Electronic Properties of Cycloaddition-Functionalized Graphene - The

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Electronic Properties of Cycloaddition-Functionalized Graphene Kelvin Suggs, Darkeyah Reuven, and Xiao-Qian Wang* Department of Physics and Center for Functional Nanoscale Materials, Clark Atlanta University, Atlanta, Georgia 30314, United States ABSTRACT: We have studied the electronic characteristics of covalently functionalized graphene by nitrene chemistry using first-principles density functional calculations. The perfluorophenylazide functionalization leads to a band-gap opening in graphene and transition from a semimetallic to a semiconducting state. The [2 þ 1] cycloaddition-induced gap is shown to be attributed to the modification of the π conjugation that depends on the concentration of aziridine adducts. The implications of tailoring the band structure of functionalized graphene for future graphene-based device applications are discussed.

’ INTRODUCTION Graphene is a one-layer sheet of carbon arranged in a honeycomb lattice. Graphene has attracted a great deal of attention due to its remarkable properties and promising potential applications.1-5 The effective application of graphene transistors, integrated circuits, and biosensors, requires an improved understanding and control of the structural and electronic properties of graphene. Because of the gapless character of the graphene band structure, the future of graphene electronics depends on developing routes to engineer a band gap. A gap can be formed in epitaxial graphene grown on a latticematched substrate.6,7 Although the approach involving latticematched substrates is straightforward, combining it with electronic transport remains a challenging task. Another promising method for gap engineering relies on spatial confinement, such as patterning graphene into nanoribbons.8,9 The gap obtained by such a method can be tuned by varying the spatial width of graphene ribbons. However, the approaches relying on spatial confinement are prone to rough edges and defects. Moreover, although graphene nanoribbon field-effect transistors have been shown to exhibit excellent properties,8,10 mass production of graphene nanoribbon-based devices is beyond the capability of current lithography technology.6 Recently, there has also been a number of studies on generating a band gap in the gapless bilayer graphene with a perpendicularly applied electric field.11-14 In bilayer graphene, the Bernal stacking can be lifted by asymmetric chemical doping or electrical gating,4 leading to a gap opening. On the other hand, a wealth of approaches has been developed for noncovalently and covalently functionalized graphene.10,15-23 Graphene contains a paucity of functional moieties and limited dispersibility in solvents, seriously hindering the realization of its great potential.16,21-23 As a result, developing chemical methods in order to tune the materials properties has become one of the most critical issues in exploring graphene technologies. Various chemical modification techniques have been shown to not only enhance its solubilities and processabilities but also render suitable r 2011 American Chemical Society

properties for graphene-based nanoelectronic and nanophotonic devices. Modification of graphene's electronic properties has been carried out by well-established chemical functionalization techniques, in which groups, such as H, OH, or F, bind covalently to carbon atoms, transforming the trigonal sp2 orbital to the tetragonal sp3 state.15,24-28 Such transformations drastically modify the local electronic properties. Recent experimental studies have demonstrated an efficient method to covalently functionalize pristine graphene with the use of nitrene chemistry, in which a perfluorophenylazide (PFPA) undergoes cycloaddition with C-C double bonds, forming an aziridine-ring linkage (see Figure 1).23 A wide range of aryl azide derivatives are available and can be further functionalized with an array of polymeric functional groups. The aziridino-ring reaction can be carried out by thermal and photochemical activation, which results in graphene being soluble in organic solvents and water. The advancement of graphene-aryl-aziridine adduct nanocomposites brings with it the need to understand their impact on the electrical properties of graphene. In lieu of the increasing amount of experimental and theoretical studies of chemically functionalized graphene, a better understanding of how covalent functionalization impacts the morphology and electron/hole transport in graphene becomes pivotal for its future application in nanoelectronics. Experimental advances have motivated our study of electronic structure characteristics of PFPA-functionalized graphene. Herein, we report on comprehensive results based on first-principles density functional calculations. PFPA-functionalized graphene perturbs the π conjugation of graphene, and the corresponding electronic properties change from metallic to semiconducting. We show that, with the increase of aziridine adducts, the resultant Received: December 7, 2010 Revised: January 11, 2011 Published: February 09, 2011 3313

dx.doi.org/10.1021/jp111637b | J. Phys. Chem. C 2011, 115, 3313–3317

The Journal of Physical Chemistry C

Figure 1. Top view of the molecular structures of perfluorophenylazide (PFPA)-functionalized graphene, with PFPA carrying alkyl, ethylene oxide, and perfluoroalkyl groups. Carbon, fluorine, nitrogen, oxygen, and hydrogen atoms are colored in gray (green for graphene), light blue, blue, red, and white, respectively.

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Figure 2. Calculated transition-state (TS) structure between the noninteracting PFPA/graphene and the PFPA-functionalized graphene with a N2 molecule. PFPA adsorbs onto the graphene surface via a nitrene radical. After losing N2, PFPA reacts with graphene via an electrophilic [2 þ 1] cycloaddition reaction. Carbon, fluorine, nitrogen, and hydrogen are colored in gray (green on graphene), light blue, blue, and white, respectively.

energy gap can be tuned. Our work thus asserts the unique opportunity of tailoring the band gap of graphene with varying chemisorption compositions.

