Radial collapse of carbon nanotubes without and with Stone–Wales defects under hydrostatic pressure

Abstract

The effects of carbon nanotube (CNT) chirality, Stone–Wales (SW) defects and defect orientation on the radial collapse and elasticity of single-walled CNTs (SWNTs) were investigated using molecular mechanics and molecular dynamics (MD) simulations. It is found that the collapse pressure (P_c) of the armchair SWNT is 13.75 times higher than that of the zigzag SWNT. Moreover, the armchair SWNT with SW defects is easier to collapse compared to the intrinsic armchair SWNT, while the zigzag SWNT with SW defects is more difficult to collapse compared to the intrinsic zigzag SWNT; the SW² defect makes P_c of SWNT (10, 10) decrease by 11.0%, while the SW⁴ defect makes P_c of SWNT (17, 0) increase by 100.0%. We introduce a model for SWNTs deformed in the radial direction according to the projection of the C–C bond along the bending direction. The model is validated for defect-free SWNTs and is then used to study the radial collapse of SWNTs with SW defects. The effect of chirality and SW defect on the radial collapse of SWNTs can be understood by the model. The strong sensitivity of radial collapse of SWNTs to chirality and SW defect can provide some guidance for high load structural applications of SWNTs.

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I Introduction

Since carbon nanotubes (CNTs) were discovered,¹ extensive experimental and theoretical studies have been made to reveal CNTs' unique physical and mechanical properties. It is well-known that the CNTs possess high axial Young's moduli (∼1 TPa),^2–4 high axial tensile strength (∼63 GPa)⁵ and high axial strain at break (∼40%).⁶ It shows that the stiffness and strength of CNTs are in the range of TPa and GPa, respectively. The fact that CNTs are extremely lightweight compared to other materials makes them potential candidates as reinforcing fibers in superstrong composites.^7–9

The mechanical properties of CNTs and CNT–polymer composites have been studied through theoretical, experimental and computational analysis.^10–12 Results reported in the recent studies have indicated that the mechanical properties obtained from experiments tend to be lower than those obtained from computational analysis.¹² Several reasons have been assigned for this disparity. On the one hand, CNTs disperse in various orientations experimentally, while CNTs in the constructed composites model usually directionally align. On the other hand, experimental processes could introduce defects into the CNTs, while computational models are based on a perfect CNT molecular material structure.¹³ Experimental observations have revealed that topological defects, such as the 5-7-7-5 Stone–Wales (SW) defects, are commonly present in CNTs.¹⁴ These local defects can alter not only the inelastic properties, but also the elastic properties of CNTs, such as Young's modulus and Poisson's ratio. Consequently, these defects may alter the longitudinal, lateral stiffness, and flexural rigidity in response to tension, torsion and bending, respectively. Because of the unique planar hexagonal structure of CNTs, topological defects can alter the deformation response and hence the elastic properties. In addition, defects can also be potential sites where an irreversible mechanical response is initiated.¹⁵

As noted above, defects in CNTs have an impact on their mechanical properties, and hence its mechanism is needed to be understood thoroughly. Recently, the degradation of mechanical properties, including axial tension and compression, of CNTs induced by defects has been well studied theoretically.^16–22 In the present paper, molecular mechanics (MM) and molecular dynamics (MD) simulations are used to investigate the effects of single-walled CNTs (SWNTs) chirality, SW defects and defect orientation on the radial collapse and elasticity of SWNTs without and with SW defects under hydrostatic pressure. The collapse pressure (P_c) of SWNTs affected by SWNT chirality, SW defect and defect orientation is specifically evaluated. What's more, we introduce a model for SWNTs with different chiralities deformed in the radial direction and apply this model to investigate their deformation characteristics and stability under hydrostatic pressure. The model is validated for defect-free SWNTs and is then used to study the collapse of SWNTs with SW defects. The model enables us to detect the chemical bonding topology unit of the chiral graphene and define the projection of C–C bond along the bending direction to evaluate the collapse of SWNTs in the radial direction. The projection is expressed in terms of bond lengths and bond angles in hexagons, pentagons or heptagons functions. The variation trend of P_c predicted for SWNTs with and without SW defects using the model is in accordance with the results of MD simulations. The effect of chirality and SW defects on the radial collapse of SWNTs can be understood by the model. The influence of SWNTs chirality and SW defects on the radial collapse of SWNTs can provide some guidance for high load structural application of SWNTs.

