Mechanical Properties of Hydrogenated Carbon Nanotubes (C4HNTs

Article pubs.acs.org/JPCC

Mechanical Properties of Hydrogenated Carbon Nanotubes (C4HNTs): A Theoretical Study Xiaofang Li,†,‡ Qingzhong Xue,*,†,‡,§ Zilong Liu,‡ Cuicui Ling,‡ Yehan Tao,‡ and Tiantian Wu‡ †

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao , Shandong 266580, People’s Republic of China ‡ College of Science, China University of Petroleum, Qingdao, Shandong 266580, People’s Republic of China § Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong, Qingdao, Shandong 266580, People’s Republic of China ABSTRACT: C4H nanotube (C4HNT) which is a novel kind of hydrogenated carbon nanotubes (CNTs) has gradually attracted much attention due to its unique structure and potential applications. In this work, we systematically studied the mechanical properties of C4HNT using classical molecular dynamics and molecular mechanics simulations. It is found that C4HNT can bear much greater radial pressure than CNT. For example, the collapse pressure of (10, 0) C4HNT can reach 25 GPa, which is more than 4 times that of (10, 0) CNT (6 GPa). However, hydrogenation weakens the value of Young’s modulus of CNT, and leads to the descent of axial strength of CNT. Besides, it is demonstrated that the collapse pressure of C4HNT decreases with increasing tube diameter while the Young’s modulus of C4HNT is independent of tube diameter. And the tube number, chirality, length have no effect on the axial and radial mechanical properties of C4HNT. The results show that C4HNT has much better radial mechanical properties than CNT so that C4HNT may be an ideal filler to enhance the local mechanical support of nanocomposites.

1. INTRODUCTION Carbon-based low dimensional nanostructures have aroused considerable interest for many years due to their novel properties and applications. Among these materials, the carbon nanotube (CNT), which possesses a one-dimensional structure, has sparked great interest since its discovery in 1991.1 Abundant studies have focused on the excellent properties of CNTs, including mechanical properties,2−4 electronic properties,5−10 and thermal properties.11−13 For example, the Young’s modulus of CNT is ranged from 0.90 TPa to 1.70 TPa at room temperature, with an average of 1.25 TPa.14 Industrial epoxy loaded with 1 wt % unpurified CNT shows a 70% increase in thermal conductivity at 40 K, rising to 125% at room temperature.11 Recently, it has been demonstrated that modification has a great effect on the properties of CNTs, including fluorination, hydrogenation, and so on. Using molecular dynamics (MD) simulations, Ling et al.15 have demonstrated that fluorinated CNT that -F groups are attached to 2.5−5.0% of carbon atoms can not only sustain the original elasticity of the intrinsic CNT, but also show 11.3−21.8% enhancement in collapse pressure. Pekker et al.16 have demonstrated that both multi-walled and single-walled CNTs can be chemically hydrogenated via a dissolved metal reduction method in liquid ammonia. Nikitin et al.17 studied the hydrogenation of single-walled CNT films with an atomic hydrogen beam, and the hydrogenation and dehydrogenation process can be cycled. By density functional © 2014 American Chemical Society

calculations within local density approximation (LDA), Park et al.18 found that hydrogenated single-walled CNTs were stable when the C/H ratio is no less than 0.2 within the energy difference of 0.3 eV/H. And the band gap of CNTs can be engineered by varying hydrogen coverage, independent of metallicity of CNTs. Jalili et al.19 have found that the geometric structures and band gap of hydrogenated CNTs can be strongly changed by varying hydrogen coverage using ab initio molecular dynamics method. Surya et al.20 studied the transverse external electric field induced desorption of chemisorbed hydrogen atoms from CNTs using first-principles calculations. Graphene, as a kind of 2-dimensional carbon nanostructure, has also attracted much attention. Modification also has great effects on the properties of graphene, including fluorination,21−25 oxygenation,26−28 hydrogenation,29−32 and so on. For example, oxygenation33,34 turns the armchair graphene nanoribbons from semiconductive to metallic in nature. Fluorination35−37 leads to a much better stability of graphene. Hydrogenation38−40 makes graphene a nonmagnetic semiconductor with a wide indirect band gap. Recently, Haberer et al.40 have successfully synthesized a stable and novel partially hydrogenated graphene, named as C 4 H graphene, by Received: December 13, 2013 Revised: June 7, 2014 Published: July 7, 2014 16087