’ RESULTS AND DISCUSSION Covalent functionalization of graphene with polymers is advantageous in that long polymer chains facilitate solubilizing graphene into a wide range of solvents, even at a low degree of functionalization.16,21-23 The soluble graphene can further undergo in situ polymerizations with the immobilized functional groups. Although important for solubility, the side chains of PFPA are not crucial to the electronic properties of this nanocomposite.29 As such, we replaced the side chains of PFPA with methyl (-CH3) groups in order to simplify electronic structure calculations. One of the important chemical reactions is the [2 þ 1] cycloaddition of nitrenes, which has been successfully used to functionalize carbon nanomaterials with high efficiency. Shown in Figure 2 is the transition path along with relative energies of the corresponding [2 þ 1] cycloaddition reaction for PFPA-functionalized graphene. The reactant constitutes the noninteracting PFPA and graphene, whereas the product is the PFPA-functionalized graphene in which the addition of a PFPA saturates a double bond between two graphene carbon atoms, forming a cyclopropane-like three-membered ring. Although the energy differences between the starting and ending configurations is fairly small (about 0.1 eV), the transition barrier is 1.92 eV, in good accordance with the experimental estimate of ∼2-3 eV.23 As the predominant contribution to the transition barrier is attributed to the breaking of a N-N double bond and the associated loss of N2, our results are in conformity with the experimental observation that functionalization occurs on the surface of graphene after [2 þ 1] cycloaddition of PFPA. We illustrate in Figure 3 the optimized conformation of PFPAfunctionalized graphene. The adduct increases the bond lengths linking to atoms on graphene. The corresponding bond length

Figure 3. Ball-and-stick representation of optimized structures of PFPA-functionalized graphene with one and two PFPA addends in the left and right panels, respectively. d and d0 are two characteristic bond lengths of 1.56 and 1.42 Å, respectively.

between the C atom on graphene and the N atom of the adduct is around 1.43 Å, whereas that of the C atom and its nearest neighbors on graphene is around 2.21 Å. The latter C-C distance is notably larger than the C-C bond length of 1.42 Å of graphene with sp2 hybridization and indicates bond breaking. The C-C bond lengths in graphene beyond the nearest neighbors are found to be little affected by the functionalization. The graphene-addend interaction in the covalent functionalization has direct consequences on the electronic properties of graphene. Previous theoretical work investigated the addition of functional groups as free radicals to graphene.24,25,29 These functional groups drastically disrupt the geometries and electronic structures of graphene by introducing local sp3 hybridization defects, which induce an sp3-type “impurity” state near the Fermi level.14,30,31 In the cases of divalent functionalization, two sp3 states induced by two neighboring functional sites are shifted away from the Fermi level due to the rehybridization into bonding and antibonding states.31 Therefore, the local bonding configuration can significantly affect the electronic structure of functionalized graphene. To further pursue this point, it is instructive to recall that, for nitrene-functionalized carbon nanotubes, the cyclopropane ring 3314

dx.doi.org/10.1021/jp111637b |J. Phys. Chem. C 2011, 115, 3313–3317


Figure 4. Calculated band structures for pristine graphene (left panel), one-PFPA-functionalized graphene (middle panel), and two-PFPAfunctionalized graphene (right panel). Γ = (0,0), K = (π/3a,2π/3a), M = (0,π/2a), where a = 17.22 Å for a 7 7 rhombus unit cell. The Fermi level is shifted to 0 eV (dashed blue line).

structure introduced by [2 þ 1] cycloadditions either can remain intact or can lead to cleavage of the sidewall bonds with the increase of the nanotube curvature, resulting in two valence tautomeric forms that display distinct electronic characteristics and markedly different transport properties in metallic tubes.30 In those cases, the nitrene chemistry introduces cyclopropane functionalities in place of the partial double bonds initially present in the π-conjugated electronic structure. Each addition saturates a conjugated bond and reverts the valence of a pair of carbon atoms from sp3 to sp2 hybridization.30,31 We depict in Figure 4 the calculated band structures for PFPAfunctionalized graphene, along with the pristine graphene for comparison. It is readily observable that, after the covalent functionalization, the π and π* linear dispersion of pristine graphene in the proximity of the Dirac point (K) largely preserves, while there exists a gap between the π and π* states. These electronic properties of PFPA-functionalized products are in sharp contrast to the sp3 rehybridization and loss of π electrons found upon addition of monovalent chemical groups in other functionalization schemes.14,31 The absence of sp3-type “impurity” states in the vicinity of the Dirac point is also consistent with the rationale that the C-C bond between the two bridgehead atoms is either broken or substantially weakened, leading to partial recovery of the π-electron system. On the other hand, our present results are clearly distinctive to those of the noncovalent functionalization.14,32,33 For noncovalent functionalization, there is little modification of band structures close to the Fermi level, and the corresponding band structure constitutes flat and dispersed bands that can be readily classified as arising from functional group and pristine graphene contributions.34 By contrast, the PFPA-functionalized graphene displays profound level hybridizations. In particular, the bandgap opening at the Dirac point implies important perturbations generated by the functionalization. All of the band gaps of the PFPA-functionalized graphene appear at the Dirac point. It is worth noting that, although the C atoms on graphene connecting to PFPA retain their sp2 hybridization, the sp2 hybridization angle is changed. As a result, the electronic structure of graphene is inevitably affected by PFPA-functionalization. An important ramification of the [2 þ 1] cycloadditioninduced perturbation is that the alteration in the electronic

