Chirality-Controlled Carbon Nanotubes Fabricated by Self-Assembly

Jul 29, 2014 - carbon nanotube, and a nearly straight graphene strip, on a basal carbon ... edge-unpassivated twisted GNRs on the surface of basal CNT...
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Chirality-Controlled Carbon Nanotubes Fabricated by Self-Assembly of Graphene Nanoribbons Cun Zhang, Zhilong Peng, and Shaohua Chen* LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China S Supporting Information *

ABSTRACT: We demonstrate by molecular dynamics simulations that carbon nanotubes can activate and guide on their surfaces the fabrication of single-walled carbon nanotubes by self-assembly of edge-unpassivated twisted graphene nanoribbons. Temperature is a governing factor, which mainly controls the self-assembly process. Three types of stable configurations exist due to the self-assembly of twisted graphene nanoribbons at constant temperatures, i.e., a helical structure, a self-assembled carbon nanotube, and a nearly straight graphene strip, on a basal carbon nanotube. Raising the temperature gradually, the helical structure can spontaneously switch to a single-walled carbon nanotube or a nearly straight graphene strip. The straight graphene strip can further turn into a self-assembled carbon nanotube through annealing technique. Furthermore, the chirality of the selfassembled carbon nanotube can be predicted by the width of the twisted graphene nanoribbon and the radius of the basal carbon nanotube. Our finding should be useful for the design of nanodevices with chirality-controlled nanotubes.

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INTRODUCTION Carbon nanomaterials, including carbon nanotubes (CNTs), carbon nanoscrolls (CNSs), and graphene sheets, have been attracting enormous attention due to their unique properties and promising applications.1−11 With a great potential to replace silicon in future electronics,12−14 many scientists are interested in graphene nanoribbons (GNRs) and have proposed different techniques to achieve high-quality GNRs with precise sizes and shapes, including unzipping of carbon nanotubes,13,14 electron beam lithography,15,16 growth of graphene on a lithographically patterned SiC substrate,17,18 self-masked plasma etching of wrinkled graphene,19 and sonochemical exfoliation.20,21 Now, it becomes possible to further self-assemble GNRs with desired shapes and sizes into various novel composite functional nanostructures, such as CNSs,22,23 twisted GNRs,24 and 3D nanostructures.25 Meanwhile, it also provides good opportunities for possibly controlled synthesis of CNTs with predefined chiralities,26−28 which has long been recognized as a fundamental impediment in applications of CNTs. Recently, an interesting molecular dynamics (MD) simulation study shows that planar GNRs could self-assemble on basal CNT surfaces or in their interiors, leading to stable graphene rings, helices, and knots at 300 K.29 Two types of selfassembled helical structures were found: a dense twisted GNR and a loose one, but without observations of the formation of CNTs.29 Almost simultaneously, Chuvilin et al.30 experimentally reported that a sulfur-terminated GNR can self-assemble from a random mixture of molecular precursors within a singlewalled carbon nanotube and first caught sight of helical twisted structures of GNR in CNTs. A subsequent experiment further showed that CNTs could be self-assembled from GNRs inside a basal CNT in some cases.31 Issues are raised beyond a doubt as to under what conditions the above helical structures could © 2014 American Chemical Society

exist stably. What factors will influence the stability of the twisted GNR? Under what conditions could self-assembled CNTs be formed? Since CNTs are fabricated from selfassembly, could we control the chirality of self-assembled CNTs through tailoring GNRs? In order to answer these questions, molecular dynamics (MD) simulations are conducted in this paper. The stability of edge-unpassivated twisted GNRs on the surface of basal CNTs under different temperatures are studied first. It is found that self-assembled structures depend significantly on temperatures. Three kinds of configurations can be produced, self-assembled CNTs, helical structures, and nearly straight graphene strips rolling on the basal CNTs. Then, methods of heating and annealing are adopted in order to achieve self-assembled CNTs consistently. Chirality of self-assembled CNTs is discussed finally. Since the self-assembly behaviors of twisted GNRs on the interior and exterior surfaces of basal CNTs are found to be similar, only the latter is considered in this paper.29,32

