First-Principles Study of Graphene and Carbon Nanotubes

Article pubs.acs.org/JPCC

First-Principles Study of Graphene and Carbon Nanotubes Functionalized with Benzyne Mahmoud Hammouri, Sanjiv K. Jha, and Igor Vasiliev* Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, United States ABSTRACT: We applied ab initio computational methods based on density functional theory to study the properties of graphene and single-walled carbon nanotubes functionalized with benzyne. The calculations were carried out using the SIESTA electronic structure code combined with the generalized gradient approximation for the exchange correlation functional. Our study showed that the reaction of cycloaddition of benzyne to pristine graphene was exothermic with the possibility of formation of both [2 + 2] and [4 + 2] reaction products. The binding energies of benzyne molecules attached to semiconducting zigzag and metallic armchair nanotubes were found to be inversely proportional to the nanotube diameter. The linear fits of the binding energies between benzyne and carbon nanotubes extrapolated to the zero curvature limit were in good agreement with the binding energies of benzyne attached to graphene. Our calculations demonstrated that the cycloaddition of benzyne could open up a nonzero gap between the valence and conduction bands of graphene and metallic carbon nanotubes. The value of the band gap was significantly affected by the geometry of benzyne attachment and by the choice of the supercell.

■

INTRODUCTION Carbon nanomaterials have attracted considerable attention in recent years. The remarkable properties of graphene and carbon nanotubes (CNTs) make them promising candidates for a variety of applications in electronics, chemistry, and materials engineering.1,2 Chemical functionalization expands the range of possible applications of carbon nanomaterials. Surface functionalization increases the solubility of graphene and CNTs in organic solvents, opening a way for the synthesis of polymer−carbon nanocomposites.3−6 Covalent functionalization alters the electronic and transport properties of carbon nanostructures, providing a basis for the development of molecular electronics.7−10 However, in the absence of surface defects, carbon nanomaterials are chemically inert and do not easily interact with molecules and functional groups. The low reactivity of graphene and CNTs emphasizes the need for finding chemically active agents that can be covalently bound to the surfaces of carbon nanostructures. Up to date, only a limited number of chemical reactions leading to covalent functionalization of pristine nonoxidized graphene and CNTs have been observed in experiments.11−21 Recent experimental studies have shown the possibility of cycloaddition of arynes, such as benzyne, to the surface of pristine graphene17,21 and to the sidewalls of CNTs.16,19 The successful functionalization of graphene and CNTs with benzyne has been confirmed by X-ray photoelectron spectroscopy (XPS), energy-dispersive X-ray (EDX) spectroscopy, Fourier transform infrared spectroscopy (FTIR), Raman spectroscopy, high-resolution transmission electron microscopy (HRTEM), and thermogravimetric analysis (TGA).16,17,21 These studies demonstrated that aryne cycloaddition provides an efficient method of chemical © 2015 American Chemical Society

modification of pristine carbon nanomaterials under mild reaction conditions. Despite significant interest in covalent functionalization of carbon nanostructures, the mechanism of cycloaddition of arynes to pristine carbon nanomaterials has not been systematically investigated. Previous theoretical studies of cycloaddition of benzyne to graphene and CNTs have focused on several selected structures.19,22,23 Denis and Iribarne investigated the interaction of benzyne with graphene, but only the [2 + 2] cycloaddition reaction was considered in their study.22 Criado et al. computed the lowest energy structures for three zigzag [(10,0), (14,0), (18,0)] and two armchair [(7,7), (10,10)] CNTs functionalized with benzyne.19 Yang et al. studied the reaction mechanism of benzyne cycloaddition to (n,n) armchair CNTs with n = 5−12 and calculated the binding energies for benzyne attached to (n,0) zigzag CNTs with n = 7−12.23 The results of these studies indicated that the topology of cycloaddition of benzyne to CNTs was sensitive to the size and type of the CNT, with the possibility of formation of both [2 + 2] and [4 + 2] reaction products.19,23 The studies of Denis and Iribarne,22 Criado et al.,19 and Yang et al.23 were performed using different computational methods, which made it difficult to compare the calculated properties of graphene and CNTs functionalized with benzyne. Furthermore, in the calculations of Criado et al. and Yang et al., CNTs were modeled using hydrogen-passivated CNT fragments of finite length. This computational model did not take into account the influence of metallic and semiconducting electronic properties on the surface reactivity of armchair and zigzag CNTs. Received: April 28, 2015 Revised: July 9, 2015 Published: July 17, 2015 18719

DOI: 10.1021/acs.jpcc.5b04065 J. Phys. Chem. C 2015, 119, 18719−18728

Article

The Journal of Physical Chemistry C In our paper, we presented a comprehensive first-principles density functional study of cycloaddition of benzyne to pristine graphene and single-walled CNTs. The computed structures, binding energies, and band structures of CNTs and graphene functionalized with benzyne were compared with the results of previous theoretical and experimental studies. On the basis of our calculations, we examined the mechanisms of cycloaddition of benzyne to graphene, zigzag CNTs, and armchair CNTs and analyzed the dependence of the binding energies between CNTs and benzyne on the type and size of the CNT. We also investigated the influence of benzyne cycloaddition on the electronic properties of CNTs and graphene.

