Molecular simulations of the carbon nanotubes intramolecular junctions under mechanical loading

Computational Materials Science 82 (2014) 503–509

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Molecular simulations of the carbon nanotubes intramolecular junctions under mechanical loading Sanjib C. Chowdhury a,⇑, Bazle Z. (Gama) Haque a,d, John W. Gillespie Jr. a,b,c,d a

Center for Composite Materials (UD-CCM), University of Delaware, Newark, DE 19716, USA Department of Materials Science & Engineering, University of Delaware, Newark, DE 19716, USA c Department of Civil & Environmental Engineering, University of Delaware, Newark, DE 19716, USA d Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA b

a r t i c l e

i n f o

Article history: Received 5 August 2013 Received in revised form 7 October 2013 Accepted 20 October 2013 Available online 12 November 2013 Keywords: CNT junction Molecular dynamics simulation Mechanical loading

a b s t r a c t In this paper, mechanical responses of the carbon nanotubes (CNTs) intramolecular junctions (IMJs) under three generic modes of mechanical loadings – tension, compression, and torsion have been studied using molecular dynamics simulations. (5,5)-(10,0), (7,7)-(14,0), (10,10)-(20,0) armchair–zigzag and (8,0)-(6,0) zigzag–zigzag IMJs have been simulated by connecting two constituent CNTs with pentagon and heptagon rings. Classical molecular dynamics based on the velocity-Verlet algorithm has been used to solve the Newtonian equation of motion and carbon–carbon interaction in the CNT has been modeled by the Brenner potential. Mechanical properties, particularly stiffness and maximum force/torque and failure modes for different loading conditions are studied. Simulation results show that stiffness of the IMJ falls between those of the constituent CNTs. Compressive failure load of the IMJ is lower than either of the constituent CNTs. However, failure loads and damage modes of the IMJs under tensile and torsional loadings depend on the transition region in the IMJs. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction

d¼

Carbon nanotubes (CNTs) can be pictured as being formed by rolling a graphite sheet into a cylinder. Various geometrical structures can be formed depending on the orientation of the rolling axis. Two extreme orientations are called armchair and zigzag nanotubes. An armchair nanotube is formed when the sheet is rolled while keeping the rolling axis perpendicular to one of the hexagonal sides of the graphite lattice. In contrast, a zigzag nanotube is formed when the rolling axis is parallel to one hexagonal side. The rotational directions, along with the rotation axis for armchair and zigzag nanotubes, are illustrated in Fig. 1. All other intermediate orientations will create other configurations called chiral nanotubes. CNT structure is described by a chiral vector which is defined as [1]:

Ch ¼ na1 þ ma2

ð1Þ

where a1 and a2 are two unit vectors in a 2D graphite lattice. n and m are two integers called the CNT index. A particular integer pair (n, m) defines a chiral vector Ch. The sheet is rolled in such a way that CNT axis becomes perpendicular to chiral vector. Length of the chiral vector defines the circumferential length of the CNT cross-section. Therefore CNT diameter can be expressed as: ⇑ Corresponding author. Tel.: +1 302 831 6931. E-mail address: [email protected] (S.C. Chowdhury). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.10.025

jCh j

p

¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a n2 þ m2 þ nm

p

¼

pffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3aCC n2 þ m2 þ nm

p

ð2Þ

where d is CNT diameter, a is unit vector length and aC–C is C–C bond length. C–C bond length is usually in the order of 0.142 nm. It is obvious that with an increase in n and m values, CNT diameter will increase. If n – 0, m = 0 or (n, 0), the CNT becomes zigzag. If n = m (or (n, n)), the CNT becomes armchair. In all other cases the CNT becomes chiral. Depending on the electrical and thermal properties, CNTs are classified into three categories – metallic, semimetallic and semiconducting. The (n, n) nanotubes are metallic while the (n, m) tubes are semimetallic if the difference between n and m (i.e., n–m) is a nonzero multiple of three, and semiconducting otherwise [1]. Connecting metallic and semiconducting CNTs, IMJ (i.e., diode) could be produced as new building blocks of nanodevices. Experimental evidence of IMJs has already been reported. IMJs can be of different shapes – Y, T, X, bent or straight. Single-walled CNT junctions are frequently observed in single-walled carbon nanotubes (SWNTs) samples produced by chemical vapor deposition (CVD) [2–4], laser ablation [5,6] and arc discharge [7] methods. Some research groups have also developed synthesis method dedicated to CNT junctions synthesis. For example, Fu et al. [8] have prepared Y-junctions CNTs by direct pyrolysis of methane without any catalyst using microwave CVD method. Deepak et al. [9] have prepared Y- and T-junctions from pyrolysis of thiophene and organometallic–thiophene