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COMPUTATIONAL METHODS

A schematic of the simulation model is shown in Figure 1, where the width of the twisted zigzag GNR is W = 19.9 Å and a

Figure 1. Schematic of a twisted GNR on a basal CNT. W, ϕ, and L represent the width, the initial helix angle, and the total length of the twisted GNR in the axis direction of the basal CNT, respectively. Received: June 11, 2014 Revised: July 27, 2014 Published: July 29, 2014 19477

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length Ls = 300.9 Å. A (15,15) CNT with a length of l = 400.0 Å and radius r = 10.17 Å is adopted as the basal CNT, which ensures successful rolling of GNRs on it.29 The initial radius of the twisted GNR is R = 13.57 Å with an initial helix angle ϕ twining round the basal CNT as shown in Figure 1. In order to avoid overlapping, the initial distance between neighboring edges should be larger than zero, which leads to ϕ < 76.5°. All simulations are performed using LAMMPS33 with free boundary conditions. A constant temperature ensemble (NVT) is used in our simulations with Nose−Hoover thermostats.34 In contrast to the CHARMM27/COMPASS force field used in Patra et al.29 and Jiang et al.,32 the AIREBO potential35 is adopted in this manuscript to describe the C−C interactions in GNRs, which can accurately reflect interactions between hydrocarbon atoms as well as the bond breaking and bond re-forming.27,36 Interactions between GNRs and the basal CNTs are depicted by the Lennard-Jones (LJ) potential ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ V = 4ϵ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎝r⎠ ⎦ ⎣⎝ r ⎠

(1)

where ϵ = 2.84 meV and σ = 3.40 Å. The time step is 1 fs, and snapshots are recorded per 1 ps, which will be analyzed by the VMD visualization package.37 35

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RESULTS AND DISCUSSION Stability of a Twisted GNR on a Basal CNT. A series of simulations have been carried out at constant temperatures T = 10, 300, and 1000 K, respectively, and the initial helix angle ϕ varies from 0° to 75° with an increment of 5°. Three types of stable structures are found at constant temperatures as shown in Figure 2 for example. The first interesting one is selfassembled CNTs, of which the neighboring GNR edges touch each other as shown in Figures 2d and 2i. The second one is helical graphene structures with edge gaps larger than a C−C bond length as shown in Figures 2a−c and 2e−f. The last one is nearly straight graphene strips as shown in Figures 2g and 2h, which are dynamically stable, twist, and straighten on the basal CNT periodically. In order to verify whether C−C bonds have been formed at the contact neighboring edges shown in Figures 2d and 2i, potential energy variations of four representative atoms A, B, C, D are further given in Figure 3. The four atoms are labeled in the insets of Figure 3. The inner atom B and the edge one C possess saturated bonds in contrast to atoms A and D with unsaturated bonds at the unpassivated GNR edges. After enough relaxation of the system at a constant temperature, it is very obvious that the final potential energies of atoms A and D are significantly different from those of atoms B and C in the stable helical structure at T = 10 K as shown in Figure 3a. However, it is surprising to find that the final potential energies of atoms A and D are identical to those of atoms B and C as shown in Figure 3b. Furthermore, the reduced potential energy is almost equal to a half of the formation energy of a C−C bond, 2.4 eV.35 All these prove that single-walled CNTs are self-assembled by twisted GNRs on basal CNTs when the neighboring edges contact each other. The diversity of self-assembled configurations should result from the complexity of the local lattice mismatch between twisted GNRs and basal CNTs. Lattice mismatch may lead to a self-lock of twisted GNRs on basal CNTs. However, thermal vibration induced by the ambient temperature not only affects the mismatch but also provides a driving force for twisted

Figure 2. Finally stable configurations of twisted GNRs rolling outside basal CNTs with different initial helix angles ϕ and constant temperatures T. df is the gap distance between neighboring edges in the finally stable structures. (see movies S1−S3 in the Supporting Information).