II Simulation methods

The simulations were carried out using a commercial software package called Materials Studio (MS) developed by Accelrys Software, Inc. MD and MM simulations were carried out on a supercell containing a SWNT using the condensed-phase optimized molecular potential for atomistic simulation studies (COMPASS) force-field method. The COMPASS force-field is a parametrized, tested and validated first ab initio force-field, which enables an accurate prediction of various gas-phase and condensed-phase properties of most of the common organic and inorganic materials.^23–26 Moreover, it has been proven to be applicable in describing the mechanical properties of CNTs.^27,28 In simulations, periodic boundary conditions were employed. MM simulations were performed to find the thermal stable morphology and achieve a conformation with minimum potential energy for all SWNTs. All MD simulations were performed in the NPT ensemble, and a fixed time step size of 1 fs was used in all cases. The Andersen thermostat method was employed to control the system at the temperature of 1 K and the interactions were determined within a cutoff distance of 9.5 Å. The SWNT was initially equilibrated at atmospheric pressure and subsequently subjected to step-wise monotonically hydrostatic pressure increments, allowing the unit cell volume to equilibrate for at least 30 ps at each step. The reduced volume ratio (V/V₀), where V and V₀ are the unit cell volumes at an applied pressure and atmospheric pressure, respectively, was measured as a function of applied hydrostatic pressure.

III Results and discussion

III.I The radial collapse of the intrinsic SWNT (10, 10)

Here, we demonstrate the existence of the shape transitions of the intrinsic SWNT under hydrostatic pressure. The simulations show that when a SWNT deforms under pressure, it undergoes two shape transitions: (1) changing from a cycle to an oval; (2) changing from an oval to collapse, as shown in Fig. 1(a). We define two critical pressures, P_m and P_c, where P_m is the pressure to make the SWNT undergo a transition from a collapsed shape to circle shape upon unloading, and P_c is the pressure to collapse the SWNT upon loading. According to the loading curve (black dash dot line) and the unloading curve (red dots line) in Fig. 1(a), we can find that the P_c and P_m of the intrinsic SWNT (10, 10) are 5.5 and 3.2 GPa, respectively. Moreover, the curve shape is a hysteresis loop.

Fig. 1 (a) Loading and unloading curves of SWNT (10, 10) as a function of hydrostatic pressure. The insets are the structures for intrinsic SWNT at different pressures. (b) Concentration profiles of the initial, elliptical and collapsed SWNT (10, 10) along the y axis.

In order to characterize the geometric deformation of the SWNT (10, 10) clearly, the concentration profiles of the initial, elliptical and collapsed SWNTs (10, 10) at 0.0001 GPa, 5.0 GPa and 5.5 GPa along the y axis are shown in Fig. 1(b), respectively. Herein, we manually placed the initial, elliptical and collapsed SWNT (10, 10) in a box with the same center of mass and orientation for comparison. The concentration profile was calculated for 3D periodic structures by computing the atom-density profile within evenly spaced slices parallel to the bc, ca and ab planes. In practice, this is equivalent to taking a, b and c components of the fractional coordinates of each atom and independently generating a plot for each component. We defined three distances of the opposite walls of the initial, elliptical and collapsed SWNT (10, 10), d₁–d₃, as shown in Fig. 1(b). As marked in Fig. 1(b), d₁ is 12.241 Å, d₂ is 10.711 Å and d₃ is 3.061 Å. The d₃ is less than 3.4 Å, which is the shortest distance of the graphite layer and almost enters the strong-adhesive-binding region of the chemical bond. So we can conclude that the SWNT (10, 10) assumes complete collapse above the critical pressure 5.5 GPa. The results are in agreement with the former experimental and simulation results.^29,30 The experimental results demonstrate that the smaller diameter SWNTs (mean diameter ∼0.8 nm) collapse at a higher pressure of 6.6 ± 0.8 GPa compared to the transitions pressure of 2.1 ± 0.2 GPa for the larger diameter SWNT (mean diameter ∼1.4 nm) material.²⁹ Our results are in the range of experimental results²⁹ and this confirms the validity of the simulation method used here.