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Zigzag (6,,0)

Ch

a1

(4,2) (3,3)

a2

Fig. 1. Schematic diagram showing the orientation of zigzag, armchair and chiral CNT. (Rolling axis is perpendicular to the corresponding chiral vector.)

mixtures. Li et al. [10] have produced Y-junction CNTs from thiophene precursor and Co/Mg or Co/Ca nitrates catalysts using the CVD method. Yao et al. [11] reported a well-controlled synthesis of the SWNT/SWNT straight junctions by a temperature-mediated CVD method. Moreover, the SWNT/SWNT junctions can also be produced experimentally by connecting different SWNTs by chemical functionalization [12], electron beam welding [13] or current welding [14]. There are several works on IMJs mainly focusing on their atomic structural and electrical properties. Saito et al. [15] have studied tunneling conductance of IMJs and predicted that these could become one of the smallest semiconductor devices. Treboux et al. [16] have investigated electronic properties of armchair-zigzag IMJs joined linearly (i.e., straight IMJ) and reported that such junction has good rectifying behavior. Chico et al. [17] have studied electronic structure of the non-linear (bent) IMJ and predicted that these junctions could be used as the building blocks of nanoscale electronic devices made entirely of carbon. Rochefort and Avouris [18] have investigated the length effect of metal-semiconductor IMJs and suggested that the (5,5)-(10,0) CNTs junction could behave as an intrinsic diode for length as small as 4 nm. Lambin and Meunier [19] have studied structural properties of the IMJs calculating their electronic energy and comparing to that of the isolated constituent nanotubes. Studies on the mechanical characterization of the IMJs are very limited [20–22]. Kang et al. [20] have investigated the buckling

behavior of IMJs using both molecular dynamics (MD) simulations and finite element analysis under compressive loading. They reported that critical compressive strain of the IMJs is dependent upon the length, radial dimensions and insensitive to the nanotube chirality. Li et al. [21] have studied the mechanical response of the IMJs under axial compressive loading using MD simulations. They have reported that under compressive loading the buckling modes of the junctions may transfer from shell buckling to column buckling with increase in the length and compared to the constituent CNTs, CNT junction has a lower critical aspect ratio at which this transition occurs. Recently, Kinoshita et al. [22] have conducted first-principles density functional theory calculations of (8,0)-(6,0) IMJ and reported that presence of heptagon–pentagon pair reduces the IMJ modulus, strength and elongation. Numerical simulations for the mechanical characterization of IMJs under tensile and torsional loadings have not been studied in the literature. In this paper, we will investigate the mechanical responses of the (5,5)-(10,0), (7,7)-(14,0), (10,10)-(20,0) metal-semiconductor and (8,0)-(6,0) semimetallic–semiconductor uniaxial straight (i.e., linear) IMJs under three generic modes of mechanical loadings – tension, compression, and torsion using MD simulations and will compare with those of the constituent CNTs. For molecular simulations we use our in-house code [23–25].

2. Model development of the CNT junction Uniaxial metal-semiconductor IMJs consisting of a (n, n) armchair and a (2n, 0) zigzag CNT. pffiffiffi Difference pffiffiffi in the radii of the (n, n) and (2n, 0) CNTs is DR ¼ 3ac—c nð2  3Þ=2p, where aC–C is the C–C bond length. In order to develop a model for the metal-semiconductor junction, two cylinders of the constituent CNTs are positioned axially and the gap between the CNTs is connected with alternating pentagon and heptagon rings (Fig. 2a). Vertical gap h between the two CNTs are adjusted such that length of the connecting bond becomes equal to the C–C bond length. In order to develop a model for the (8,0)-(6,0) semimetallic–semiconductor junction, two cylinders of the constituent CNTs are positioned axially. Two diametrically opposite hexagons of the (6,0) CNT near the transition (i.e., connecting) region are converted into heptagons and the gap between the CNTs is connected by connecting the neighboring atoms of the two CNTs (Fig. 3a). This gives two pairs of pentagon and heptagon in the (8,0)-(6,0) IMJ. Finally the molecular models of the junctions have been relaxed to get the optimum configuration. Fig. 2b shows a (10,10)-(20,0) junction and Fig. 3b

Armchair Structure

Connecting Region

h

7 5

7

5

7

5

7

Zigzag Structure

(a)

(b)

Fig. 2. (a) Schematic of armchair-zigzag nanotubes connection and (b) a (10,10)-(20,0) IMJ.