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commercial software package called Materials Studio (MS) developed by Accelrys Software Inc. MD and MM simulations were carried out on a supercell containing a C4HNT. The interatomic interactions are described using the condensedphase optimized molecular potential for atomistic simulation studies (COMPASS) force field method, which is a parametrized, tested, and validated first ab initio force-field. The COMPASS force field has been widely used for various gasphase and condensed-phase properties of many common organic and inorganic materials.52,53 What’s more, it has been proven to be feasible in describing the properties of metal, metal oxide,54 graphene,55,56 and CNT.57,58 In these simulations, the interactions are determined within a cutoff distance of 18.5 Å for all the simulations. The convergence criteria is 2.0 × 10−5 kcal/mol for energy, 0.001 GPa for stress, and 1.0 × 10−5 Å for displacement in all cases. MM and MD simulations are performed in periodic boundary conditions. In this study, we construct various periodic C4HNTs and CNTs to study their mechanical properties. In order to describe the radial mechanical properties, we change the volume of C4HNT and CNT gradually by applying hydrostatic pressure. In order to study the axial mechanical properties, we can measure the energy for each axial stretch to be as a function of the deformation degree. Young’s modulus can be calculated according to the relationship between the energy and deformation degree.

interacting hydrogen plasmas with Au-supported graphene, in which the C/H ratio is 4:1, as shown in Figure 1. They found that C4H graphene was a semiconductor with a wide band gap of 3.5 eV, making it a promising material for opoelectronic devices.

Figure 1. C4HNT model rolled-up from C4H layer. (Gray and white balls represent carbon and hydrogen atoms, respectively.)

Similar to getting a CNT from a graphene sheet, C4HNT can be constructed by rolling up the C4H graphene along a direction of lattice vector L (L = na + mb), where a and b are the unit cell vectors of C4H graphene, as shown in Figure 1. Thus, the C4HNT can be classified by the notation (n, m). The physical properties of C4HNT, in which the C/H ratio is 4:1, have been studied. They found that C4HNT exhibited excellent thermodynamic properties and had a wide band gap regardless of the tube chirality and diameter.41 As Noted, the hydrogenated carbon bonds in C4H graphene and C4HNT are sp3 hybridization. Therefore, C4HNT is a novel structure composed of hydrogen atoms and sp2 and sp3 mixed carbon atoms, while CNT is merely composed of sp2 carbon atoms. Until now, to our best knowledge, there have been only a few studies on the mechanical properties of C4HNT, which are particularly important for its applications in sensors, nanoresonators, and composite materials. In this work, we make a systematic study on mechanical properties of C4HNT using MD and molecular mechanics (MM) simulations, and the effect of tube diameter, chirality, length, and number on the mechanical properties of C4HNT is carefully evaluated.

3. RESULTS AND DISCUSSION 3.1. Radial Deformation. Figure 2 shows unit cells of two kinds of C4HNTs, the size of (10, 0) C4HNT is a = b = 11.176 Å, c = 4.260 Å while the size of (6, 6) C4HNT is a = b = 11.483 Å, c = 2.460 Å. Figure 3(a),(b) show 4 unit cells of (10, 0) CNT and (10, 0) C4HNT, and they have the same sizes (a = b = 11.176 Å, c = 17.040 Å). Figure 3(c),(d) show 8 unit cells of (6, 6) CNT and (6, 6) C4HNT, and they have the same sizes (a = b = 11.483 Å, c = 19.676 Å). We choose 4 unit cells for each tube in the simulations considering the computational amount and computational time. Here, we will manifest the existence of the shape change of C4HNT and CNT under hydrostatic pressure. Figures 4 and 5 show that C4HNTs undergo two shape changes, which are similar to that of CNTs. When the pressure is small, the volume radio changes little and the tube becomes oval. When the pressure reaches a critical value (Pc), which is the critical collapse pressure of C4HNT (or CNT) during loading, the volume ratio changes a lot and the tube collapses. And a parameter d, which is the shortest distance (3.4 Å) of graphite layers, is used to justify whether the model can collapse or not. If the distance d is close to 3.4 Å, then the model can be considered to be collapsed. In these simulations, we choose different kinds of tube models, such as (n, 0) C4HNT, (n, 0) CNT (n = 9, 10, 12, 14, 16, 17, 19, 21), (n, n) C4HNT and (n, n) CNT (5 ⩽ n ⩽ 12).