We tracked some kinds of energies in the system to reveal the physical mechanism of the collapse of SWNT (10, 10), as shown in Table 1, where the total energy consists of the internal energy and the non-bond energy which consists of the van der Waal (vdW) energy and electrostatic energy. Herein, the electrostatic energy of the intrinsic SWNTs is zero. Upon loading, the external pressure makes the total energy of the system increase and the increment of the internal energy is larger than the decrement of the vdW energy. The increment of the internal energy indicates that there exists the stress on the laterals of SWNTs due to the structure deformation of SWNTs. The decrement of the vdW energy indicates that the opposite walls of SWNTs have almost entered the strong-adhesive-binding region of the chemical bonds and the attractive vdW force exists between the opposite walls of the collapsed SWNT. When the system unloads the external pressure, the stress on the laterals of SWNTs must overcome the attractive vdW force primarily and then make the SWNT (10, 10) transition from a collapsed to circle shape. Therefore, the SWNT (10, 10) shows the hysteretic radial elasticity and its loading and unloading curve shapes are hysteresis loops.

Table 1 Energy details of cylindrical and collapsed SWNTs

Chirality	Energy (Kcal mol^−1)	Cylindrical SWNT (E1)	Collapsed SWNT (E2)	ΔE = E2 − E1
(10, 10)	Total energy	1768.819	2974.537	1205.718
	Internal energy	1256.938	2575.833	1318.895
	vdW energy	511.881	398.704	−113.177
	Electrostatic energy	0	0	0

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III.II The effect of chirality on radial collapse of SWNTs

We first calculated P_c of the perfect SWNTs with different chiralities. The initial atomic configurations of periodic SWNTs were obtained by creating the planar hexagonal carbon atom network corresponding to a (n, m) SWNT cut open axially. The corresponding chiral angle θ and diameter D_n of a SWNT with (n, m) indices could be determined using the rolling graphene model:³¹

Where B is the C–C bond length. Each C–C bond length was 1.42 Å. The total number of atoms, diameters and lengths for each SWNT are presented in Table 2.

Table 2 Total number of atoms, diameter and length of each chiral nanotube utilized in MD simulations

Type of SWNTs	C	Nanotube (D)	Length	Angle
(10,10)	1200	13.56	73.800	30.00
(12, 8)	1216	13.65	74.276	23.43
(13, 7)	1216	13.76	74.884	20.18
(14, 5)	1164	13.36	72.670	14.71
(15, 4)	1204	13.58	73.908	11.52
(17, 0)	1156	13.31	72.420	0.00

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The chirality dependence of SWNT collapse has been studied, as shown in Fig. 2. The SWNTs with different chiralities and similar sizes were performed in the MD simulations. Fig. 2(a) shows the loading and unloading curves of the SWNTs with different chiralities as a function of applied hydrostatic pressure. We can find that except for the armchair SWNT the loading and unloading curves of SWNTs with other chiralities don't shape the hysteresis loops. This shows that the radial elasticity of the armchair SWNT is superior to that of the other chiral SWNTs. In other words, the collapse state of the SWNT (10, 10) is metastable; the collapse state of other chiral SWNTs is energetically favorable. As shown in Fig. 2(b), we can find that the P_c of SWNTs are as follows: P_c (10, 10) > P_c (12, 8) > P_c (13, 7) > P_c (14, 5) > P_c (15, 4) > P_c (17, 0) (P_c (n, m) denotes P_c of the SWNTs with chirality (n, m)). It shows that the SWNT chirality has much influence on the radial collapse of SWNTs. The P_c of the armchair SWNT is 13.75 times higher than that of the zigzag SWNT and is 2.5 times higher than that of the SWNTs with other chiralities. In addition, we can find that when θ is between 11.52° and 23.43°, the chirality has little influence on the collapse of SWNT, which is in agreement with the results reported before.²⁹

Fig. 2 Effect of different chiralities on the collapse of SWNTs. (a) Loading and unloading curves of SWNTs with different chiralities as a function of applied hydrostatic pressure and (b) collapse pressure P_c as a function of the SWNT chirality.

The energy difference ΔE of the cylindrical and collapsed SWNTs with different chiralities is shown in Table 3. We can find that the increment of internal energy of the SWNTs is less than the decrement of vdW energy of the SWNTs, except for SWNT (10, 10). In other words, upon unloading, the stress on laterals of collapsed SWNTs isn't strong enough to overcome the attractive vdW force between the opposite walls of the collapsed SWNTs; so the collapsed state of the chiral SWNTs, except for SWNT (10, 10), is energetically favorable. Therefore, the loading and unloading curves of the SWNTs, except for the SWNT (10, 10), don't shape hysteresis loops. For SWNT (10, 10), it has been shown that the loading and unloading curves of SWNT (10, 10) can shape a hysteresis loop in the former section, which indicates that the collapse state of SWNT (10, 10) is metastable. In other words, the radial elasticity of SWNT (10, 10) is superior to that of SWNTs with other chiralities.