5 7

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505

Zigzag Structure

7

Connecting Region

5 Zigzag Structure

(a)

(b)

Fig. 3. (a) Schematic of zigzag–zigzag nanotubes connection and (b) a (8,0)-(6,0) IMJ.

Lo

(a) Tension

(b) Compression

Atomistic models with boundary and loading conditions of the tension, compression and torsion tests are shown in Fig. 4. Each incremental displacement (axial displacement in tension and compression, angular in torsion) of the CNT is followed by 1000 MD steps to achieve equilibration of the system. During the equilibration period, end atoms are kept fixed in their original plane. This type of boundary condition creates radial and hoop stresses in axial loading and axial stress in torsional loading in the vicinity of the ends. A thorough study of various boundary conditions has been reported in [29]. Results showed that these types of boundary conditions do not significantly affect the CNT failure loads and damage modes [29]. A MD time step of 0.2 fs (femto-second) is considered to solve the equations of motion using velocity-Verlet algorithm and the temperature of the system is kept constant at 300 K by velocity scaling. Applied axial displacement rate is 15 m/s and angular displacement rate is 8.7 Grad/s. At a particular displacement, axial force F is calculated by summing up the total inter atomic force of the end atoms in the axial direction. Axial deformation is calculated using the following formula.

x ¼ DL ¼ L  L 0

ð3Þ

where x = DL is the axial deformation, L0 is the initial gage length including the constituent CNTs and transition region (Fig. 4a), and L is the current gage length. In torsional loading, torque at a certain angle of twist is calculated by summing up the torque experienced by all of the rigidly moved end atoms, which can be expressed as:

(c) Torsion Fig. 4. Atomistic model of CNT under different monotonic loading conditions.

shows a (8,0)-(6,0) junction developed following the procedure described above. In the molecular model of the junctions, constituent CNTs of almost equal length have been considered so that the connecting region can be placed at mid-length of the IMJs.

T¼

k X ðr  Fy þ r  Fx Þ

ð4Þ

i¼1

where k is the number of rigidly moved end atoms, r is the position vector of the atom, Fx and Fy are the x- and y- component of force of the atom aligned with the geometric X- and Y-axis (Z-axis is parallel to the CNT axis). 4. Results and discussion

3. Molecular dynamics simulation method Classical MD based on velocity-Verlet algorithm [26] has been used. Interatomic interaction is modeled by the Brenner potential [27]. Details of this potential with corresponding parameters are reported elsewhere [23–25]. In the Brenner potential, the cut-off function f(r) introduces a dramatic increase in the interatomic force near the bond-breaking length. Value of the cut-off parameter R1 = 0.20 nm is used in order to avoid overestimation of the force required for bond breaking [23–25,28].

MD simulations of (5,5)-(10,0), (7,7)-(14,0), (10,10)-(20,0), and (8,0)-(6,0) IMJs of length 6 nm along with their constituent isolated CNTs of the same length have been subjected to three load cases – tension, compression and torsion. In another study [29] we have reported that, SWNT length does not affect the tensile, compressive and torsional stiffness and tensile strength. But it affects the compressive and torsional strength which are related to structural stability. We expect similar length effect on IMJ properties. This is an important topic for future studies. For all

S.C. Chowdhury et al. / Computational Materials Science 82 (2014) 503–509

200

12

150

10

Torque, T, nN-nm.

Axial force, F, nN.

506

100

50

0 (5,5) CNT (10,0) CNT (5,5)-(10,0) IMJ

-50

-100 -1.0

-0.5

0

0.5

1.0

8

6

4 (5,5) CNT (10,0) CNT (5,5)-(10,0) IMJ

2

1.5

0

2.0

0

25

50

75

100

Axial deformation, ΔL, nm.

Angle of twist, θ, deg.

(a)

(b)

125

150

200

18

150

15

Torque, T, nN-nm.

Axial force, F, nN.

Fig. 5. Variations of (a) axial force with axial deformation and (b) torque with angle of twist for (5,5)-(10,0) IMJ and its constituent isolated CNTs.