2. METHODS Recently, many researchers have investigated the Young’s modulus2,14,42,43 and radial collapse44−51 of CNTs using MD simulations, and demonstrate that the theoretical results are in well agree with experimental results. In this work, we will study the radial collapse and Young’s modulus of C4HNT using MD simulations. The simulations have been carried out using a

Figure 2. Molecular model of a tube unit cell. (a) (10, 0) C4HNT and (b) (6, 6) C4HNT. 16088

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easily from a circle shape to an oval shape, because it is easier to change the bond angle than the bond length. What’s more, the transformation from a circle to an oval is a continuous change. The tube becomes bent more easily after the first change. When the hydrostatic pressure reaches Pc, the second change takes place and the tube collapses after Pc. Figure 6 shows the effect of tube diameter on the collapse pressure of C4HNTs and CNTs. It can be found that the collapse pressure of C4HNTs (or CNTs) decreases with increasing tube diameter. As noted, the collapse pressure of both (n, 0) C4HNTs and (n, n) C4HNTs is much larger than that of the (n, 0) CNTs and (n, n) CNTs at the same tube diameter, which indicates that C4HNTs can bear much greater pressure than CNTs with the same tube diameter. For example, the collapse pressure of (10, 0) C4HNT can reach 25 GPa, which is more than 4 times that of (10, 0) CNT (6 GPa). In other words, hydrogenation can greatly strengthen the radial mechanical properties of CNT. Therefore, C4HNT, due to its better radial mechanical properties, may be an ideal filler to enhance the local mechanical support of nanocomposites. We can understand the effect of tube diameter on collapse pressure of C4HNTs (or CNTs) by elastic model and MM.59 The collapsed process is the competition between the compressive strain energy and the bending strain energy. The collapse leads to the equilibrium between the compressive strain energy and the bending strain energy. The bending energy of C4HNT (or CNT) increases with decreasing diameter so that the minor diameter C4HNT (or CNT) can need larger hydrostatic pressure to overcome the bending strain energy. Therefore, the collapse pressure of C4HNTs (or CNTs) decreases with increasing tube diameter. As discussed above, C4HNT is a novel structure composed of hydrogen atoms and sp2 and sp3 mixed carbon atoms while CNT is merely composed of sp2 carbon atoms. As we know, sp3 hybridization can form four σ bonds while sp2 hybridization forms three σ bonds and one π bond. The electron cloud of π bond is much farther from the nucleus than that of σ bond. Besides, the electron cloud of the π bond is not centralized between two bonding atoms and its overlap is weaker than that of σ bond. Therefore, σ bond is much more stable than π bond so that C4HNT with sp3 hybridization has much better radial mechanical properties than CNT with the same tube diameter. 3.2. Determination of Young’s Modulus. Young’s modulus is one of the crucial characterizations to represent the mechanical properties of materials. Young’s modulus is a reflection of cohesion in the material. It can help understand

Figure 3. Molecular models of intrinsic CNT and C4HNT. (a) (10, 0) CNT, (b) (10, 0) C4HNT, (c) (6, 6) CNT, and (d) (6, 6) C4HNT.