Table 3 Energy difference of cylindrical and collapsed SWNTs with different chiralities

ΔE (Kcal mol^−1)	(10, 10)	(12, 8)	(13, 7)	(14, 5)	(15, 4)	(17, 0)
ΔE(vdW energy)	−396.15	−738.032	−682.589	−719.117	−756.789	−710.265
ΔE(internal energy)	3888.388	657.833	682.445	683.452	750.759	689.504

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III.III The effect of SW defects on the radial collapse of SWNTs

Topological defects, such as SW defects, are commonly present in CNTs, which play an important role in the load transfer in CNTs. In the following section, we study the effect of SW defects on the radial collapse of SWNT (10, 10) and SWNT (17, 0) with nearly equal radius and length. A SW defect can be formed by π/2 bond rotation in a graphene network, which transforms four hexagons into two pentagons and two heptagons, as shown in Fig. 3. Fig. 3 shows illustrations of armchair SWNT (10, 10) and zigzag SWNT (17, 0) with SW defects. The SW defects with different orientations are marked by SW¹, SW², SW³ and SW⁴ (the red carbon atoms represent the structure of a SW defect). The structural phase transition to a defective phase is eventually arrested by a defect–defect interaction at high defect density. Therefore, in our study the defect density is low enough that this interaction does not significantly disturb the onset of radial collapse. As shown in Fig. 3, in the model of SWNT (10, 10), there exists a SW defect in the length of ten cycles, for SWNT (17, 0) tube there exists a SW defect in the length of six cycles. In other words, the SW defects concentrations of SWNT (10, 10) and SWNT (17, 0) are 0.041 Å⁻¹. MM simulations were performed to find the thermal stable morphology and achieve a conformation with minimum potential energy for SWNTs with SW defects.

Fig. 3 Illustrations of armchair SWNT (10, 10) and zigzag SWNT (17, 0) with SW defects; the SW defects with different orientations are marked by SW¹, SW², SW³ and SW⁴ (the red carbon atoms represent the structure of a SW defect).

The radial collapse of SWNT (10, 10) and SWNT (17, 0) with SW defects was investigated using MD simulations. Fig. 4 shows the loading and unloading curves of the SWNTs without and with defects. We can find that the P_c of the intrinsic SWNT (10, 10), SWNT (10, 10) with the SW¹ defect and SWNT (10, 10) with the SW² defect are 5.5, 5.1 and 4.9 GPa, respectively, while the P_c of the intrinsic SWNT (17, 0), SWNT (17, 0) with the SW³ defect and SWNT (17, 0) with the SW⁴ defect are 0.4, 0.5 and 0.8 GPa, respectively. The results show that the armchair SWNT with SW defects is easy to collapse compared to the intrinsic armchair SWNT, while the zigzag SWNT with SW defects is difficult to collapse compared to the intrinsic zigzag SWNT; the SW² defect makes P_c of SWNT (10, 10) decrease by 11.0%, while the SW⁴ defect makes P_c of SWNT (17, 0) increase by 100.0%, which indicates that the SW defect orientation has a large influence on the radial collapse of the SWNTs.

Fig. 4 Loading and unloading curves of the SWNTs without and with SW defects.

III.IV The mechanism of radial collapse of SWNTs without and with SW defects

The ability of radial bending of SWNTs’ walls under the external force should be determined in order to understand the mechanism of radial collapse of SWNTs without and with SW defects under hydrostatic pressure. Herein, we introduce a model to understand the mechanism of the radial deformation of SWNTs. The model enables us to detect the chemical bonding topology unit of chiral graphene and define the projection of the C–C bond along the bending direction, which can be used to evaluate the collapse of SWNTs with and without SW defects.