100

50

0 (7,7) CNT (14,0) CNT (7,7)-(14,0) IMJ

-50

-100 -1.0

-0.5

0

0.5

1.0

12

9

6 (7,7) CNT (14,0) CNT (7,7)-(14,0) IMJ

3

1.5

0

2.0

0

20

40

60

80

Axial deformation, ΔL, nm.

Angle of twist, θ, deg.

(a)

(b)

100

120

200

30

150

25

Torque, T, nN-nm.

Axial force, F, nN.

Fig. 6. Variations of (a) axial force with axial deformation and (b) torque with angle of twist for (7,7)-(14,0) IMJ and its constituent isolated CNTs.

100 50 0 (10,10) CNT (20,0) CNT (10,10)-(20,0) IMJ

-50 -100 -1.0

-0.5

0

0.5

1.0

20 15 10 (10,10) CNT (20,0) CNT (10,10)-(20,0) IMJ

5

1.5

2.0

0

0

15

30

45

60

Axial deformation, Δ L, nm.

Angle of twist, θ, deg.

(a)

(b)

75

90

Fig. 7. Variations of (a) axial force with axial deformation and (b) torque with angle of twist for (10,10)-(20,0) IMJ and its constituent isolated CNTs.

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12

200 (6,0) CNT (8,0) CNT (8,0)-(6,0) IMJ

100 50 0

8 6 4

-50 -100 -1.0

(6,0) CNT (8,0) CNT (8,0)-(6,0) IMJ

10

Torque, T, nN-nm.

Axial force, F, nN.

150

2

-0.5

0

0.5

1.0

1.5

0

2.0

0

50

100

150

200

Axial deformation, Δ L, nm.

Angle of twist, θ , deg.

(a)

(b)

250

300

Fig. 8. Variations of (a) axial force with axial deformation and (b) torque with angle of twist for (8,0)-(6,0) IMJ and its constituent isolated CNTs.

Table 1 Linear stiffness (LS) and non-linear coefficient (NLC) of IMJs and their constituent isolated CNTs. T

T

Type

Tensile LS kA1 (nN/nm)

Tensile NLC kA2 (nN/nm2)

Comp.LS kA1 (nN/nm)

Comp. NLC kA2 (nN/nm2)

Torsional LS kT1 (nN nm/deg)

Torsional NLC kT2 (nN nm/deg2)

(5,5) Armchair CNT (10,0) Zigzag CNT (5,5)-(10,0) IMJ (7,7) Armchair CNT (14,0) Zigzag CNT (7,7)-(14,0) IMJ (10,10) Armchair CNT (20,0) Zigzag CNT (10,10)-(20,0) IMJ (6,0) Zigzag CNT (8,0) Zigzag CNT (8,0)-(6,0) IMJ

95 103 98 135 147 139 195 215 200 59 83 67

26 29 27 38 41 39 55 62 55 17 24 20

99 101 100 136 161 139 193 238 199 61 88 67

15 08 11 19 14 22 21 62 61 0 3 1

0.0659 0.1068 0.0809 0.1868 0.2896 0.2246 0.5557 0.8373 0.6580 0.0242 0.0554 0.0340

5.0  105 4.7  105 5.9  105 17.4  105 15.1  105 18.7  105 72.7  105 52.2  105 63.4  105 1.14  105 2.41  105 3.33  105

C

C

Table 2 Ratio of the non-linear coefficient to the linear stiffness of IMJs and their constituent isolated CNTs. T

T

Type

Tension ðkA2 =kA1 Þ (%)

Compression ðkA2 =kA1 Þ (%)

Torsion ðkT2 =kT1 Þ (%)

(5,5) Armchair CNT (10,0) Zigzag CNT (5,5)-(10,0) IMJ (7,7) Armchair CNT (14,0) Zigzag CNT (7,7)-(14,0) IMJ (10,10) Armchair CNT (20,0) Zigzag CNT (10,10)-(20,0) IMJ (6,0) Zigzag CNT (8,0) Zigzag CNT (8,0)-(6,0) IMJ

