Electronic properties of α-graphyne nanotubes

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8 4 ( 2 0 1 5 ) 2 4 6 –2 5 3

Available at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/locate/carbon

Electronic properties of a-graphyne nanotubes Baotao Kang, Jin Yong Lee

*

Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Republic of Korea

A R T I C L E I N F O

A B S T R A C T

Article history:

We constructed a-graphyne nanotubes (aGyNTs) and performed density functional theory

Received 31 August 2014

calculations to investigate the electronic properties of zigzag and armchair aGyNTs. We

Accepted 1 December 2014

found that all zigzag graphyne nanotubes (Z-aGyNTs) were semiconductors. In particular,

Available online 5 December 2014

the band gap of Z-aGyNTs showed an oscillatory dependence on tube size which could be further classified into three families with Nz = 3 m  1, 3 m and 3 m + 1 where m is a positive integer. This resulted in band gap magnitudes in the following rank order: 3 m  1 > 3 m + 1 > 3 m. Armchair aGyNTs were also calculated to be semiconductor with very small band gaps when tube size is small, though they become metallic as the tube size increases.  2014 Elsevier Ltd. All rights reserved.

1.

Introduction

Due to the unique ability of carbon to form different structures, many new carbon allotropes have been synthesized and characterized in recent years, including fullerenes [1,2], carbon nanotubes (CNTs) [3,4] and graphene [5]. Since their first observation in 1991 [6], CNTs have received enormous attention because of their excellent electrical, mechanical and thermal properties [7]. On the basis of different structures, CNTs are either metallic or semiconducting that have been intensively studied and exploited in electronic devices [8]. Pure CNTs comprise only sp2-like hybridized carbons that form fundamental hexagons. However, other carbon allotropes have never been flattened to a single atomic layer. Recently new kinds of carbon allotropes, namely graphyne and its derivative graphdiyne, have been envisioned, and interest in these allotropes is growing. Graphyne, which was first proposed by Baughman et al. [9], is built by inserting an acetylenic linkage (AC„CA) between two bonded carbons in graphene. The sp and sp2 hybrid networks as demonstrated in Fig. 1 endow graphyne systems with outstanding properties, including uniformly located pores, tunable electronic * Corresponding author: Fax: +82 31 290 7075. E-mail address: [email protected] (J.Y. Lee). http://dx.doi.org/10.1016/j.carbon.2014.12.002 0008-6223/ 2014 Elsevier Ltd. All rights reserved.

properties, good chemical stability, large surface area and excellent electronic conductivity [10]. These unique properties indicate that graphyne has the potential to be applied in Li ion batteries [11], H2 storage devices [12] and fuel cells [13]. Because CNTs can be considered to be seamless cylinders of graphene sheets, graphyne nanotubes can be constructed following the same approach. Graphyne nanotubes have received less attention than graphene nanotubes (conventional carbon nanotubes), which motivated us to undertake the present study. Recently, Li et al. successfully synthesized graphdiyne nanotubes (GDyNTs) with high-performance field emission properties [14]. Even though the synthesized GDyNTs were 15 nm-thick, this study opened up a new research field in carbon materials: the synthesis of single walled graphyne or graphdiyne nanotubes could be realized in the near future. Several theoretical studies have been carried out to investigate c-graphyne nanotubes (cGyNTs). It has been reported that the band gap of cGyNTs exhibits a damped oscillation, and that thermal conductance increases slightly with diameter for both armchair and zigzag nanotubes [15]. Wang et al. reported a decorated c-GyNTs as hydrogen storage media [16]. a-graphyne can be built by