■

COMPUTATIONAL METHODS Our computational approach was based on density functional theory (DFT) combined with the pseudopotential approximation.24,25 Calculations were carried out using the SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) electronic structure code.26,27 Within the SIESTA code, electronic wave functions were expanded in a basis of Gaussian-type atomic orbitals. We employed the Kleinman− Bylander form28 of norm-conserving Troullier−Martins pseudopotentials.29 The exchange-correlation energy functional was evaluated using the generalized gradient approximation (GGA) parametrized by Perdew, Burke, and Ernzerhof.30 Computational methods based on DFT combined with the GGA functional have been successfully used in the past to study the properties of functionalized graphene and CNTs.22,31−36 To improve the accuracy of the computed binding energies and equilibrium interatomic distances, all calculations were conducted using the double-ζ plus polarization (DZP) basis set.37 The Hartree and exchange-correlation potentials were computed by projecting the electronic density and wave functions onto a real-space grid. The energy cutoff, which corresponded to the grid spacing, was set to 400 Ry for graphene and to 270−370 Ry for CNTs. The mechanism of surface functionalization of carbon nanomaterials with benzyne is shown in Figure 1. The numbers 1 through 6 indicate the different positions of benzyne molecules attached to graphene, zigzag CNTs, and armchair CNTs. The structures of graphene sheets and CNTs functionalized with benzyne were obtained using a periodic supercell method within the SIESTA code. Graphene sheets were modeled by 6 × 6 and 8 × 8 hexagonal supercells containing 72 and 128 carbon atoms, respectively. The Brillouin zone was sampled with a Monkhorst−Pack 12 × 12 × 1 k-point mesh for the 6 × 6 graphene supercell and a 8 × 8 × 1 k-point mesh for the 8 × 8 graphene supercell. Zigzag and armchair CNTs were modeled by periodic supercells containing 3 and 4 unit cells, respectively. The Brillouin zone was sampled with a 4 × 1 × 1 k-point mesh for semiconducting zigzag CNTs and a 20 × 1 × 1 k-point mesh for metallic armchair CNTs. To eliminate the effects of artificial periodicity, the dimensions of the supercells in the directions orthogonal to the graphene plane and to the axis of the CNT were selected to be greater than the cutoff radii of the SIESTA basis orbitals. Structural optimization of pristine and functionalized carbon nanostructures was performed via the conjugate gradient method. The residual interatomic forces were required to be smaller than 0.03 eV/Å. For pristine graphene, our SIESTA calculations predicted an equilibrium C−C bond length of 1.44 Å, which was in good agreement with the experimental value of 1.42 Å for graphite and graphene.

Figure 1. Surface functionalization of graphene and CNTs with benzyne. The numbers 1 through 6 show different attachment positions of benzyne molecules to (a) graphene, (b) zigzag CNTs, and (c) armchair CNTs.

■

RESULTS AND DISCUSSION Cycloaddition of Benzyne to Graphene. First, we examined the cycloaddition reaction of benzyne to pristine graphene. The optimized structures of graphene sheets functionalized with benzyne in the 1−2 [2 + 2], 1−3 [3 + 2], and 1−4 [4 + 2] attachment configurations are shown in Figure 2. We found that the interaction with benzyne induced significant structural changes in graphene. The attached benzyne molecule was almost orthogonal to the surface of graphene. After the attachment of benzyne to graphene, the C− C bonds near the functionalization sites increased in length from 1.44 to 1.51−1.52 Å, whereas the bond angles decreased from 120° to 112°−116°. The reduction of the angles between the C−C bonds indicated a significant buckling of the graphene layer near the functionalization sites. The buckling could be explained by a partial change of hybridization of the C atoms at the functionalization sites from sp2 to sp3 and the creation of new covalent bonds between benzyne and graphene. The structural changes observed in graphene functionalized with benzyne were similar to those previously reported in graphene functionalized with hydrogen, hydroxyl, carboxyl, epoxy, nitrene, and methyl chemical groups.32,34,35,41−45 The calculated binding energies, Eb, and equilibrium C−C bond lengths, deq, for benzyne molecules attached to pristine graphene are shown in Table 1. The equilibrium C−C bond lengths between benzyne and graphene were defined as the distances between the C atoms of the benzyne molecule and the C atoms of graphene at the functionalization sites. The binding energies between benzyne and graphene were evaluated as E b = ECn + C6H4 − ECn − EC6H4 , where EC6H4, ECn, and ECn + C6H4 were the total energies of an isolated benzyne molecule, pristine graphene, and functionalized graphene, respectively. The negative values of Eb corresponded to thermodynamically stable structures. To eliminate the localized basis set superposition error (BSSE) in SIESTA calculations, the binding energies were computed using the counterpoise correction method proposed by Boys and Bernardi.38 Within 18720