27 28 28 28 28 28 28 29 28 29 29 30

15 8 11 14 9 16 11 26 31 0 3 1

<1 <1 <1 <1 <1 <1 <1 <1 <1 <1 <1 <1

isolated and junction CNTs, force versus axial deformation and torque versus angle of twist curves have been plotted and damage modes of failure have been investigated. From the force-deformation and torque-angle of twist curves, corresponding stiffness and maximum force/torque have been determined. Figs. 5–8 show the force-deformation and torque-angle of twist curves for the (5,5)-(10,0), (7,7)-(14,0), (10,10)-(20,0), and (8,0)(6,0) IMJs along with their constituent isolated CNTs. In the force versus axial deformation curves, tensile force and deformation are designated as positive while compressive force and

C

C

deformation are designated as negative. Compressive force-displacement and torsional torque-angle of twist curves have almost linear behavior up to failure. However, tensile forcedisplacement curves show significant nonlinearity. To consider both the linear and non-linear behavior, the following second order equations are used to fit these curves up to the failure.

F ¼ kA1 DL  kA2 ðDLÞ2 ; T ¼ kT1 h  kT2 h2 ;

for axial loading

ð5aÞ

for torsional loading

ð5bÞ

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Table 3 Maximum force, torque of IMJs with their constituent isolated CNTs and failure mode location in the IMJs.

*

Type

Max. tensile force (nN)

IMJ tensile failure location

Max. comp. force (nN)

IMJ comp. failure location

Max. torque (nN nm)

IMJ torsional failure location

(5,5) Armchair CNT (10,10) Zigzag CNT (5,5)-(10,0) IMJ (7,7) Armchair CNT (14,0) Zigzag CNT (7,7)-(14,0) IMJ (10,10) Armchair CNT (20,0) Zigzag CNT (10,10)-(20,0) IMJ (6,0) Zigzag CNT (8,0) Zigzag CNT (8,0)-(6,0) IMJ

83.7 90.0 83.7 (0%)* 117.7 125.8 117.7 (0%)* 167.5 177.8 167.5 (0%)* 51.0 70.4 49.4 (3%)*

– – End tearing at (5,5) CNT – – End tearing at (7,7) CNT – – End tearing at (10,10) CNT – – Tearing at transition

53.7 60.2 48.4 62.3 70.2 49.1 67.5 73.4 49.8 36.1 54.9 32.7

– – Buckling – – Buckling – – Buckling – – Buckling

6.2 7.6 6.4 (+3%)* 10.9 13.0 11.5 (+6%)* 21.1 25.4 21.1 (0%)* 4.6 5.7 3.7 (20%)*

– – Buckling – – Buckling – – Buckling – – Buckling

*

(10%)

(21%)*

(36%)*

(10%)*

at transition

at transition

at transition

at transition

at (5,5) CNT

at (7,7) CNT

at (10,10) CNT

at transition

Percentage value is calculated based on the corresponding value of the smallest diameter CNT. + sign indicates increase,  sign indicates reduction.

where, F is axial force, DL is axial deformation, T is torque, h is angle of twist. kA1 and kA2 are linear axial stiffness and non-linear axial coefficient while kT1 and kT2 are linear torsional stiffness and nonlinear torsional coefficient, respectively. In order to determine the stiffness, curves presented in Figs. 5–8 have been fitted with Eq. (5) up to failure. Table 1 summarizes the linear stiffness and non-linear coefficients of all IMJs along with the individual constituent CNTs. In addition, the ratios of the non-linear coefficient to the linear stiffness are also presented in Table 2 to assess the degree of nonlinearity in the response. Axial and torsional linear stiffness of the IMJs is bounded by the stiffness of the constituent CNTs. Ratio of the tensile non-linear coefficient   T T to the tensile linear stiffness kA2 =kA1 in the range of 27%–30% signifies non-linearity under tensile loading, however, this ratio for torsion (kT2/kT1) is less than 1% which signifies linear behavior under torsion. The compressive behavior shows a range of   C C response where the ratio of kA2 =kA1 varies from linear to significant non-linearity depending on the specific IMJ configuration.

(a)

(b)

(c)

Fig. 9. Snapshot of tensile failure modes. (a) End block tearing of (10,10)-(20,0) IMJ. (b) Failure at the transition region of the (8,0)-(6,0) CNT. (c) Breaking of the critical bond at the transition region of the (8,0)-(6,0) IMJ.