We can understand the collapse process of C4HNT and CNT by elastic model and MM.59 On the basis of elastic models in loading, initially, there are mainly two kinds of energies including the compressive strain energy due to the reduced circumference of the tube and bending strain energy due to the increased curvature of the tube. When the compressive strain energy is strong enough to overcome the bending strain energy, the first change occurs from circle shape to oval shape at a critical pressure. This is the result of the competition between compression and bending of the tube under hydrostatic pressure. The structure of tube can convert

Figure 4. Relationship between volume ratio and pressure for (17, 0) tube. (a) (17, 0) CNT and (b) (17, 0) C4HNT. 16089

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Figure 5. Relationship between volume ratio and pressure for (10, 0) tube. (a) (10, 10) CNT and (b) (10, 10) C4HNT.

F=

EAΔl Lc

(2)

And the strain energy U is calculated by the following: U=

∫ Fdl = 12 EVε2

(3)

where V = ALc is the volume of the intrinsic C4HNT and CNT. Therefore, Young’s modulus can be calculated by the following: E=

1 ∂ 2U V ∂ 2ε

(4)

In these simulations, the strain energy U is the changed energy by stretching ΔL and is computed as a function of strain ε. According to eq 4, Young’s modulus is obtained by fitting U−ε curves. 3.3. Young’s Modulus of C4HNTs. In these simulations, we built different tube models with periodic boundary conditions. The unit cell along radial direction is expanded to reduce the interaction with adjacent tubes during the simulations. The final energy of the structure is obtained by stretching the tube along axial direction. In order to compare the numerical results with other predictions of Young’s modulus, all the computational results of Young’s modulus of armchair CNTs and C4HNTs, and zigzag CNTs and C4HNTs are given in Tables 1 and 2, respectively. It can be found that our calculated values of Young’s modulus of CNT agree with the existing experimental and theoretical values well.2,14 Figures 7(a),(b) show ΔU-ε curves of armchair and zigzag C4HNTs with different diameters. According to eq 4, we calculate the Young’s modulus using the curves obtained. The Young’s modulus of the C4HNT is plotted as a function of diameter as shown in Figure 7(c). It is found that the Young’s

Figure 6. Collapse pressure (Pc) of CNT and C4HNT with different tube diameters. (a) armchair tube and (b) zigzag tube.

structural integrity and limitation as a mechanical material. Therefore, Young’s modulus can be used to evaluate the mechanical properties of the material. To determine Young’s modulus of C4HNT and CNT, the cell parameter c and angle α, β, γ of the unit cell are fixed first. Then we stretch a positive displacement ΔL along c axis. In classical mechanics, the Young’s modulus (E) is defined by the following:

Table 1. Young’s Modulus (E) of Armchair Tubes with Different Diameters tube (5, (6, (7, (8, (9, (10, (11, (12,

FLc σ = (1) ε AΔl where σ is axial stress, ε is the strain, F is the axial tensile force impacted on the material, A is the cross-sectional area, Lc is the initial length, and Δl is the elongation under the force F. The force F can be defined as follows: E=

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5) 6) 7) 8) 9) 10) 11) 12)

diameter (Å)

E of CNT (Tpa)

E of C4HNT (Tpa)

6.78 8.14 9.49 10.85 12.20 13.56 14.92 16.27

0.749 0.747 0.744 0.742 0.741 0.740 0.606 0.739

0.647 0.620 0.641 0.646 0.632 0.647 0.641 0.700

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modulus of C4HNTs is independent of tube diameter. Young’s modulus (E)-diameter curves for armchair and zigzag C4HNTs are made in the same coordinates as shown in Figure 7(c). It can be found that the effect of tube chirality and diameter on the Young’s modulus of C4HNT is very weak. Figure 8 shows

Table 2. Young’s Modulus (E) of Zigzag Tubes with Different Diameters tube (9, (10, (12, (14, (16, (17, (19, (21,

0) 0) 0) 0) 0) 0) 0) 0)

diameter (Å)

E of CNT (Tpa)

E of C4HNT (Tpa)

7.05 7.83 9.39 10.96 12.53 13.31 14.87 16.44

0.950 0.917 0.616 0.611 0.949 0.960 0.678 0.961

0.500 0.525 0.510 0.514 0.525 0.516 0.498 0.502

Figure 8. Young’s modulus (E) of different tubes. (a) armchair CNT and C4HNT and (b) zigzag CNT and C4HNT.