Article

The Journal of Physical Chemistry C

between benzyne and graphene may be observed in experimental studies.21 In contrast, the reaction of 1−3 [3 + 2] cycloaddition of benzyne to pristine graphene was found to be endothermic with the binding energy of +0.44 eV. The results of our calculations for graphene functionalized with benzyne were consistent with previous observations that arynes can react with polycyclic aromatic compounds by [2 + 2] or [4 + 2] cycloadditions, whereas the [3 + 2] cycloaddition is expected to be energetically unfavorable.39,40 Our calculated binding energy for the [2 + 2] cycloaddition of benzyne to pristine graphene was in good agreement with a previous theoretical study performed by Denis and Iribarne, which predicted the binding energies in the range from −12.2 kcal mol−1 (−0.53 eV) to −16.3 kcal mol−1 (−0.71 eV) using the 4 × 4 and 5 × 5 hexagonal graphene supercells combined with several different basis sets.22 The calculated electronic band structures of pristine graphene and graphene functionalized with benzyne in the 1−2 [2 + 2] and 1−4 [4 + 2] attachment positions are shown in Figure 3. The energy bands were computed using the 6 × 6 and 8 × 8 hexagonal graphene supercells. The Γ, K, and M points in the energy band plots correspond to the center, the corner, and the edge center of the first Brillouin zone, respectively. Pristine graphene is a zero-gap material. The valence and conduction bands of pristine graphene have a conical shape and touch each other at the Dirac points located at the K and K′ corners of the first Brillouin zone.46 In the 6 × 6 and 8 × 8 hexagonal graphene supercells, the Dirac points are located at the Γ and K points, respectively. Our calculations demonstrated that the cycloaddition of benzyne opened up a nonzero gap between the valence and conduction bands of graphene. We also found that cycloaddition of benzyne to graphene produced several new energy bands located above and below the Fermi level. These bands were associated with the electronic states resulting from the interaction between benzyne molecules and graphene. Table 2 presents the calculated direct band gaps at the Γ and K points and the minimum band gaps for graphene functionalized with benzyne in the 1−2 [2 + 2] and 1−4 [4 + 2] attachment positions. The band gaps were computed for n × n hexagonal graphene supercells with n = 3−9. In supercells in which n was not a multiple of 3, the Dirac point in pristine graphene was located at the K point of the first Brillouin zone. However, in supercells in which n was a multiple of 3, the Dirac point in pristine graphene appeared at the Γ point due to the projection of the K point to the center of the first Brillouin zone. Our calculations showed that the cycloaddition of benzyne to graphene opened up a nonzero gap at the Γ point in graphene supercells with n = 3, 6, and 9. The band gap increased with decreasing the size of the graphene supercell and increasing the effective concentration of benzyne molecules attached to the surface of graphene. A similar relationship between the size of the band gap and the effective concentration of adsorbates has previously been reported for graphene functionalized with other chemical groups.31,33,43,47,48 We also observed the opening of a nonzero gap at the K point in hexagonal supercells in which n was not a multiple of 3. However, in these supercells the valence and conduction bands of graphene functionalized with benzyne touched each other between the Γ and K or K and M points. Consequently, the minimum value of the band gap was equal to zero in supercells with n = 4, 5, 7, and 8.22 Our study indicated that the choice of the supercell significantly affected the calculated band gap

Figure 2. Optimized structures of graphene sheets functionalized with benzyne in the 1−2 [2 + 2], 1−3 [3 + 2], and 1−4 [4 + 2] attachment positions. The graphene sheets modeled by the 6 × 6 hexagonal supercells are shown.

Table 1. Binding Energies, Eb, and Equilibrium C−C Bond Lengths, deq, for Graphene Functionalized with Benzynea graphene 6 × 6 + C6H4

graphene 8 × 8 + C6H4

attachment position

cycloaddition reaction

Eb (eV)

deq (Å)

Eb (eV)

deq (Å)

1−2 1−3 1−4

[2 + 2] [3 + 2] [4 + 2]

−0.69 +0.45 −0.57

1.55 1.57 1.59

−0.73 +0.44 −0.58

1.55 1.57 1.59

Calculations were carried out using 6 × 6 and 8 × 8 hexagonal graphene supercells.

a

this method, the BSSE was corrected by including additional wave functions without any atomic potential into the basis set. The results of our calculations indicated a good convergence of the computed structures and binding energies with respect to the size of the graphene supercell. The interaction energies between benzyne and graphene computed using the 6 × 6 and 8 × 8 hexagonal supercells agreed to within 0.01−0.04 eV, and the equilibrium bond lengths were almost identical. Our study demonstrated that the reactions of 1−2 [2 + 2] and 1−4 [4 + 2] cycloaddition of benzyne to graphene were exothermic with the binding energies of −0.73 and −0.58 eV, respectively. The 1−2 [2 + 2] attachment was found to be ∼0.15 eV lower in energy than the 1−4 [4 + 2] attachment. A relatively small difference between the energies of these structures suggested that both the [2 + 2] and [4 + 2] cycloaddition reactions 18721


Article


Figure 3. Band structures of (a,d) pristine graphene and graphene functionalized with benzyne in the (b,e) 1−2 [2 + 2] and (c,f) 1−4 [4 + 2] attachment positions. The electronic energy bands were computed using the 6 × 6 and 8 × 8 hexagonal graphene supercells. The zero energy corresponds to the Fermi level.

Table 2. Direct Band Gaps, Eg, at the Γ and K Points and the Minimum Band Gaps, Emin g , for Graphene Functionalized with Benzyne in the 1−2 [2 + 2] and 1−4 [4 + 2] Attachment Positionsa 1−2 [2 + 2] attachment graphene supercell 3 4 5 6 7 8 9 5

× × × × × × × ×

3 4 5 6 7 8 9 5 (2)

Eg(Γ)

Eg(K)

Emin g

0.20 2.09 1.34 0.063 1.55 1.15 0.028 0.46

1.87 0.74 0.52 1.44 0.28 0.22 1.18 0.86

0.20 0 0 0.063 0 0 0.028 0

positions are shown in Figure 4. The computed band gaps are presented in the last line of Table 2. Our calculations indicated that the addition of the second benzyne molecule per supercell did not fundamentally change the band structure of functionalized graphene. Similarly to the case of the 5 × 5 graphene supercell functionalized with one benzyne molecule, we observed the opening of a nonzero gap at the K point, whereas the minimum value of the band gap was equal to zero due to the fact that the valence and conduction bands touched each other between the Γ and K or K and M points. The computed densities of states (DOS) of graphene functionalized with benzyne in the 1−2 [2 + 2] and 1−4 [4 + 2] attachment positions are shown in Figure 5. The DOS plots were obtained using a 50 × 50 × 1 k-point sampling of the 6 × 6 hexagonal graphene supercell. For comparison, the DOS of pristine graphene was also included in the plots. The zero energy in Figure 5 was set at the Fermi level. We found that near the Fermi level the DOS curves of pristine graphene and graphene functionalized with benzyne were similar to each other. The position of the Dirac point in graphene functionalized with benzyne was not noticeably changed compared to that in pristine graphene. At the same time, the positions of the van Hove peaks50 in the DOS of graphene functionalized with benzyne were shifted compared to that in pristine graphene due to structural distortions of the carbon lattice. The DOS of functionalized graphene also exhibited several additional peaks located above and below the Fermi level. These peaks were associated with the new energy bands produced by the cycloaddition of benzyne to graphene. Cycloaddition of Benzyne to Carbon Nanotubes. Next, we examined the cycloaddition reaction of benzyne to carbon nanotubes. The equilibrium structures of the (8,0) zigzag and (5,5) armchair CNTs functionalized with benzyne in different attachment positions are shown in Figures 6 and 7, respectively. The 3−6 [4 + 2] attachment configuration for the (5,5) CNT