Failure force and failure torque of the IMJs and constituent CNTs are presented in Table 3. Percentage reductions in the IMJs failure load and failure location in the IMJs are also presented in Table 3. Note that since the diameters of the constituent CNTs in the IMJs are different, we do not calculate failure stress. Tensile and torsional failure load of the (5,5)-(10,0), (7,7)-(14,0), and (10,10)(20,0) IMJs are close to that of the smallest diameter constituent CNT. However, the tensile and torsional failure load of the (8,0)(6,0) IMJ are 3% and 10% lower than those of the smallest diameter constituent CNT. Bonds in the transition region of the relaxed (8,0)(6,0) IMJ are found to be highly stretched. These stretched bonds are mainly responsible for lower tensile failure load and torsional failure torque of the (8,0)-(6,0) IMJ. Compressive failure load of all IMJs are lower than those of the constituent CNTs. IMJs compressive failure loads are 10%–36% less than those of the smallest diameter constituent CNTs. Low compressive load carrying capacity of IMJs may be due the eccentric loading at the tapered transition region which initiates buckling. It should be mentioned that presence of pentagon-heptagon rings in isolated CNT in the form of Stone–Wales (SW) defect degrades CNTs axial and torsional stiffness and strength [23–25,30,31]. Failure modes of the IMJs and their constituent isolated CNTs have been checked. For tensile loading, end block tearing occurs for all isolated constituent CNTs and all IMJs except (8,0)-(6,0) IMJ. In the (5,5)-(10,0), (7,7)-(14,0), (10,10)-(20,0) IMJs, end block tearing occurs in the smaller diameter CNT (Fig. 9a) while in the (8,0)-(6,0) IMJ failure occurs at the transition region (Fig. 9b). Kinoshita et al. [22] have also reported (8,0)-(6,0) IMJ failure at the transition region. This indicates presence of pentagon– heptagon rings does not weaken the (5,5)-(10,0), (7,7)-(14,0), (10,10)-(20,0) IMJs but it does weaken the (8,0)-(6,0) IMJ. In the (5,5)-(10,0), (7,7)-(14,0), (10,10)-(20,0) IMJs transition of diameter is smooth, no bonds in the transition region in the relaxed IMJs are stretched. However, in the relaxed (8,0)-(6,0) IMJ some bonds in the transition region are highly stretched due to the presence of pentagon-heptagon rings. For this reason tensile failure occurs at the transition region in the (8,0)-(6,0) IMJ. These stretched bonds (i.e., critical bonds) are associated with the pentagon and heptagon. Fig. 9c shows critical bond breaking (dotted line) in the transition region of (8,0)-(6,0) IMJ which initiates IMJ tensile failure. Under compressive loading, shell type buckling with peanut shape cross-section at the transition region (Fig. 10) is observed for all IMJs. Shell type buckling is also observed for the constituent CNTs. This peanut shape shell type buckling is basically due to low aspect ratio [25,32]. At the torsional loading, buckling occurs at the lower diameter CNT in the (5,5)-(10,0), (7,7)-(14,0), (10,10)-(20,0) IMJs (Fig. 11a) while buckling occurs at the transition region in the (8,0)-(6,0) IMJ (Fig. 11b).

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509

MD simulations under three load cases – tension, compression and torsion. IMJs have been simulated by connecting two constituent CNTs with the pentagon and heptagon rings. Simulation results show that axial (i.e., tensile and compressive) and torsional stiffness of the IMJ fall within the bounds of the constituent CNTs. Compressive failure loads of the IMJs are lower than those of the constituent CNTs due to eccentric loading created by the transition (i.e., connecting) region that reduced buckling loads. However, tensile failure load and torsional failure torque of the IMJs depends on the transition region morphology. IMJ with weak transition region (i.e., transition region with stretched bonds at no load condition) has lower tensile failure load and torsional failure torque compared to its constituent CNTs. Regarding failure modes, shell buckling occurs at the transition region in all IMJs in compressive loading. In tensile and torsional loadings, failure modes depend on the IMJs transition region morphology. Tensile and torsional failure occurs at the transition region in the IMJs with weak transition region while failure occurs at the smallest diameter CNT in all others IMJs. Reference

Fig. 10. Snapshot of shell buckling mode in compressive loading of IMJ.

(a)

(b)

Fig. 11. Snapshot of torsional failure modes. (a) (10,10)-(20,0) IMJ and (b) (8,0)(6,0) IMJ.

5. Conclusions In summary, mechanical response of uniaxial metal-semiconductor and semimetallic-semiconductor intramolecular junctions (IMJs) and their constituent isolated CNTs have been studied using

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