Density-Functional Theory Studies of Step-Kinked Carbon Nanotubes

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Density-Functional Theory Studies of Step-Kinked Carbon Nanotubes Xiaojun Wu,†,‡ Rulong Zhou,§,|| Jinlong Yang,†,^ and Xiao Cheng Zeng*,§ Department of Materials Science & Engineering, ^Department of Chemical Physics, and †Hefei National Lab for Physical Materials at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China § Department of Chemistry and Nebraska Center for Materials and Nanoscience, University of Nebraska—Lincoln, Lincoln, Nebraska 68588, United States School of Materials Science and Engineering, Hefei University of Technology, Hefei, Anhui 230009, China

)

‡

ABSTRACT: Using density-functional theory (DFT) methods, we investigate structural, electronic, and transport properties of step-kinked single-walled carbon nanotubes (SWCNT). To devise a sensible model for the joint section of the kinked nanotube, we examine relative stability of two (6,0) carbonnanotube-based C672 isomers, namely, a carbon nanoring and a carbon hexagonal nanotorus. We find that the hexagonal nanotorus C672 is energetically more favorable than the isomeric nanoring (i.e., circular nanotorus) C672. By use of the kinked section of the hexagonal nanotorus as a model joint, the periodic step-kinked carbon nanotubes can be built. According to the DFT calculation using the hybrid B3LYP functional, we find that introduction of the periodic kinks turns the perfect (5,0) SWCNT with zero band gap (J. Phys. Chem. Lett. 2010, 1, 2946) into a semiconductor with a band gap ∼0.76 eV. In contrast, the step-kinked (6,0) SWCNT is still a metal with zero band gap, like the perfect (6,0) SWCNT. We also compare the electronic transport properties of a perfect (5,0) SWCNT with the step-kinked (5,0) SWCNT. The former has a nonzero steplike electron transmission distribution near the Fermi level, while the latter shows some sharp transmission peaks around the Fermi level.

I. INTRODUCTION Since the discovery of carbon nanocluster C60 (or the buckyball) in 1985,1 a variety of new carbon nanostructures have been revealed,2-31 such as carbon nanotubes, single-layer graphenes, and graphene nanoribbons.2-4 The unique 1D structure of carbon nanotubes and associated quantum-confinement effect endows the nanotubes with many novel properties. For example, a single-walled carbon nanotube (SWCNT) can be either a metal or a semiconductor, depending on its chirality.2 Based on the unique structural and electronic properties of CNTs, many new multifunctional CNT-based architectures have been designed, including, among others, carbon nanorings, helical coiled CNT, Y-shaped and T-shaped CNT, beaded CNT, waved CNT, carbon nanopeapod, and nanobuds. Many of them have been realized in the laboratory.28 Indeed, CNT-based architectures by design open possibilities of making all-carbon superstructures with tailored functionality for applications. For instance, coiled CNTs can be used as high-performance nanoscale mechanical springs, sensors, or resonators.13-15 A recent experiment suggests that carbon nanorings could be used as templating nanoreactors.12 Carbon nanobuds, fabricated by covalently attaching C60 fullerenes to CNTs, can capture properties of both C60 and CNTs and thus may be utilized as highly efficient field emitters.25,26 It has also been shown by previous experimental and theoretical studies that CNT-based carbon architectures such as Y-shaped or Z-shaped CNT can be constructed through making r 2011 American Chemical Society

intramolecular junctions among CNTs.28 The helically coiled carbon nanotube can be constructed by joining pieces of CNT with different diameters or by introducing heptagon-pentagon defects in CNT.15,29 These specially designed CNT architectures may be applied as rectifiers, field-effect transistors, switches, or amplifiers. A recent experiment demonstrated that a periodically bent SWCNT can be produced by introducing SWCNTsubstrate lattice interaction and by controlling the gas flow in the synthesis of SWCNT.30 Lieber and co-workers9 recently synthesized single-crystalline kinked semiconductor nanowires through controlling nucleation and growth of nanowire. Motivated by the successful synthesis of kinked nanowires and T-shaped CNTs, herein we present a new CNT-based architecture, namely, the step-kinked CNTs. To our knowledge, this CNT architecture has not been reported in the literature. For the nanostructure design, (5,0) and (6,0) SWCNTs are used as the elemental building units. Structural, electronic, and transport properties of the step-kinked CNTs are computed by the densityfunctional theory (DFT) method.