1−4 [4 + 2] attachment Eg(Γ)

Eg(K)

Emin g

0.26 2.44 1.56 0.035 1.57 1.20 0.013 1.54

2.50 0.72 0.56 1.53 0.29 0.23 1.21 0.88

0.26 0 0 0.035 0 0 0.013 0

Calculations were carried out for n × n hexagonal graphene supercells with n = 3−9. The last line of the table shows the band gaps for graphene functionalized with two benzyne molecules per supercell. All values are in eV. a

values in graphene functionalized with benzyne. The results of our calculations were consistent with a previous theoretical study of graphene functionalized with hydrogen atoms, which demonstrated a strong dependence of the band gap opening at the Dirac point of graphene on the size of the supercell and the periodicity of the adsorbed hydrogen atoms.49 To test the influence of inhomogeneous distribution of the attached benzyne molecules on the electronic properties of graphene, we computed the band structures of graphene functionalized with two benzyne molecules per supercell. The benzyne molecules were attached to the opposite sides of the graphene sheet. The energy bands were computed using the 5 × 5 hexagonal graphene supercell. The calculated electronic band structures of graphene functionalized with two benzyne molecules in the 1−2 [2 + 2] and 1−4 [4 + 2] attachment 18722


Article


Figure 4. Band structures of (a) pristine graphene and graphene functionalized with two benzyne molecules in the (b) 1−2 [2 + 2] and (c) 1−4 [4 + 2] attachment positions. The electronic energy bands were computed using the 5 × 5 hexagonal graphene supercell. The zero energy corresponds to the Fermi level.

Figure 6. Optimized structures of the (8,0) zigzag CNTs functionalized with benzyne in different attachment positions. Figure 5. Calculated electronic densities of states (DOS) of graphene functionalized with benzyne in the (a) 1−2 [2 + 2] and (b) 1−4 [4 + 2] attachment positions. The zero energy corresponds to the Fermi level.

bonds near the functionalization sites increased in length by 4% to 5%, whereas the bond angles decreased by 3° to 6°. The increase of the bond lengths and the reduction of the angles between the C−C bonds could be explained by the change of hybridization of the C atoms at the functionalization sites from sp2 to sp3 due to the formation of new covalent bonds between benzyne and CNTs. Table 3 presents the calculated binding energies, Eb, and equilibrium C−C bond lengths, deq, for benzyne molecules

was found to be unstable and spontaneously converged into the 1−2 [2 + 2] attachment configuration. Overall, the changes observed in the geometries of CNTs functionalized with benzyne were consistent with the results of our calculations for graphene. After the attachment of benzyne to CNTs, the C−C 18723


Article


molecule, pristine CNT, and functionalized CNT, respectively. Our calculations demonstrated that the interaction energies between benzyne and CNTs strongly depended on the relative orientation of the benzyne molecule with respect to the longitudinal axis of the CNT. The cycloadditions of benzyne to the (8,0) zigzag CNT favored the attachment configurations in which the plane of the benzyne molecule was parallel to the axis of the CNT, whereas the [2 + 2] cycloaddition of benzyne to the (5,5) armchair CNT favored the attachment configuration in which the plane of the benzyne molecule was orthogonal to the axis of the CNT. According to our study, the 1−2 [2 + 2] cycloaddition of benzyne to the (8,0) and (5,5) CNTs produced the most stable reaction products. For the (5,5) armchair CNT, the 1−2 [2 + 2] attachment configuration was ∼0.9 eV lower in energy than the 1−4 [4 + 2] attachment configuration. For the (8,0) zigzag CNT, the energies of the 1− 2 [2 + 2] and 3−6 [4 + 2] benzyne attachments were almost identical. The absolute values of the binding energies between benzyne and CNTs were found to be significantly larger than those between benzyne and graphene. It is interesting to note that our study predicted the possibility of exothermic [3 + 2] cycloaddition reactions of benzyne with the (8,0) and (5,5) CNTs. The results of our study indicated that the sidewalls of CNTs were significantly more reactive toward the cycloaddition of arynes than the surface of pristine graphene. Figure 8 shows the calculated electronic band structures of the (8,0) zigzag and (5,5) armchair CNTs functionalized with

Figure 7. Optimized structures of the (5,5) armchair CNTs functionalized with benzyne in different attachment positions. The 3−6 [4 + 2] attachment configuration for the (5,5) CNT spontaneously converges into the 1−2 [2 + 2] attachment configuration.