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247

Fig. 1 – Illustration of a-graphyne nanotubes. inserting AC„CA units in a different fashion than in c-graphyne to form graphene-like hexagons [17–20]. However, compared with cGyNTs, a-graphyne nanotubes (aGyNTs) have received little experimental or theoretical attention. In the present paper, we investigated the electronic properties of zigzag aGyNTs (Z-aGyNTs) and armchair aGyNTs (A-aGyNTs) as demonstrated in Fig. 1. Earlier studies predicted the electronic properties of Z-aGyNTs and A-aGyNTs by using the tight-binding (TB) method, but the results reported were conflicting [21–23]. In Refs. [21,22], Z-aGyNTs were reported to be either semi3conductors or metals depending on tube diameter, while A-aGyNTs were predicted to be metals. However, in Ref. [23], all aGyNTs had semiconductor properties and the band gaps of A-aGyNTs were much larger than those of Z-aGyNTs. There are two very important parameters ignored in the TB method: (1) the r–p hybridization effect which is very important for small diameter SWNTs [24] and (2) the presence of two kinds of carbon (sp and sp2 hybridized) in graphyne systems. Ab-initio calculations are highly required to gain deeper insight into aGyNTs. To this end, we performed density functional theory (DFT) calculations, and investigated cohesive energy, Mulliken charge distribution, and band structures of aGyNTs.

2.

Computational method

In this study, DFT-D calculations were carried out using the DMol3 module [25] in Material Studio 5.5. In our simulations, the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional [26,27] was utilized with consideration of DFT-D correction. This PBE-D method has been intensively used to study carbon-related materials [28,29]. The structure of each nanotube was first fully optimized with a Brillouin zone k-point mesh of 1 · 1 · 4. Then, the k-point mesh was increased to 2 · 2 · 50 to compute the electronic band structures (50 is the maximum ˚ value allowed by Dmol3) with k-point separation of 0.001 A (the minimum value allowed by Dmol3). Mulliken population

was taken into account to investigate the charge distribution. No spin restriction was imposed during the calculations. For ˚ vacuum space was imposed to avoid all calculations, a 20 A interlayer interactions. All electron treatments were performed and a double numerical plus polarization (DNP) basis set was used. The convergence tolerance of energy was 105 hartree, and the maximum allowed force and displacement ˚ and 0.005 A ˚ , respectively. For all aGyNTs, were 0.002 hartree/A we imposed spin multiplicity as singlet and triplet states, the obtained energy indicated that the singlet state was more stable than the triplet one. For each tube, the cohesive energy (Ecoh) was calculated as follows: Ecoh ¼ ðEtotal  nEc Þ=n where Etotal, n, and Ec represent the total energy, number of carbon atoms, and energy of isolated carbon atoms, respectively. A more negative Ecoh implies an energetically more stable structure.

3.

Results and discussion

The unit cell of 2D a-graphyne was fully optimized with 2D hexagonal symmetry, and the lattice constant (a) was com˚ . Because of insertion of a AC„CA unit, puted to be 6.968 A all C1 atoms (sp carbons) were positively charged, while all C2 atoms (sp2 carbons) were negatively charged. The charges of C1 and C2 were calculated to be 0.097 and 0.291 e, respectively. a-Graphyne had a zero band gap similar to graphene as noted in Fig. 2. Our results are in good agreement with earlier reports [12,21,30,31]. Similar to graphene and CNTs, 1D aGyNTs were constructed by rolling up 2D graphyne sheet and the nomenclature (n, m) was applied to characterize the tubes’ chirality. With this notation, (n, 0)- and (n, n) represent zigzag and armchair nanotubes, respectively, as depicted in Fig. 1. These tubes were denoted as Nz-Z-aGyNTs and Na-A-aGyNTs, where Nz and Na refer to the tube size of the zigzag and armchair nanotubes, respectively. For a given Nz and Na, diameters

248

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4 3

Energy (ev)

2 1 0 -1 -2 -3 -4 Fig. 2 – Band structure of 2D a-graphyne film.

can be obtained by the relationship dz = Nz · a/p and pffiffiffi da ¼ 3  Na  a=p, respectively. Fig. 3(a) shows the variation in cohesive energy (Ecoh) according to tube size (Nz or Na),

(a)