II. COMPUTATIONAL METHODS DFT calculations were carried out by a linear combination of atomic orbital DFT method implemented in the DMol3 Received: November 9, 2010 Revised: January 8, 2011 Published: February 22, 2011 4235

dx.doi.org/10.1021/jp110717k | J. Phys. Chem. C 2011, 115, 4235–4239

The Journal of Physical Chemistry C

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Table 1. Cohesive Energy per Carbon Atom, Average Length of C-C Bonds, and HOMO-LUMO Gap or Band Gap of Carbon Hexagonal Nanotorus, Nanoring, Fullerene, and SWCNT Ecoh, eV

dcc, Å

gap, eV

(5,0) nanotorus C444

8.724

1.439

0.079 (0.87a)

(6,0) nanotorus C672

8.877

1.435

0.063 (1.62a)

(6,0) nanoring C672

8.722

1.443

0.67

C60

8.875

1.417

1.67

(5,0) SWCNT

8.743

1.426

0.20

(6,0) SWCNT

8.888

1.434

0.0

a

The HOMO-LUMO gap is calculated by the B3LYP hybrid density functional method.41

Figure 1. (a) (5,0) Hexagonal nanotorus C444 and (b) (6,0) hexagonal nanotorus C672. The pentagons and heptagons at a joint region are highlighted in red. (c) (6,0) Nanoring C672. (d) C60 Fullerene.

package.32-34 The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form35 together with an all-electron double numerical (DNP) basis set augmented with polarized function were chosen for the spin-restricted DFT calculation. A test calculation with a spin-unrestricted method gave the same results. Real-space global cutoff radius was set to be 3.70 Å. In the end of geometric optimization, the forces on all atoms were less than 0.05 eV 3 Å-1. For the geometric optimization, a tetragonal supercell of size 35 35 c Å3 was used, where c is the periodic length along the tube direction; c = 60.33 Å for (6,0) step-kinked SWCNT and c = 47.63 Å for (5,0) step-kinked SWCNT. The nearest distance between two neighboring stepkinked SWCNTs was about 20 Å. Only the Γ point was considered in the Brillouin zone for geometric optimization. For computing electronic properties of step-kinked nanotube structures, the Brillouin zone was sampled by 1 1 20 k-points via the Monkhorst-Pack scheme.36 In addition, the electronic transport behavior of step-kinked and straight (5,0) SWCNT was studied by the real-space nonequilibrium Green’s method, implemented in ATK software.37,38 The electron transmission spectra were calculated within the local-density approximation, together with the single-ζ basis set. The mesh cutoff was set to be 150 Ry.

III. RESULTS AND DISCUSSION A. Relative Stability of Hexagonal Nanotorus and Nanoring and Model Carbon Joint. From a structural point of view, a

nanoring can be also seen as a circular nanotorus (see Figure 1c). Carbon nanorings have been synthesized via self-assembling fullerenes and applied as templating nanoreactors for growing silver nanoparticles within the central cavity.18 Previous theoretical studies have also predicted that metallic carbon nanorings possess new properties such as giant paramagnetic response.39 We have designed two hexagonal nanotorus structures, namely, (5,0) hexagonal nanotorus C444 and (6,0) hexagonal nanotorus C672. The hexagonal nanotori can be constructed by joining six equal-length SWCNTs consecutively (see Figure 1a,b). In the region of the six joints, both pentagonal and heptagonal defects are introduced to yield an abrupt change in local curvature,

thereby reducing the local stress at the joints. These defects are highlighted in red [see Figure 1a,b]. There are one heptagonal and two pentagonal defects at each joint of the (5,0) hexagonal nanotorus, while there are two heptagonal and two pentagonal defects at each joint of the (6,0) hexagonal nanotorus. For the purpose of comparison, we have also considered a (6,0) carbon nanoring isomer C672 (Figure 1c) with the same number of atoms as the (6,0) hexagonal nanotorus C672. The calculated cohesive energy per atom, average carboncarbon bond length, and gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for the two carbon hexagonal nanotori, one nanoring, two SWCNTs, and the fullerene C60 are summarized in Table 1. The cohesive energy per atom is defined as Ecoh = (nEC - Etotal)/n, where Etotal and EC are the total electronic energy of the carbon-nanotube nanostructure and a single carbon atom, respectively, and n is the total number of carbon atoms in each carbon-nanotube nanostructure unit and the fullerene. The calculated cohesive energy per atom suggests that the (6,0) hexagonal nanotorus C672 is more stable than the (6,0) nanoring C672 isomer. In fact, the cohesive energy per atom of the (6,0) hexagonal nanotorus is greater than that of the buckyball C60 and only slightly less than that of an infinitely long (6,0) SWCNT. The slightly reduced cohesive energy is due to the existence of defects at the joints of the hexagonal nanotorus. In addition, due to the local strain effect, the average carbon-carbon bond length of the (6,0) hexagonal nanotorus or (6,0) nanoring is slightly longer than that of the perfect (6,0) SWCNT. Note also that the cohesive energy per atom of (5,0) hexagonal nanotorus C444 is also slightly greater than that of (6,0) nanoring C672, suggesting that our design of the joint (or kinked) section of (5,0) hexagonal nanotorus is very reasonable from the energetic point of view. On the electronic properties, we find that although the (6,0) SWCNT possesses a zero band gap,40 a small HOMO-LUMO gap is found for the (6,0) hexagonal nanotorus C672. In contrast, the circular (6,0) nanoring C672 has a HOMO-LUMO gap about an order of magnitude larger than that of the (6,0) hexagonal nanotorus (see Table 1 and Figure 2f), even though both nanoclusters have the same tubular diameter. It appears that the perfect circular bending of a finite-size (6,0) SWCNT leads to a larger HOMO-LUMO gap compared to the stepwise bending as in the hexagonal nanotorus. It is well-known that DFT within the general gradient approximation (GGA) underestimates the band gap of semiconductors. So we have also computed the HOMO-LUMO gaps of (5,0) and (6,0) nanotori C444 and C672 by using the B3LYP version of the DFT method (both C444 and 4236