It is well-known that the CNTs can be visualized as seamlessly rolled-up graphene sheets (ribbons); the topology units of CNT and graphene are the hexagon ring made up of six C–C bonds. Fig. 5(a) shows the atomic surface area partition of a chiral tube. This atomic surface area partition of a chiral tube can be regarded as the bending of graphene along the bending direction. The bending ability of the graphene sheet along the bending direction should determine the radial collapse character of SWNT. In addition, we find that the orientation of the hexagon ring is different along the bending direction and the z axis of the graphene sheet. As shown in Fig. 5(b), along the bending direction of graphene, we can find the topological unit of zigzag graphene in the armchair SWNT, and the topological unit of armchair graphene in the zigzag SWNT. We can investigate the mechanism of the chirality effect on the collapse of SWNT by studying the bending ability of chiral graphene sheets along the bending direction.

Fig. 5 (a) Atomic surface area partition of a chiral tube and (b) six types of SWNTs with different chiralities along the z axis and six graphene chiralities along the bending direction (the red carbon atoms represent the structure of a hexagon ring).

Fig. 6(a) shows the structure of the chiral graphene sheet. It can be obtained by rotating armchair graphene degrees (θ) towards the right. Herein, θ is the chiral angle of graphene and the angles α, β and γ depend on the chiral angle. We define L as the projection of six C–C bonds in a hexagon ring along the bending direction.

Fig. 6 (a) The structure of the chiral graphene sheet; (b) change of L following the change of the SWNT chirality.

L = 2B(cosα + sinβ + cosγ) (2)

α = θ + 30°, β = θ, γ = 30° − θ (3)

The magnitude of L represents the obstacle that needs to be overcome in the bending process of graphene. In other words, the larger L is, the more difficult it is for graphene to bend.

With the chiral angles θ, we can calculate the project vertical to the bending direction of six C–C bonds in graphene sheet as shown in Table 4. Therefore, we can obtain the change of L following the change of the SWNT chirality, as shown in Fig. 6(b). We can find that the values of L are as follows: L(10,10) > L(12,8) > L(13,7) > L(14,5) > L(15,4) > L(17,0) (L (n,m) denotes L of SWNTs with chirality (n,m)). These results show that the zigzag SWNT is the easiest to bend and collapse, while armchair SWNT is the most difficult to bend and collapse. Moreover, a similar phenomenon is also found in other research.³² We can find that the structural transition law of SWNTs with different chiralities predicted by the model is in accordance with the results of MD simulations, which suggests that the effect of chirality on the radial collapse of SWNTs can be understood by the present model.

Table 4 Projection vertical to the bending orientation of six C–C bonds

SWNT	(17, 0)	(15, 4)	(14, 5)	(13, 7)	(12, 8)	(10, 10)
Graphene	armchair (30)	11.52	14.71	20.18	23.43	zigzag (0)
α (°)	30	41.52	44.71	50.18	53.43	60
β (°)	0	11.52	14.71	20.18	23.43	30
γ (°)	30	18.48	15.29	9.82	6.57	0
L	4.9190	5.3871	5.4789	5.5968	5.6427	5.6800

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The sp²-hybridized carbon atoms can arrange themselves into a variety of different polygons, not only hexagons, but also different structures, such as pentagons and heptagons.³³ Therefore, we can proceed to apply the present model to SWNTs with SW defects. The chemical bonding topology of the graphene with SW defects can be detected and used to reveal the physical mechanisms of radial collapse of the SWNTs with SW defects. The SWNT with SW defects can be visualized as seamlessly rolled-up graphene sheets with SW defects along the bending direction. The collapse process of the SWNT with SW defects can be considered to be the bending process of the graphene nanoribbon with SW defects. Herein, in order to study the influence of SW defects on the radial collapse of SWNTs, we calculate the L of all C–C bonds in a SW defect and compare them to that of all C–C bonds in four hexagons transformed due to the same sp²-hybridization of the hexagons, pentagons and heptagons.

Fig. 7 shows the atomic networks of four hexagons transformed and generated SW defects in SWNTs; we can obtain the structure b, c, d (2, 3, 4) by rotating structure a (1) degrees (ϕ) towards the right. Fig. 8 shows the bond lengths and bond angles in the SW defect structure. We marked five kinds of bond length for b₁, b₂, b₃, b₄, b₅ and five kinds of bond angle for α, β, γ, φ, θ in the structure of the SW defect. So, the general formulas for L of the four hexagons transformed and the generated SW defects along bending direction can be followed as

Fig. 7 Atomic networks of four hexagons transformed and generated SW defects. (a,1) Structures of four hexagons^a and generated a SW¹ defect in SWNT (10, 10), (b, 2) structures of four hexagons^b and generated a SW² defect in SWNT (10, 10), (c, 3) structures of four hexagons^c and generated a SW³ defect in SWNT (17, 0), and (d, 4) structures of four hexagons^d and generated a SW⁴ defect in SWNT (17, 0).