GNRs to slide or rotate on basal CNTs. For the same reason, GNRs exhibit diverse dynamic behaviors, including rotation, translation, and helical twisting on the surface of the basal nanotube, which are similar to the experimental observations in Chamberlain et al.38 Fabrication of CNTs from Twisted GNRs by a Temperature-Controlling Process. As Patra et al.29 said, helical structures could be thermally decoupled from their locked positions. Can stable helical structures turn into selfassembled CNTs if the system temperature is raised gradually? Four stable helical structures at constant temperature 10 K with initial helix angles ϕ = 25°, ϕ = 30°, ϕ = 35°, and ϕ = 75° are checked, when the system temperature is raised up from 10 to 300 K within 0.3 ns. The total potential energies of the four helical structures as well as the temperature varying with the time are shown in Figure 4. It is found that all the four helical structures switch to self-assembled CNTs with transition temperatures 204.3, 224.8, 140.8, and 126.9 K, respectively. The potential energy of each helical structure increases about 3/2Nk(T − T0) before transition, where N, kB,T, T0 are the number of GNR atoms, Boltzmann constant, current temper19478

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down very sharply due to the formation of a self-assembled CNT. Since the formation of self-assembled CNTs from helical structures is an essentially chemical reaction, many factors may influence the forming possibility. According to the transitionstate theory,39 the possibility P follows P = ν e−E b / kBT

(2)

where Eb, kB, ν, and T are the energy barrier, Boltzmann constant, attempt frequency, and temperature, respectively. e−Eb/kBT denotes the possibility of a given collision resulting in a chemical reaction. The improvement of ambient temperatures not only makes the edge atoms overcome their activation energies but also enhances the attempt frequency. The uncertainty leads to different and irregular transition temperatures in different systems. Though the possibility of forming a self-assembled CNT at contact temperature 10 K is very small, a few new bonds are still found at edges of the helical structures as shown in Figure 5a. At a low temperature, the attempt velocity is sufficient to

Figure 3. Potential energies of four representative atoms in a twisted GNR as a function of the relaxation time: (a) in the case with a constant temperature T = 10 K; (b) in the case with a constant temperature T = 300 K. The positions of the four atoms A, B, C, and D are labeled in the insets.

Figure 5. Bonds and defects formed during the self-assembly of twisted GNRs rolling on basal CNTs. (a) Bonds formed at a constant temperature T = 10 K. (b) Defects formed at a constant temperature T = 300 K.

form several bonds but not sufficient for the remaining edges to overcome their activation energy barriers. Such behaviors demonstrate that edge bridging is not in a collective manner at a low temperature.39 A rapidly collective manner induced by a high temperature may lead to defects at edges as shown in Figure 5b, where a ringlike defect is induced. One should be noted that not all helical structures at 10 K may switch to selfassembled CNTs in a rising temperature field. Helical structures may relock on the basal CNT when the temperature is raised from 10 to 300 K with a low rate. In regard to the stable helical structures at constant temperature 300 K, we also raise the temperature from 300 to 1000 K with different rates (within 0.0, 0.2, 1.0, 2.0 ns) to check whether the helical structures can switch to selfassembled CNTs. The results show that helical structures either turn into self-assembled CNTs during the temperature rising process or nearly straight graphene strips stretching and rolling on basal CNTs periodically. Typical examples are shown in Figure 6 with initial helix angles ϕ = 40° and ϕ = 65°. The total potential energy of the case with ϕ = 40° is always

Figure 4. Total potential energies of twisted GNRs rolling on basal CNTs as a function of the relaxation time, where the system temperature is raised from a constant temperature 10 to 300 K.

ature, and initial temperature, respectively. When the system temperature rises to a transition one, the potential energy drops 19479

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Figure 6. Total potential energies of stable helical structures on basal CNTs at 300 K as a function of the relaxation time when the system temperature is raised up to 1000 K. (a) Potential energy increasing with the increasing simulation time, resulting in a relocked helical structure. (b) Potential energy increases initially with the temperature and then decreases sharply, leading to a self-assembled CNT. (see movies S4, S5 in the Supporting Information).