dx.doi.org/10.1021/jp110717k |J. Phys. Chem. C 2011, 115, 4235–4239


Figure 2. Profiles of (a) HOMO and (b) LUMO of (5,0) hexagonal nanotorus C444 and (d) HOMO and (e) LUMO of (6,0) hexagonal nanotorus C672, where the isosurface value is 0.01 au. Corresponding density of states (DOS) of (c) (5,0) hexagonal nanotorus and (5,0) SWCNT and (f) (6,0) hexagonal nanotorus, (6,0) nanoring, and (6,0) SWCNT are also shown. The Fermi level is marked by a vertical dotted line.

C672 nanotori are optimized at B3LYP/6-31G level of theory41) as suggested in a recent study.40 As listed in Table 1, the HOMO-LUMO gaps of (5,0) and (6,0) nanotori become significantly larger, 0.87 and 1.62 eV, respectively. Distribution profiles of the HOMO and LUMO of the two hexagonal nanotori are displayed in Figure 2. The HOMO of both hexagonal nanotori is mainly contributed by the carbon atoms located in the straight nanotube part of the hexagonal nanotori, which retains characteristics of the valence band of the corresponding SWCNT. However, the LUMO of the (5,0) hexagonal nanotorus is mainly contributed by the carbon atoms located at the joint regions. In contrast, the LUMO of the (6,0) hexagonal nanotorus is contributed by the whole carbon nanostructure. Hence, the frontier orbital of the hexagonal nanotorus suggests that the joint regions of nanotorus are likely more chemically reactive than the straight nanotube parts. B. Periodic Step-Kinked Carbon Nanotube. Having obtained two robust (5,0) and (6,0) CNT-based joints (i.e., the kinked section of nanotori), we design two periodic step-kinked carbon nanotubes, based on the (5,0) and (6,0) SWCNTs and the joints of (5,0) and (6,0) hexagonal nanotori. For the step-kinked (5,0) SWCNT, 276 carbon atoms are included in the unit cell and the periodic length is 47.63 Å (after geometry optimization), while for the step-kinked (6,0) SWCNT, 448 carbon atoms are included in the unit cell and the periodic length is 60.33 Å. The average carbon-carbon bond lengths are 1.439 and 1.434 Å for the step-kinked (5,0) and (6,0) SWCNT, respectively, which is nearly the same as that of the nanotori (see Table 1). The calculated electronic band structures (based on the PBE/GGA calculation) of the perfect and step-kinked SWCNTs are displayed in Figure 3c. Although the (5,0) SWCNT is expected to be a semiconductor with a small band gap (0.20 eV from this PBE/GGA calculation), it was recently shown that the (5,0) SWCNT may be metallic according to the B3LYP calculation40 with the Crystal 06 package.42 According to our DFT/PBE calculation, the band gap of the step-kinked (5,0) SWCNT is about 0.035 eV. In contrast, from the DFT/B3LYP/STO-3G calculation using the Crystal 06 package,42 the band gap of the step-kinked (5,0) SWCNT is ∼0.76 eV. This suggests that the introduction of periodic kinks and the pentagon-heptagon defects turns the metallic (5,0) SWCNT40 into a semiconductor.15 We also notice that the

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Figure 3. (a, b) Optimized structures of periodic step-kinked (5,0) and (6,0) SWCNTs. The periodic lengths are 47.63 and 60.33 Å, respectively. (c) Calculated band structures for perfect and step-kinked SWCNTs. The Fermi energy level is marked by a red dotted line.