the Young’s modulus of C4HNT and CNT. We can find the Young’s modulus of C4HNT is less than that of CNT. This can be understood that hydrogenation leads to bond transition from CC bonds to CH bonds and the convert of hybridization from sp2 to sp3 in C4HNTs. In other words, double bonds in CNT partly become single bonds because of hydrogenation. The strength of double bond is much stronger than that of the single bond. And the boundary carbon atoms are pulled away from the original CNT and the sp3-hybridized carbon atoms destroy the stable structure of the CNT. Besides, the σ bond is much easier to rotate than π bond. Therefore, the Young’s modulus of C4HNT is smaller than that of CNT with the same tube diameter. Figure 9 shows that tube length has little effect on the Young’s modulus of C4HNT, which is different from that of CNT, whose Young’s modulus can change with tube length.60 3.4. 4-Tube Model. In order to investigate the effect of tube number on the mechanical properties of C4HNT, we built a 4-tube model for (5, 5) C4HNT and (9, 0) C4HNT in one unit cell, as shown in Figure 10. Figure 11 shows the relationship between the volume ratio and the pressure of C4HNTs. When the pressure is small, the volume ratio changes little and the tube becomes oval. When the pressure reaches a critical value, the volume ratio changes a lot and the tube collapses. It is found that the critical pressures of 4-(5, 5) C4HNT and 4-(9, 0) C4HNT are 32 and 30 GPa, which are similar to that of single (5, 5) C4HNT and (9, 0)

Figure 7. (a) ΔU−ε curves for armchair C4HNT with different tube diameters. (b) ΔU−ε curves for zigzag C4HNT with different tube diameters. (c) Young’s modulus (E) of both zigzag and armchair C4HNT with different tube diameters.

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Figure 11. Relationship between volume ratio of C4HNT and pressure. (a) (5, 5) C4HNT and (b) (9, 0) C4HNT.

Figure 9. Relationship between Young’s modulus (E) of C4HNT and the tube length. (a) (9, 0) C4HNT and (b) (5, 5) C4HNT.

Table 3. Average Young’s Modulus (E) per One Tube in 4Tube Model tube (5, (9, (6, (10, (7, (12, (8,

Figure 10. 4-tube model. (a) (5, 5) C4HNT and (b) (9, 0) C4HNT.

E of C4HNT (Tpa)

E of CNT (Tpa)

0.578 0.575 0.573 0.575 0.565 0.448 0.578

0.950 0.725 0.750 0.953 0.745 0.615 0.728

5) 0) 6) 0) 7) 0) 8)

properties of C4HNTs. C4HNT has much better radial mechanical properties than CNT so that it may be an ideal filler to enhance the local mechanical support of nanocomposites.

C4HNT (30 and 28 GPa). As we know, the interaction between the four tubes is internal interaction, and this interaction makes 4 tubes as a whole. When we apply an external pressure on the 4-tube model, 4 tubes can be regarded as a total system and the interaction can be ignored. The number of the tube has little effect on the radial mechanical properties of C4HNT. Table 3 shows the average Young’s modulus per tube in 4-tube model, which is similar to that of a single tube.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

4. CONCLUSIONS In this study, we investigate the mechanical properties of C4HNTs using MD and MM simulations. It is found that C4HNT can bear much greater radial pressure than CNT. However, hydrogenation weakens the value of Young’s modulus of CNT, and leads to the descent of axial strength of CNT. Besides, it is demonstrated that the collapse pressure of C4HNT decreases with increasing tube diameter while the Young’s modulus of C4HNT is independent of tube diameter. It is also found that the tube number, chirality, length have no effect on the axial and radial mechanical properties of C4HNT. And the number of tube has little effect on the mechanical

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ACKNOWLEDGMENTS This work is supported by the Natural Science Foundation of China (11374372), Taishan Scholar Foundation (ts20130929), Graduate Innovation Fund of China University of Petroleum (YCX2014070), and National Super Computing Center in Jinan.

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