increasing for an increasing temperature as shown in Figure 6a, which results in unlocked helical structures (nearly straight graphene strips) as shown in the inset of Figure 6a. The total potential energy of the case with ϕ = 65° increases first with the increasing temperature and then drops down at 370 K as shown in Figure 6b, which leads to self-assembled CNTs forming from helical structures as shown in the inset of Figure 6b. Straight graphene strips at a constant temperature of 1000 K are stable structures. How can we turn such structures to CNTs? High-temperature annealing technique is adopted in this paper. It is found that straight graphene strips almost switch to self-assembled CNTs or relocked helical structures on basal CNTs when the temperature drops from 1000 to 300 K with different rates (within 0.0, 0.05, 0.2, or 1.0 ns). The whole

process is demonstrated in Figure 7, and the total potential energy varies with the decreasing temperature as shown in Figure 8, where self-assembled CNTs form at the moment of a sharp reducing potential energy and the length variation of the self-assembled CNT in the axial-direction is shown in the inset. Chirality Prediction of a Self-Assembled CNT. Our simulation shows that the chirality of a self-assembled CNT does not depend on the initial helix angle but depends on the width W of the initially twisted GNR and the radius r of the basal CNT. The chiral angle θ of the self-assembled CNT can be predicted theoretically as

sin θ = 19480

W 2πR

(3)

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⎢ ⎥ 3(4π 2R2 − W 2) − W + 0.5⎥ n=⎢ ⎢⎣ ⎥⎦ 3a

(7)

where ⌊x⌋ denotes the nearest integer of x. A series of simulations are carried out to find the chirality of a self-assembled CNT forming from a twisted GNR on a basal CNT. A good consistency between the MD and theoretically predicted results is found. Table 1 gives a comparison for a typical example, in which the width of the twisted GNR varies from 1.2764 to 4.2540 nm and the chirality of the basal CNT is (15,15). Table 1. Comparisons between Theoretical Predictions and MD Simulation Results of the Chiralities of Self-Assembled CNTs by Twisted GNRs on a (15, 15) Basal CNT

Figure 7. Schematics of the self-assembly process of nearly straight graphene strips, when the temperature drops down from 1000 to 300 K with different cooling rates.

chirality (m, n)

where R = r + 0.34 nm for twisted GNRs outside basal CNTs; R = r − 0.34 nm for twisted GNRs inside basal CNTs. The relationship among the chiral angle θ, radius R, and chirality (m, n) is tan θ =

3m 2n + m

m2 + n2 + mn =

MD simulations

12.764 17.018 21.272 25.526 34.032 38.286 42.540

(31,6) (30,8) (29,10) (27,12) (24,16) (22,18) (20,20)

(32,6) (30,8) (29,10) (27,12) (24,16) (22,18) (20,20)

CONCLUSIONS In summary, we have demonstrated that a basal CNT can activate and guide on its surface the fabrication of a singlewalled CNT by self-assembly of an edge-unpassivated twisted GNR. During the self-assembly process, the system temperature and the initial helix angle are two dominating roles. A selfassembled CNT can be realized by heating from low to high or high-temperature annealing if it could not be spontaneously formed at a constant temperature. Furthermore, the chirality of the self-assembled carbon nanotube can be predicted from the

2

(5)

where a = 0.246 nm is the lattice constant of graphene. Solving eqs 3−5 yields ⎥ ⎢ 2W m=⎢ + 0.5⎥ ⎦ ⎣ 3a

theoretical predictions

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(4)

⎛ 2πR ⎞ ⎜ ⎟ ⎝ a ⎠

width W (Å)

(6)

Figure 8. Variation of the total potential energy during self-assembly of a CNT from a nearly straight graphene strip, when the system temperature decreases from 1000 to 300 K. 19481

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width of the twisted graphene nanoribbon and the radius of the basal carbon nanotube. The findings in this paper should be helpful for fabrication of chirality-controlled CNTs, which are often required in the design of intelligent microdevices.

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ASSOCIATED CONTENT

S Supporting Information *

Movies related to the self-assembly of twisted GNRs on basal CNTs at constant temperatures and rising temperatures. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Science Foundation of China (Grant No. 11125211, 11372317) and the 973 Nanoproject (2012CB937500). MD simulations were carried out at Supercomputing Center of Chinese Academy of Sciences.

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