-6.84

Cohesive Energy (eV)

which has never been considered before. Cohesive energy decreased monotonically as tube size and diameter increased for both Z-aGyNTs and A-aGyNTs, which implies a gradual reduction in surface strain for the larger diameter of the nanotubes. Moreover, the cohesive energy of A-aGyNTs was always smaller than that of Z-aGyNTs when Nz = Na, because A-aGyNTs have a larger diameter and hence less surface strain than Z-aGyNTs. Thus, we plotted the Ecoh of aGyNT as a function of diameter in Fig. 3(b). Interestingly, Z-aGyNTs and A-aGyNTs with the same diameter had nearly the same Ecoh value (difference <0.005 eV/atom). That is, the cohesive energy of aGyNTs was correlated with tube diameter, not tube type (zigzag or armchair). As tube size increased, the cohesive energy of Z- and A-aGyNTs gradually converged from 6.84 and 6.95 to 7.02 eV. Even though the cohesive energies of aGyNTs are smaller than that of graphene (7.906 eV/atom by the PBE method [32], which is consistent with our obtained value of 8.02 eV/atom using the PBE-D method), it is comparable to that of fullerene (7.29 eV/atom) [33]. These results

Z- GyNTs A- GyNTs

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-6.87 -6.90 -6.93 -6.96 -6.99 -7.02 0

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Diameter (angstrom) Fig. 3 – Cohesive energy vs. (a) tube size and (b) diameter of zigzag and armchair graphyne nanotubes.

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indicate that successful synthesis of GDyNTs will allow the realization of single-walled aGyNTs in the near future. In 2D a-graphyne film, all C1 atoms were positively charged and all C2 atoms were negatively charged. In contrast, in 1D aGyNTs, all C2 atoms were equivalent, but C1 atoms could be further divided into two groups, which are marked in red (C1R) and green (C1G) in Fig. 4. As shown in Fig. 5(a), significant charge redistribution occurred when tube size was small. The charge of C1R/C1G in graphyne film (0.097 e) was 0.059/0.129 e and 0.070/0.099 e for 2-Z-a-GyNT and 2-A-a-GyNT, respectively, while that of C2 (0.291 e) changed to 0.248 and 0.268 e, respectively. The charge of C2 decreased with tube size, and converged to 0.29 e, which is equivalent to the case of 2D graphyne. For C1, the two types (C1R and C1G) showed opposite tendencies. The charges of C1R atoms increased and reached a plateau as tube size increased, while the charge of C1G atoms decreased and reached a plateau. Finally, as the tube diameter increased, the charges of all carbon atoms converged to the case of 2D graphyne. Charge distribution as a function of diameter is shown in Fig. 5(b). Interestingly, the charge of C2 was correlated only with tube diameter, not tube type. When the tube diameter was small, Z-a-GyNTs displayed more marked splitting in C1 charges than A-a-GyNTs. The electronic band structure of each nanotube was obtained. The band structures of Z-aGyNTs with Nz = 5, 6, and 7 are plotted in Fig. 6 and those of the other graphyne nanotube size are available in Supporting information (Fig. S1). For Z-aGyNTs, the valence band maximum (VBM) reached the Fermi level (EF) and the conduction band minimum (CBM) was located above EF, inducing a direct band gap (Eg) at the high symmetric gamma (C) point. The band gaps of 5-, 6-, and 7-Z-aGyNTs showed oscillatory behavior with calculated values of 0.555, 0.082, and 0.287 eV. To elucidate the size dependence of the band gap, the variation in Eg as a function of Nz was examined, as shown in Fig. 7. Zigzag graphyne nanotubes showed an oscillatory band gap dependence on tube size. According to band gap variation, Nz-Z-aGyNTs could be classified into the three families of Nz = 3 m  1, 3 m, and 3 m + 1, where m is a positive integer. It is notable