Table 3. Binding Energies, Eb, and Equilibrium C−C Bond Lengths, deq, for (8,0) Zigzag and (5,5) Armchair CNTs Functionalized with Benzyne in Different Attachment Positions (8,0) CNT + C6H4 attachment position 1−2 1−3 1−4 1−5 1−6 3−6

cycloaddition reaction [2 [3 [4 [3 [2 [4

+ + + + + +

2] 2] 2] 2] 2] 2]

(5,5) CNT + C6H4

Eb (eV)

deq (Å)

Eb (eV)

deq (Å)

−2.44 −0.86 +0.54 +0.55 −1.92 −2.35

1.54 1.56/1.57 1.63 1.58 1.54 1.56

−2.37 +0.21 −1.52 −1.46 −1.95 −

1.49 1.57/1.59 1.58 1.55 1.54 −

attached to the (8,0) zigzag and (5,5) armchair CNTs. The equilibrium C−C bond lengths between benzyne and CNTs were defined as the distances between the C atoms of the benzyne molecule and the C atoms of CNTs at the functionalization sites. The binding energies between benzyne and CNTs were evaluated as E b = ECNT + C6H4 − ECNT − EC6H4 , where EC6H4, ECNT, and ECNT+C6H4 were the total energies of an isolated benzyne

Figure 8. Calculated band structures of the (a,b) (8,0) zigzag and (c,d) (5,5) armchair CNTs functionalized with benzyne in the [2 + 2] and [4 + 2] attachment positions. The energy bands of pristine and functionalized CNTs are shown by the dashed and solid lines, respectively. The zero energy corresponds to the Fermi level. 18724


Article


in Table 4. For all studied zigzag CNTs, the 1−6 [2 + 2] and 1−4 [4 + 2] attachments of benzyne were found to be

benzyne in the most stable [2 + 2] and [4 + 2] attachment positions. The energy bands were computed using the periodic supercells containing three unit cells for the (8,0) CNT and four unit cells for the (5,5) CNT, respectively. The zero energy in Figure 8 corresponded to the Fermi level. The valence and conduction bands of the semiconducting (8,0) CNT are separated by a relatively large gap, whereas the metallic (5,5) CNT has a zero gap between the valence and conduction bands at the Fermi level. Our calculations demonstrated that the attachment of benzyne reduced the size of the band gap of the semiconducting (8,0) CNT. In contrast, we found that the cycloaddition of benzyne in the 1−4 [4 + 2] attachment position opened up a gap between the valence and conduction bands of the metallic (5,5) CNT. At the same time, the effect of the cycloaddition of benzyne in the 1−2 [2 + 2] attachment position on the band structure of the (5,5) CNT was relatively small. Similarly to the case of graphene, the functionalization of CNTs with benzyne produced several new energy bands associated with the electronic states resulting from the interaction between benzyne molecules and the CNTs. The appearance of impurity bands has previously been observed in CNTs functionalized with other chemical groups.36 The calculated band gaps of the (8,0) zigzag and (5,5) armchair CNTs functionalized with benzyne in different attachment positions are plotted in Figure 9 as a function of

Table 4. Binding Energies, Eb, for Semiconducting Zigzag CNTs of Different Diameters, D, Functionalized with Benzyne in the Most Stable 1−2 [2 + 2] and 3−6 [4 + 2] Attachment Positions Eb (eV) (n,m)

D (Å)

1−2 [2 + 2]

3−6 [4 + 2]

(5,0) (7,0) (8,0) (11,0) (14,0) (16,0)

3.92 5.48 6.27 8.62 11.0 12.5

−3.80 −2.66 −2.44 −1.89 −1.61 −1.43

−3.93 −2.77 −2.35 −1.83 −1.55 −1.48

significantly higher in energy than the 1−2 [2 + 2] and 3−6 [4 + 2] attachments. At the same time, our calculations revealed that the energies of the 1−2 [2 + 2] and 3−6 [4 + 2] cycloadditions of benzyne to zigzag CNTs were close to each other and differed by less than 0.15 eV. A relatively small difference between the energies of these structures suggested that both the [2 + 2] and [4 + 2] cycloaddition reactions between benzyne and zigzag CNTs may be observed in experimental studies. We found that for the (5,0), (7,0), and (16,0) CNTs the 3−6 [4 + 2] attachments of benzyne were slightly lower in energy than the 1−2 [2 + 2] attachments. In contrast, for the (8,0), (11,0), and (14,0) CNTs, the 1−2 [2 + 2] benzyne attachments were slightly lower in energy than the 3−6 [4 + 2] attachments. Our computed binding energies for the 1−2 [2 + 2] and 3−6 [4 + 2] cycloadditions of benzyne to (7,0), (8,0), and (11,0) zigzag CNTs were in reasonably good agreement with a previous theoretical study carried out by Yang et al.23 Overall, our binding energies for the attachments of benzyne to zigzag CNTs were approximately 0.3−0.5 eV lower than the corresponding values of Yang et al. The calculated binding energies, Eb, for metallic armchair CNTs of different diameters, D, functionalized with benzyne in the most stable attachment positions are shown in Table 5. Our

Figure 9. Calculated band gaps of the (a) (8,0) zigzag and (b) (5,5) armchair CNTs functionalized with benzyne in different attachment positions plotted as a function of the number of CNT unit cells. The dashed line corresponds to the calculated bend gap of the pristine (8,0) CNT.

Table 5. Binding Energies, Eb, for Metallic Armchair CNTs of Different Diameters, D, Functionalized with Benzyne in the Most Stable 1−2 [2 + 2], 1−6 [2 + 2], and 1−4 [4 + 2] Attachment Positions

the number of CNT unit cells. Our calculations showed that the influence of chemical functionalization on the electronic properties of the (8,0) and (5,5) CNTs became more pronounced with decreasing the size of the supercell and increasing the effective concentration of the attached benzyne molecules. The computed band gaps of the functionalized metallic (5,5) CNT strongly depended on the position and orientation of the attached benzyne molecule. For the 1−6 [2 + 2] and 1−4 [4 + 2] attachments of benzyne to the (5,5) CNT the band gaps were in the range of ∼0.1−0.4 eV, whereas for the 1−2 [2 + 2] attachment configuration the band gap was close to zero. The results of our calculations were consistent with a previous theoretical study, which predicted a strong dependence of the band gap opening in metallic CNTs functionalized with various chemical groups on the positions of the chemisorption sites on the surface of the CNT.51 The calculated binding energies, Eb, for semiconducting zigzag CNTs of different diameters, D, functionalized with benzyne in the most stable attachment positions are presented

Eb (eV) (n,m)