Fig. 8 (a) Lengths of C–C bonds (bond lengths) in the SW defect structure and (b) angles between C–C bonds (bond angles) in the SW defect structure.

Herein, we marked the L of four hexagons^a and SW¹ defects in SWNT (10, 10) for L_a, L₁; marked L of four hexagons^b and SW² defects in SWNT (10, 10) for L_b, L₂; marked L of four hexagons^c and SW³ defect in SWNT (17, 0) for L_c, L₃ and marked L of four hexagons^d and SW⁴ defect in SWNT (17, 0) for L_d, L₄. We can calculate the L_a, L₁, L_b, L₂, L_c, L₃, L_d, L₄ for 18.46 Å, 18.25 Å, 17.75 Å, 16.96 Å, 14.76 Å, 15.20 Å, 15.99 Å, 17.44 Å; and it shows L_a > L₁, L_b > L₂ and L_c < L₃, L_d < L₄. It indicates that the SW defects have much influence on the collapse of SWNTs. Moreover, these results show that the SWNT (10, 10) with SW defects is easy to collapse compared to intrinsic SWNT (10, 10), while the SWNT (17, 0) with SW defects is difficult to collapse compared to intrinsic SWNT (17, 0). Fig. 9 shows illustrations of collapsed SWNT (10, 10) with a SW² defect and collapsed SWNT (17, 0) with a SW⁴ defect. We can find that the collapse of SWNT (10, 10) easily happens at the local defect, while the collapse of SWNT (17, 0) easily happens at the planar hexagons. It once again proves that the SWNT (10, 10) with SW defects is easier to collapse compared to intrinsic SWNT (10, 10), while the SWNT (17, 0) with SW defects is more difficult to collapse compared to intrinsic SWNT (17, 0). In addition, we can calculate that (L₄ − L_d)/L_d (8.6%) > (L₃ − L_c)/L_c (2.9%) and (L_b − L₂)/L_b (4.5%) > (L_a − L₁)/L_a (1.1%). It shows that the influence of the SW defect orientation on the collapse of SWNT (17, 0) is larger than that of the SW defect orientation on the collapse of SWNT (10, 10), which is agreement with the third section's results. According to the discussion above, the variation trend of P_c predicted using this model for SWNTs with and without SW defects is in accordance with the results of MD simulations. The effect of chirality and SW defect on the radial collapse of SWNTs can be understood by the model proposed.

Fig. 9 Illustrations of the SWNT (10, 10) with a SW² defect, SWNT(17, 0) with a SW⁴ defect, collapsed SWNT (10, 10) with a SW² defect and collapsed SWNT (17, 0) with a SW⁴ defect (the red carbon atoms represent the structure of a SW defect).

Conclusions

In this study, we investigated the effects of CNT chirality, SW defects and defect orientation on the radial collapse and elasticity of SWNTs using MM and MD simulations. It is found that the P_c of the armchair SWNT is 13.75 times higher than that of the zigzag SWNT. Moreover, the armchair SWNT with SW defects is easier to collapse compared to the intrinsic armchair SWNT, while the zigzag SWNT with SW defects is more difficult to collapse compared to the intrinsic zigzag SWNT; the SW² defect makes P_c of SWNT (10, 10) decrease by 11.0%, while the SW⁴ makes P_c of SWNT (17, 0) increase by 100.0%. We introduced a model for SWNTs deformed in the radial direction according to the projection of the C–C bond along the bending direction. The model is validated for defect-free SWNTs and is then used to study the radial collapse of SWNTs with SW defects. The effect of chirality and SW defects on the radial collapse of SWNTs can be understood by the model. The strong sensitivity of radial collapse of SWNTs to chirality and SW defects can provide some guidance for high load structural application of SWNTs.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (10974258), the Fundamental Research Funds for the Central Universities (11CX05002A, 11CX0460A) and the Natural Science Foundation of Shandong Province (ZR2010AL009, ZR2011AL023).