energy bands of the step-kinked (5,0) SWCNT are less dispersed than those of the perfect (5,0) SWCNT due to the break in symmetry. A sizable empty region can be seen above the Fermi level for the step-kinked (5,0) SWCNT. For the (6,0) SWCNT, it is known that the perfect (straight) (6,0) SWCNT is metallic. Contrary to the step-kinked (5,0) tube, both our DFT/PBE and DFT/B3LYP/STO-3G calculations suggest that the step-kinked (6,0) SWCNT is metallic (Figure 3b). Again, the energy bands of the step-kinked (6,0) SWCNT are flatter than those of the perfect (6,0) SWCNT due to the break in symmetry. One possible reason for the difference between the electronic properties of step-kinked (5,0) and (6,0) SWCNT is due to the difference in introduced local defects in the two SWCNTs. In the step-kinked (5,0) SWCNT, two pentagons and one heptagon are introduced in the joint region, forming a defect neck between two straight stems. In the step-kinked (6,0) SWCNT, two pentagons and two heptagons are introduced at the convex and concave side, respectively, and the two neighboring straight stems are still connected by sp2-hybridized carbon atoms in the joint region, as shown in Figure 1a,b. The partial DOS (PDOS) analysis for the kinked and straight nanotubes also suggests that both kinked and straight sections of the step-kinked (5,0) SWCNT contribute equally to the total DOS near the Fermi energy level, whereas straight sections of the step-kinked (6,0) SWCNT give a much larger contribution to the total DOS than kinked sections, as shown in Figure 4. Hence, the introduction of periodic kinks in a SWCNT may significantly change the band structures of the parent SWCNT, thereby offering tunable band gaps. To understand the modulation of electronic structure due to the formation of step-kinked junction inside the SWCNT, we have studied electronic transport properties of a straight (5,0) SWCNT and a step-kinked (5,0) SWCNT. The step-kinked and straight (5,0) SWCNT-based molecular devices are shown in Figure 5 panels a and b, respectively. For the step-kinked (5,0) SWCNT device, one period of the architecture is chosen as the molecular junction sandwiched between two half-infinite (5,0) SWCNT electrodes. For the straight (5,0) SWCNT device, four unit cells of the (5,0) SWCNT are chosen as the molecular junction sandwiched between two half-infinite (5,0) SWCNT 4237



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straight (5,0) SWCNT has a nonzero steplike electron transmission distribution near the Fermi level, while the step-kinked (5,0) nanotube shows some sharp transmission peaks around the Fermi energy level. The diversity in CNT-based morphologies, combined with their robust mechanical properties and tunable electronic properties, can be exploited for future applications in nanoelectronics.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

Figure 4. Total density of states (DOS) and projected DOS on the junctions and stem parts of step-kinked (5,0) and (6,0) SWCNTs, plotted with black, red, and green lines, respectively [with a smearing width (DMol3) of 0.04 eV]. The Fermi energy level is set as zero.

’ ACKNOWLEDGMENT We are grateful for valuable discussions with Dr. Jing Huang and Honghui Shang. This work is supported by grants from the ONR (N00014-09-1-0943), ARO (W911NF1020099), NSF (CMMI-0709333), NSFC (Grant 1004180), NKBRPC (Grant 2011CB921400), the Nebraska Research Initiative, and the University of Nebraska’s Holland Computing Center. ’ REFERENCES

Figure 5. (a) Structure of step-kinked (5,0) SWCNT-based electronic device. (b) Straight (5,0) SWCNT-based electronic device. (c) Calculated electron transmission spectrum of straight and step-kinked (5,0) SWCNT-based devices (no external voltage applied).

electrodes. As shown in Figure 5c, the calculated electron transmission spectrum suggests that the introduced junction within the (5,0) SWCNT electrodes largely affects the electronic transport behavior of the tube. The straight (5,0) SWCNT has a nonzero steplike transmission distribution near the Fermi level, while the step-kinked (5,0) SWCNT has some small sharp transmission peaks around the Fermi energy level.

IV. CONCLUSION In conclusion, we have designed a new CNT-based architecture named step-kinked carbon nanotubes. According to DFT calculation with the B3LYP hybrid functional, the introduction of periodic kinks turns the perfect (5,0) SWCNT from a metal to a semiconductor, while the (6,0) step-kinked SWCNT is still a metal. The periodic kinks introduced in the SWCNT can also significantly affect electron transport properties. We find the

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Density-Functional Theory Studies of Step-Kinked Carbon Nanotubes

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