http://refhub.elsevier.com/S0927-0256(13)00585-5/h0290http://refhub.elsevier.com/S0927-0256(13)00585-5/h0285http://refhub.elsevier.com/S0927-0256(13)00585-5/h0285http://refhub.elsevier.com/S0927-0256(13)00585-5/h0280http://refhub.elsevier.com/S0927-0256(13)00585-5/h0280http://refhub.elsevier.com/S0927-0256(13)00585-5/h0315http://refhub.elsevier.com/S0927-0256(13)00585-5/h0315http://refhub.elsevier.com/S0927-0256(13)00585-5/h0270http://refhub.elsevier.com/S0927-0256(13)00585-5/h0270http://refhub.elsevier.com/S0927-0256(13)00585-5/h0265http://refhub.elsevier.com/S0927-0256(13)00585-5/h0265http://refhub.elsevier.com/S0927-0256(13)00585-5/h0265http://refhub.elsevier.com/S0927-0256(13)00585-5/h0260http://refhub.elsevier.com/S0927-0256(13)00585-5/h0260http://refhub.elsevier.com/S0927-0256(13)00585-5/h0255http://refhub.elsevier.com/S0927-0256(13)00585-5/h0250http://refhub.elsevier.com/S0927-0256(13)00585-5/h0250http://refhub.elsevier.com/S0927-0256(13)00585-5/h0250http://refhub.elsevier.com/S0927-0256(13)00585-5/h0245http://refhub.elsevier.com/S0927-0256(13)00585-5/h0245http://refhub.elsevier.com/S0927-0256(13)00585-5/h0240http://refhub.elsevier.com/S0927-0256(13)00585-5/h0235http://refhub.elsevier.com/S0927-0256(13)00585-5/h0230http://refhub.elsevier.com/S0927-0256(13)00585-5/h0225http://refhub.elsevier.com/S0927-0256(13)00585-5/h0225http://refhub.elsevier.com/S0927-0256(13)00585-5/h0220http://refhub.elsevier.com/S0927-0256(13)00585-5/h0215http://refhub.elsevier.com/S0927-0256(13)00585-5/h0215http://refhub.elsevier.com/S0927-0256(13)00585-5/h0210http://refhub.elsevier.com/S0927-0256(13)00585-5/h0210http://refhub.elsevier.com/S0927-0256(13)00585-5/h0205http://refhub.elsevier.com/S0927-0256(13)00585-5/h0200http://refhub.elsevier.com/S0927-0256(13)00585-5/h0200http://refhub.elsevier.com/S0927-0256(13)00585-5/h0195http://refhub.elsevier.com/S0927-0256(13)00585-5/h0195http://refhub.elsevier.com/S0927-0256(13)00585-5/h0190http://refhub.elsevier.com/S0927-0256(13)00585-5/h0190http://refhub.elsevier.com/S0927-0256(13)00585-5/h0185http://refhub.elsevier.com/S0927-0256(13)00585-5/h0180http://refhub.elsevier.com/S0927-0256(13)00585-5/h0180http://refhub.elsevier.com/S0927-0256(13)00585-5/h0175http://refhub.elsevier.com/S0927-0256(13)00585-5/h0175http://refhub.elsevier.com/S0927-0256(13)00585-5/h0170http://refhub.elsevier.com/S0927-0256(13)00585-5/h0170http://refhub.elsevier.com/S0927-0256(13)00585-5/h0165http://refhub.elsevier.com/S0927-0256(13)00585-5/h0165http://refhub.elsevier.com/S0927-0256(13)00585-5/h0160http://refhub.elsevier.com/S0927-0256(13)00585-5/h0160http://refhub.elsevier.com/S0927-0256(13)00585-5/h0155http://refhub.elsevier.com/S0927-0256(13)00585-5/h0155http://refhub.elsevier.com/S0927-0256(13)00585-5/h0150http://refhub.elsevier.com/S0927-0256(13)00585-5/h0150http://refhub.elsevier.com/S0927-0256(13)00585-5/h0145http://refhub.elsevier.com/S0927-0256(13)00585-5/h0145http://refhub.elsevier.com/S0927-0256(13)00585-5/h0140http://refhub.elsevier.com/S0927-0256(13)00585-5/h0135http://refhub.elsevier.com/S0927-0256(13)00585-5/h0130http://refhub.elsevier.com/S0927-0256(13)00585-5/h0125http://refhub.elsevier.com/S0927-0256(13)00585-5/h0125http://refhub.elsevier.com/S0927-0256(13)00585-5/h0120http://refhub.elsevier.com/S0927-0256(13)00585-5/h0120http://refhub.elsevier.com/S0927-0256(13)00585-5/h0115http://refhub.elsevier.com/S0927-0256(13)00585-5/h0115http://refhub.elsevier.com/S0927-0256(13)00585-5/h0110http://refhub.elsevier.com/S0927-0256(13)00585-5/h0110http://refhub.elsevier.com/S0927-0256(13)00585-5/h0105http://refhub.elsevier.com/S0927-0256(13)00585-5/h0105http://refhub.elsevier.com/S0927-0256(13)00585-5/h0105http://refhub.elsevier.com/S0927-0256(13)00585-5/h0105http://refhub.elsevier.com/S0927-0256(13)00585-5/h0100http://refhub.elsevier.com/S0927-0256(13)00585-5/h0100