D (Å)

1−2 [2 + 2]

1−6 [2 + 2]

1−4 [4 + 2]

(3,3) (4,4) (5,5) (8,8)

4.07 5.43 6.80 10.9

−4.56 −3.10 −2.37 −1.32

−3.11 −2.33 −1.95 −1.46

−2.56 −1.88 −1.52 −1.08

calculations demonstrated that for all studied armchair CNTs the 1−2 [2 + 2] and 1−6 [2 + 2] cycloadditions of benzyne were significantly lower in energy than the 1−4 [4 + 2] cycloadditions. Our study predicted that for the (3,3), (4,4), and (5,5) CNTs, the 1−2 [2 + 2] attachments of benzyne were lower in energy than the 1−6 [2 + 2] attachments. In contrast, we found that for the (8,8) CNT the 1−2 [2 + 2] benzyne attachment was slightly higher in energy than the 1−6 [2 + 2] attachment. Our computed binding energies for the 1−2 [2 + 2], 1−6 [2 + 2], and 1−4 [4 + 2] cycloadditions of benzyne to 18725


Article


hydroxyl, amine, and carboxyl chemical groups.52 The results of our study indicated that the linear fits of Eb vs 1/D extrapolated to the limit of D → ∞ were in very good agreement with the computed binding energies of benzyne attached to pristine graphene in the 1−2 [2 + 2] and 1−4 [4 + 2] positions. Figure 11 shows the variations of the calculated binding energies, Eb, vs the CNT inverse diameter for metallic armchair CNTs functionalized with benzyne in the 1−2 [2 + 2], 1−6 [2

(5,5) and (8,8) armchair CNTs for the most part agreed with the results of the previous theoretical study performed by Yang et al.23 Overall, our computed binding energies for the attachments of benzyne to armchair CNTs were approximately 0.2−0.7 eV lower than the corresponding values obtained by Yang et al. The discrepancy between our binding energies and those of Yang et al. could be attributed to the difference in the computational models: in our calculations the structures of CNTs were modeled using periodic supercells, whereas in the study of Yang et al. CNT structures were modeled using hydrogen-passivated CNT fragments. The variations of the calculated binding energies, Eb, for semiconducting zigzag CNTs functionalized with benzyne in the most stable 1−2 [2 + 2] and 3−6 [4 + 2] attachment positions are plotted in Figure 10 as functions of the CNT

Figure 10. Binding energies, Eb, for semiconducting zigzag CNTs functionalized with benzyne in the (a) 1−2 [2 + 2] and (b) 3−6 [4 + 2] attachment positions plotted as a function of the CNT inverse diameter, 1/D. The limit of D → ∞ corresponds to the binding energies of benzyne attached to graphene in the (a) 1−2 [2 + 2] and (b) 1−4 [4 + 2] positions. The best linear fits of Eb vs 1/D are shown by the dashed lines.

inverse diameter. The dashed lines show the best linear fits of Eb vs 1/D. Our calculations demonstrated that the surface reactivity of zigzag CNTs toward the cycloaddition of benzyne increased with decreasing the diameter of the CNT and increasing the curvature of the CNT sidewall. The binding energies of benzyne molecules attached to semiconducting zigzag CNTs were found to be inversely proportional to the CNT diameter. A similar linear dependence of Eb on 1/D has previously been observed for CNTs functionalized with

Figure 11. Binding energies, Eb, for metallic armchair CNTs functionalized with benzyne in the (a) 1−2 [2 + 2], (b) 1−6 [2 + 2], and (c) 1−4 [4 + 2] attachment positions plotted as a function of the CNT inverse diameter, 1/D. The limit of D → ∞ corresponds to the binding energies of benzyne attached to graphene in the (a), (b) 1−2 [2 + 2] and (c) 1−4 [4 + 2] positions. The best linear fits of Eb vs 1/D are shown by the dashed lines. 18726



■

+ 2], and 1−4 [4 + 2] attachment positions. We found that, similarly to the case of zigzag CNTs, the surface reactivity of armchair CNTs toward benzyne increased with decreasing the diameter of the CNT and increasing the curvature of the CNT sidewall. The absolute values of the binding energies of benzyne molecules attached to metallic armchair CNTs in the 1−6 [2 + 2] and 1−4 [4 + 2] positions increased in inverse proportion to the CNT diameter. At the same time, we observed deviations from the linear relationship between Eb and 1/D for the 1−2 [2 + 2] attachments of benzyne to armchair CNTs. The observed differences in the dependence of Eb on 1/D for the 1−2 [2 + 2], 1−6 [2 + 2], and 1−4 [4 + 2] cycloadditions of benzyne to armchair CNTs could be attributed to a geometrical factor. For armchair CNTs functionalized with benzyne in the 1−2 [2 + 2] attachment position, the plane of the benzyne molecule was orthogonal to the axis of the CNT. We found that the angles between the C−C bonds at the functionalization sites were more strongly affected by the curvature of the CNT sidewall when the benzyne molecule was orthogonal to the CNT axis. This observation could explain the nonlinear dependence of Eb on 1/D for the 1−2 [2 + 2] cycloaddition of benzyne to armchair CNTs.