249

that the Eg of 2-Z-aGyNT is not consistent with the fitted curve of the 3 m  1 subgroup. Such disharmony could be ascribed to the effect of the very large curvature of 2-Z-aGyNT on its band structure. As clearly displayed in Fig. S1, the VBM reached EF at the Z high symmetric point and the CBM was located above EF at the C point, inducing an indirect Eg of 0.430 eV. Among those three families, the band gap magnitude was of the following order: 3 m  1 > 3 m + 1 > 3 m, and band gap decreased gradually as tube size increased. Furthermore, it should be emphasized that the band gap of the family with Nz = 3 m never reached zero in our calculations. Such oscillatory behavior of Eg for Z-aGyNTs is consistent with Refs. [21,22], not Ref. [23]. However, Z-aGyNTs with Nz = 3 m were predicted to be metallic in Refs. [21,22] and the Eg of other Z-aGyNTs followed the order 3 m + 1 > 3 m  1. To confirm our findings, other methods including LDA with the PWC functional [34], and GGA with the PW91 [34] and BLYP [35] functionals were employed to investigate the band structures of aGyNTs. The Eg of Z-aGyNTs with Nz up to 10 were recomputed and are listed in Table 1. It is notable that the different methods gave nearly the same results. Thus, we concluded that all Z-aGyNTs are semiconductors (Z-aGyNTs in the 3 m subgroup are expected to be metallic when m becomes large enough). These distinct differences between our study and previous studies could originate from the fact that previous studies applied TB approximation while we employed the DFT-D method that takes dispersive interactions into account. In the previous TB approximations, all carbon atoms were simply treated by one 2pz orbital with nearest-neighbor interactions, which was used to study CNTs two decades ago. It has been reported that when tube diameter decreases, TB approximation may fail to accurately simulate the electronic properties of the tube because of neglect of the tube’s high curvature [36–38]. Furthermore, dispersive interactions are important in electronic structure calculations of carbon materials such as graphene [39]. This paper is the first to report that for Eg of Z-aGyNTs, 3 m  1 > 3 m + 1 > 3 m. We compared the electronic structures of aGyNTs with CNTs. It is well-known that zigzag (n, 0) CNTs are either typical semiconductor when n 5 3 m, and that the band

Fig. 4 – Two types of sp carbon atoms (C1) in 6-Z-aGyNT (left) and 6-A-aGyNT (right). (A color version of this figure can be viewed online.)

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Z- GyNTs C2 C1G

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0.05

C1R

C1R -0.25

-0.30 0

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50

Diameter (Angstrom) Fig. 5 – Atomic charges as a function of (a) tube size and (b) tube diameter. (A color version of this figure can be viewed online.)

gap of the 3 m  1 subgroup is larger than that of the 3 m + 1 subgroup as confirmed by DFT calculations and experiments on optical transition [40,41]. Zigzag (n, 0) CNTs with n = 3 m were predicted to be metallic by the TB method [42,43]. However, the curvature of CNTs alters the overlap of p electrons to produce a small energy band gap [44], which has been confirmed by DFT calculations [45,46] as well as an experimental study [47]. In experiment, (n, 0) SWCNTs with n = 3 m showed tiny band gaps: 0.080 ± 0.005 eV for (9, 0), 0.042 ± 0.004 eV for (12, 0) and 0.029 ± 0.004 eV for (15, 0) SWCNT. That is, Z-aGyNTs and zigzag CNTs have qualitatively similar oscillatory band gap behavior. The Eg values of zigzag CNTs obtained by LDA or GGA methods are slight underestimated compared with experimental values, which supports our conclusion revealing the semiconducting property of Z-aGyNTs.