References

1. S. Lijima, Nature, 1991, 354, 56–58.
2. P. Poncharal, Z. L. Wang, D. Ugarte and W. A. De Heer, Science, 1999, 283, 1513–1516.
3. C. Y. Li and T. W. Chou, Int. J. Solids Struct., 2005, 40, 2487–2499.
4. M. F. Yu, O. Lourie, M. J. Dyer, K. Moloni, T. F. Kelly and R. S. Ruoff, Science, 2000, 287, 637–640.
5. B. I. Yakobson, M. P. Campbell, C. J. Brabec and J. Bernholc, Comput. Mater. Sci., 1997, 8, 341–348.
6. M. Zhang, K. R. Atkinson and R. H. Baughman, Science, 2004, 306, 1358–1361.
7. K. Suggs and X. Q. Wang, Nanoscale, 2010, 2, 385–388.
8. A. Laachachi, A. Vivet, G. Nouet, B. B. Doudou, C. Poilane, J. Chen, J. Bo Bai and M. Ayachi, Mater. Lett., 2008, 62, 394–397.
9. A. Vivet, B. B. Doudou, C. Poilane, J. Chen and M. Ayachi, J. Mater. Sci., 2011, 46, 1322–1327.
10. R. Zhu, E. Pan and A. K. Roy, Mater. Sci. Eng., A, 2007, 447, 51–57.
11. J. Gou, B. Minaie, B. Wang, Z. Liang and C. Zhang, Comput. Mater. Sci., 2004, 31, 225–236.
12. H. D. Wagner, Chem. Phys. Lett., 2002, 361, 57–61.
13. J. A. Rodríguez-Manzo, A. Tolvanen, A. V. Krasheninnikov, K. Nordlund, A. Demortière and F. Banhart, Nanoscale, 2010, 2, 901–905.
14. T. W. Ebbesen and T. Takada, Carbon, 1995, 33, 973–978.
15. B. I. Yakobson, C. J. Brabec and J. Bernholc, Phys. Rev. Lett., 1996, 76, 2511–2514.
16. N. Chandra, S. Namilae and C. Shet, Phys. Rev. B, 2004, 69, 094101.
17. Y. Miyamoto, A. Rubio, S. Berber, M. Yoon and D. Tomanek, Phys. Rev. B, 2004, 69, 121413(R).
18. X. Huang, H. Y. Yuan, K. J. Hsia and S. Zhang, Nano Res., 2010, 3, 32–42.
19. S. L. Mielke, D. Troya, S. Zhang, J. L. Li, S. Xiao, R. Car, R. S. Ruoff, G. C. Schatz and T. Belytschko, Chem. Phys. Lett., 2004, 390, 413–420.
20. Q. Lu and B. Bhattacharya, Nanotechnology, 2005, 16, 555–566.
21. K. Talukdar and A. K. Mitra, Compos. Struct., 2010, 92, 1701–1705.
22. J. R. Xiao, J. Staniszewski and J. W. Gillespie Jr, Compos. Struct., 2009, 88, 602–609.
23. K. Y. Yan, Q. Z. Xue, D. Xia, H. J. Chen, J. Xie and M. D. Dong, ACS Nano, 2009, 3, 2235–2240.
24. J. Xie, Q. Z. Xue, H. J. Chen, D. Xia, C. Lv and M. Ma, J. Phys. Chem. C, 2010, 114, 2100–2107.
25. H. Sun, P. Ren and J. R. Fried, Comput. Theor. Polym. Sci., 1998, 8, 229–246.
26. H. Sun, J. Phys. Chem. B, 1998, 102, 7338–7364.
27. Q. Wang, W. H. Duan, K. M. Liew and X. Q. He, Appl. Phys. Lett., 2007, 90, 033110.
28. Q. Wang, Nano Lett., 2009, 9, 245–249.
29. J. A. Elliott, J. K. W. Sandler, A. H. Windle, R. J. Young and M. S. P. Shaffer, Phys. Rev. Lett., 2004, 92, 095501.
30. X. P. Yang, G. Wu and J. M. Dong, Appl. Phys. Lett., 2006, 89, 113101.
31. M. Al-Haik, M. Y. Hussaini and H. Garmestani, J. Appl. Phys., 2005, 97, 074306.
32. L. Y. Chu, Q. Z. Xue, T. Zhang and C. C. Ling, J. Phys. Chem. C, 2011, 115, 15217–15224.
33. F. Banhart, J. Kotakoski and A. V. Krasheninnikov, ACS Nano, 2011, 5, 26–41.

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