REFERENCES

(1) Dresselhaus, M. S.; Dresselhaus, G.; Avouris, Ph. Carbon nanotubes: Synthesis, Structure, Properties, and Applications; SpringerVerlag: Berlin, 2001. (2) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183−191. (3) Chen, J.; Hamon, M. A.; Hu, H.; Chen, Y.; Rao, A. M.; Eklund, P. C.; Haddon, R. C. Solution Properties of Single-WalledCarbon Nanotubes. Science 1998, 282, 95−98. (4) Dai, L.; Mau, A. W. H. Controlled Synthesis and Modification of Carbon Nanotubes and C60: Carbon Nanostructures for Advanced Polymeric Composite Materials. Adv. Mater. 2001, 13, 899−913. (5) Stankovich, S.; Dikin, D. A.; Dommett, G. H. B.; Kohlhaas, K. M.; Zimney, E. J.; Stach, E. A.; Piner, R. D.; Nguyen, S. T.; Ruoff, R. S. Graphene-Based Composite Materials. Nature 2006, 442, 282−286. (6) Worsley, K. A.; Ramesh, P.; Mandal, S. K.; Niyogi, S.; Itkis, M. E.; Haddon, R. C. Soluble Graphene Derived from Graphite Fluoride. Chem. Phys. Lett. 2007, 445, 51−56. (7) Anantram, M. P.; Leonard, F. Physics of Carbon Nanotube Electronic Devices. Rep. Prog. Phys. 2006, 69, 507−561. (8) Balasubramanian, K.; Lee, E. J. H.; Weitz, R. T.; Burghard, M.; Kern, K. Carbon Nanotube Transistors - Chemical Functionalization and Device Characterization. Phys. Status Solidi A 2008, 205, 633−646. (9) Sarkar, S.; Bekyarova, E.; Haddon, R. C. Covalent Chemistry in Graphene Electronics. Mater. Today 2012, 15, 276−285. (10) Tang, Q.; Zhou, Z.; Chen, Z. F. Graphene-Related Nanomaterials: Tuning Properties by Functionalization. Nanoscale 2013, 5, 4541−4583. (11) Georgakilas, V.; Kordatos, K.; Prato, M.; Guldi, D. M.; Holzinger, M.; Hirsch, A. Organic Functionalization of Carbon Nanotubes. J. Am. Chem. Soc. 2002, 124, 760−761. (12) Tagmatarchis, T.; Prato, M. Functionalization of Carbon Nanotubes via 1,3-Dipolar Cycloadditions. J. Mater. Chem. 2004, 14, 437−439. (13) Delgado, J. L.; de la Cruz, P.; Langa, F.; Urbina, A.; Casadoc, J.; Lopez Navarrete, J. T. Microwave-Assisted Sidewall Functionalization of Single-Wall Carbon Nanotubes by Diels-Alder Cycloaddition. Chem. Commun. 2004, 1734−1735. (14) Alvaro, M.; Atienzar, P.; de la Cruz, P.; Delgado, J. L.; Garcia, H.; Langa, F. Sidewall Functionalization of Single-Walled Carbon Nanotubes with Nitrile Imines. Electron Transfer from the Substituent to the Carbon Nanotube. J. Phys. Chem. B 2004, 108, 12691−12697. (15) Gomez-Escalonilla, M. J.; Atienzar, P.; Fierro, J. L. G.; Garcia, H.; Langa, F. Heck Reaction on Single-Walled Carbon Nanotubes. Synthesis and Photochemical Properties of a Wall Functionalized SWNT-Anthracene Derivative. J. Mater. Chem. 2008, 18, 1592−1600. (16) Criado, A.; Gomez-Escalonilla, M. J.; Fierro, J. L. G.; Urbina, A.; Pena, D.; Guitian, E.; Langa, F. Cycloaddition of Benzyne to SWCNT: Towards CNT-Based Paddle Wheels. Chem. Commun. 2010, 46, 7028−7030. (17) Zhong, X.; Jin, J.; Li, S.; Niu, Z.; Hu, W.; Li, R.; Ma, J. Aryne Cycloaddition: Highly Efficient Chemical Modification of Graphene. Chem. Commun. 2010, 46, 7340−7342. (18) Bekyarova, E.; Sarkar, S.; Niyogi, S.; Itkis, M. E.; Haddon, R. C. Advances in the Chemical Modification of Epitaxial Graphene. J. Phys. D: Appl. Phys. 2012, 45, 154009. (19) Criado, A.; Vizuete, M.; Gomez-Escalonilla, M. J.; GarciaRodriguez, S.; Fierro, J. L. G.; Cobas, A.; Pena, D.; Guitian, E.; Langa, F. Efficient Cycloaddition of Arynes to Carbon Nanotubes under Microwave Irradiation. Carbon 2013, 63, 140−148. (20) Peng, X.; Li, Y.; Zhang, G.; Zhang, F.; Fan, X. Functionalization of Graphene with Nitrile Groups by Cycloaddition of Tetracyanoethylene Oxide. J. Nanomaterials 2013, 2013, 841789. (21) Magedov, I. V.; Frolova, L. V.; Ovezmyradov, M.; Bethke, D.; Shaner, E. A.; Kalugin, N. G. Benzyne-Functionalized Graphene and Graphite Characterized by Raman Spectroscopy and Energy Dispersive X-ray Analysis. Carbon 2013, 54, 192−200. (22) Denis, P. A.; Iribarne, F. [2 + 2] Cycloaddition sonto Graphene. J. Mater. Chem. 2012, 22, 5470−5477.

■

CONCLUSION We applied first-principles density functional computational methods to study the cycloaddition of benzyne to graphene and single-walled CNTs. Our calculations were performed using the SIESTA electronic structure code. The exchange-correlation energy functional was evaluated using the generalized gradient approximation. Our study demonstrated that the reactions of [2 + 2] and [4 + 2] cycloaddition of benzyne to pristine graphene were exothermic. The sidewalls of CNTs were found to be significantly more reactive toward benzyne than the surface of graphene. The binding energies of benzyne molecules attached to semiconducting zigzag and metallic armchair CNTs were, in most cases, inversely proportional to the CNT diameter. Our calculations showed that for the semiconducting zigzag CNTs the [2 + 2] and [4 + 2] cycloadditions of benzyne were close to each other in energy, whereas for the metallic armchair CNTs the [2 + 2] cycloadditions of benzyne were significantly lower in energy than the [4 + 2] cycloadditions. These results suggested a possibility of separating different chiral and electronic types of CNTs using the reaction of aryne cycloaddition. The computed electronic band structures of graphene and CNTs functionalized with benzyne showed that cycloaddition reactions involving arynes could potentially be used for band gap engineering of graphene and CNTs.