The band structures of A-aGyNTs with Na = 5, 6 and 7 calculated using the PBE method are plotted in Fig. 6 and those of the other sizes of A-aGyNTs are shown in Fig. S2. The band structures of A-aGyNTs had a VBM that reached EF, and the CBM seemed to be located slightly above EF (insets in Fig. 6). Further calculations revealed that the CBM was actually located slightly above EF resulting in a direct band gap as depicted in the insets of Fig. 6. The Eg values of 5-, 6-, and 7-A-aGyNTwere calculated to be 0.025, 0.024 and 0.017 eV, respectively. This decreasing behavior of Eg depending on tube size was clearly demonstrated in Fig. 7, where the Eg value converged to almost zero when Na P 9. This phenomenon was further verified by the calculations with other methods as listed in Table 1. Thus, based on these more reliable results, we argue that the rather large band gap of A-aGyNTs reported in Ref. [23], where band gap increased as tube size increased, are incorrect. Such a

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Fig. 6 – Band structures of Z-aGyNTs and A-aGyNTs for Nz/Na = 5, 6 and 7. small band gap could be induced by finite curvature during rolling of 2D graphyne film to 1D tubes. Opening of a small band gap (less than 0.004 eV) was also theoretically predicted by the DFT method for armchair CNTs [40], which were experimentally determined to be true metallic CNTs through STM experiments [47,48]. Considering the larger band gap of AaGyNTs than armchair CNTs, A-aGyNTs when Na 6 8 could be considered to be semiconductors, while aGyNTs when Na P 9 becomes metallic, which differs from the conclusions of Refs. [21,22] that all aGyNTs are metallic.

4.

Conclusions

We performed DFT-D calculations to investigate the electronic structures of aGyNTs. Charge redistribution occurred due to

rolling, and gradually converged to the case of 2D graphyne sheet as tube size increased. All Z-aGyNTs are semiconductors and exhibit strong dependence on tube size, as confirmed by different DFT methods. Nz-Z-aGyNTs can be classified into three families according to band gap variation: Nz = 3 m  1, Nz = 3 m, and Nz = 3 m + 1 where m is a positive integer, resulting in the following rank order of band gap magnitudes: 3 m  1 > 3 m + 1 > 3 m. The band gap of the family with Nz = 3 m never reached zero in our calculations, though it will approach zero when m becomes large enough. Such oscillatory behavior has also been observed for zigzag CNTs, which have similar hexagonal carbon rings. Moreover, A-aGyNTs were concluded to be semiconductors with very small band gaps as well when tube size is small, though the band gaps further decreased on tube size finally resulting metallic property when

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Nz=3m-1

0.6

Z- GyNTs A- GyNTs

Band Gap (eV)

0.5

0.4 Nz=3m+1 0.3

0.2

0.1

Nz=3m

0.0 2

4

6

8

Size(Nz/Na)

10

12

14

16

Fig. 7 – The variation of aGyNTs’ band gaps as a function of tube size.

Table 1 – Calculated band gap by different DFT functionals (unit is given in eV). Size

2 3 4 5 6 7 8 9 10

Z-aGyNT

A-aGyNT

PWC

PW91

PBE

BLYP

PWC

PW91

PBE

BLYP

0.365 0.139 0.329 0.571 0.094 0.286 0.392 0.041 0.231

0.392 0.131 0.313 0.574 0.079 0.293 0.395 0.038 0.226

0.430 0.087 0.313 0.555 0.082 0.287 0.393 0.035 0.230

0.446 0.131 0.294 0.563 0.097 0.269 0.398 0.042 0.218

0.020 0.018 0.026 0.013 0.027 0.018 0.008 0.003 0.001

0.030 0.017 0.024 0.026 0.025 0.014 0.006 0.002 0.001

0.022 0.022 0.027 0.025 0.024 0.017 0.010 0.003 0.001

0.007 0.013 0.026 0.006 0.024 0.019 0.011 0.007 0.002

Na P 9. Based on their electronic properties, zigzag graphyne nanotubes are potential semiconductors candidates with band gap that can be controlled by tuning the tube diameter.

Acknowledgements This work was supported by National Research Foundation (NRF) Grants funded by the Korean Government (MEST) (2007-0056343). B.K. acknowledges financial support from the postdoctoral research program of Sungkyunkwan University (2014). The authors would like to acknowledge the support of the KISTI Supercomputing Center through the strategic support program for supercomputing application research [No. KSC-2013-C2-027].

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.carbon. 2014.12.002.

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