■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported by the National Science Foundation under Grant No. CHE-1112388 and by a New Mexico State University Graduate Research Enhancement Grant. 18727


Article


(46) Wallace, P. R. The Band Theory of Graphite. Phys. Rev. 1947, 71, 622−634. (47) Milowska, K.; Birowska, M.; Majewski, J. A. Mechanical and Electrical Properties of Carbon Nanotubes and Graphene Layers Functionalized with Amine. Diamond Relat. Mater. 2012, 23, 167−171. (48) Milowska, K.; Majewski, J. A. Stability and Electronic Structure of Covalently Functionalized Graphene Layers. Phys. Status Solidi B 2013, 250, 1474−1477. (49) Garcia-Lastra, J. M. Strong Dependence of Band-Gap Opening at the Dirac Point of Graphene upon Hydrogen Adsorption Periodicity. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 235418. (50) van Hove, L. The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal. Phys. Rev. 1953, 89, 1189−1193. (51) Garcia-Lastra, J. M.; Thygesen, K. S.; Strange, M.; Rubio, A. Conductance of Sidewall-Functionalized Carbon Nanotubes: Universal Dependence on Adsorption Sites. Phys. Rev. Lett. 2008, 101, 236806. (52) Doudou, B. B.; Chen, J.; Vivet, A.; PoiLane, C. Ab Initio Study of the Size-Dependent Effect on the Covalent Functionalization of Single Walled Carbon Nanotubes with Hydroxyl, Amine, and Carboxyl Groups. J. Nanosci. Nanotechnol. 2012, 12, 8635−8639.

(23) Yang, T.; Zhao, X.; Nagase, S. Cycloaddition of Benzyne to Armchair Single-Walled Carbon Nanotubes: [2 + 2] or [4 + 2]? Org. Lett. 2013, 15, 5960−5963. (24) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864−B871. (25) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133− A1138. (26) Ordejon, P.; Artacho, E.; Soler, J. M. Self-Consistent Order-N Density-Functional Calculations for Very LargeSystems. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 53, R10441−R10444. (27) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. The Siesta Method for Ab Initio Order-N Materials Simulation. J. Phys.: Condens. Matter 2002, 14, 2745−2779. (28) Kleinman, L.; Bylander, D. M. Efficacious Form for Model Pseudopotentials. Phys. Rev. Lett. 1982, 48, 1425−1428. (29) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for PlaneWave Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 43, 1993−2006. (30) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868; 1997, 78, 1396. (31) Boukhvalov, D. W.; Katsnelson, M. I. Tuning the Gap in Bilayer Graphene Using Chemical Functionalization: Density Functional Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 085413. (32) Boukhvalov, D. W.; Katsnelson, M. I. Chemical Functionalization of Graphene. J. Phys.: Condens. Matter 2009, 21, 344205. (33) Boukhvalov, D. W.; Katsnelson, M. I. A New Route towards Uniformly Functionalized Single-Layer Graphene. J. Phys. D: Appl. Phys. 2010, 43, 175302. (34) Al-Aqtash, N.; Vasiliev, I. Ab Initio Study of Carboxylated Graphene. J. Phys. Chem. C 2009, 113, 12970−12975. (35) Al-Aqtash, N.; Vasiliev, I. Ab Initio Study of Boron- and Nitrogen-Doped Graphene and Carbon Nanotubes Functionalized with Carboxyl Groups. J. Phys. Chem. C 2011, 115, 18500−18510. (36) Milowska, K.; Majewski, J. A. Functionalization of Carbon Nanotubes with -CHn, -NHn Fragments, -COOH and -OH Groups. J. Chem. Phys. 2013, 138, 194704. (37) El-Mellouhi, F.; Mousseau, N.; Ordejon, P. Sampling the Diffusion Paths of a Neutral Vacancy in Silicon with Quantum Mechanical Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 205202. (38) Boys, F.; Bernardi, F. The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies.Some Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553−566. (39) Pellissier, H.; Santelli, M. The Use of Arynes in Organic Synthesis. Tetrahedron 2003, 59, 701−730. (40) Sanz, R. Recent Applications of Aryne Chemistry to Organic Synthesis. A Review. Org. Prep. Proced. Int. 2008, 40, 215−291. (41) Elias, D. C.; Nair, R. R.; Mohiuddin, T. M. G.; Morozov, S. V.; Blake, P.; Halsall, M. P.; Ferrari, A. C.; Boukhvalov, D. W.; Katsnelson, M. I.; Geim, A. K.; Novoselov, K. S. Control of Graphene’s Properties by Reversible Hydrogenation: Evidence for Graphane. Science 2009, 323, 610−613. (42) Flores, M. Z. S.; Autreto, P. A. S.; Legoas, S. B.; Galvao, D. S. Graphene to Graphane: a Theoretical Study. Nanotechnology 2009, 20, 465704. (43) Yan, J.-A.; Chou, M. Y. Oxidation Functional Groupson Graphene: Structural and Electronic Properties. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 125403. (44) Pei, Q.-X.; Zhang, Y.-W.; Shenoy, V. B. Mechanical Properties of Methyl Functionalized Graphene: A Molecular Dynamics Study. Nanotechnology 2010, 21, 115709. (45) Denis, P. A.; Iribarne, F. Monolayer and Bilayer Graphene Functionalized with Nitrene Radicals. J. Phys. Chem. C 2011, 115, 195−203. 18728


First-Principles Study of Graphene and Carbon Nanotubes

Recommend Documents