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Figure 5. Isosurface plot of charge densities of the hybridized valence band maximum (VBM), conduction band minimum (CBM), and the next near-gap states at the band center. The isovalue is 0.025 au.

structure of graphene increases with incrementing PFPA functionalization concentration. We have investigated the functionalization of graphene at a higher addend concentration by including another PFPA functional group in the unit cell (see Figure 3). The results from geometry optimizations indicate that bridgehead C-C bond breaking persists at higher concentrations. The extracted energy gap is 0.16 and 0.29 eV for one and two PFPA addends on a graphene unit cell consisting of 98 carbon atoms, respectively. Closer scrutiny of the band alignments32 and dispersions near the Dirac point reveals that the gap opening is primarily attributed to the functionalization-induced modifications of the π conjugation. The disruption of the original π conjugation is manifested in the level hybridization, as seen in the band structure (Figure 4). Specifically, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular level (LUMO) of PFPA line up with the π and π* bands of graphene at about -1 and 1 eV, respectively. The band alignment is such that the interaction between flat and dispersed bands leads to hybridizationinduced level avoided-crossing, which leads to the split of π and π* bands of graphene into two hybridized bands each. We show in Figure 5 charge densities of the corresponding hybrized bands at the band center (the Γ point). For those states, the charge density distributions display predominant charge confinements on PFPA addends for hybridized conduction and valence bands. This is to be contrasted to the conjugated π and π* pattern on graphene. As can be seen in Figure 5, the increase of the addend concentration leads to a proportional increase of the change of the π conjugation. This correlates with the associated increase of the band gap and thus provides support of the suggested scenario of the functionalization-induced band-gap opening. Careful examination of the charge density distributions also indicates the existence of σ and σ* bonds in the hybridized states that contribute to the gap formation as well. A few remarks are in order. (i) The semimetallic graphene is more sensitive to the π-conjugation changes than the metallic single-walled carbon nanotubes. For the latter to open a gap, it is necessary to have a higher functionalization concentration.30,31 This appears to be attributed to the curvature of the nanotube.30 (ii) The formation of a band gap in PFPA-functionalized graphene is analogous to the epitaxial graphene in that StoneWales defects and the graphene-substrate interaction generate band gaps due to the disruption of π conjugation. (iii) In this work, we focus mainly on the electronic structure characteristics, 3315



Figure 6. Calculated band structures for (a) PFPA-functionalized graphene and (b) NH-functionalized graphene, along with that for the pristine graphene (blue dashed lines).

specifically, the mechanism of band-gap formation for PFPAfunctionalized graphene. The issue of solubility of alkyl, ethylene oxide, and perfluoroalkyl groups can be addressed by alternative theoretical approaches, such as density functional tight-binding calculations. (iv) In addition to the absence of midgap impurity states, it is worth noting that the gap formation mechanism of PFPAfunctionalized graphene is qualitatively distinct from that of NHfunctionalized graphene.35 We illustrate in Figure 6 the calculated band structure. As is readily observable from Figure 6 that, although both schema lead to a gap at the Dirac point (K) that is attributed to the functionalization-induced symmetry breaking,35 NH-functionalized graphene generates a crossing in the vicinity of the Dirac point. By contrast, the PFPA-functionalized graphene sustains the gap formation. This clearly demonstrates the crucial difference between NH-radical and aziridine-ring linkages. (v) The concentration dependence of the [2 þ 1] cycloaddition is investigated with additional PFPA absorption on the same side of the graphene, in accordance with an experimental study.23 If the absorption is on two different sides of graphene, our results indicate that the gap is still opened, but the value of the gap is almost identical (slightly smaller) than the single adsorption. This shows that the distortion of the π-conjugation network depends sensitively on the adsorption configurations as well.

’ CONCLUSIONS In summary, we have studied the electronic characteristics of PFPA-functionalized graphene. We have shown that the [2 þ 1] cycloaddition preserves the sp2 hybridization network of the carbons on graphene. However, the π conjugation of graphene near the Fermi level is greatly disturbed by functionalization, which leads to the opening of a band gap dependent upon the addend concentration. This contrasts with the free-radical functionalization case where an sp3-type band is induced close to the Fermi level. Such dependence of the electronic properties on the degree of functionalization of graphene suggests a novel and controllable method for the “band engineering” of graphene. Our findings on the nature of a PFPA-functionalization-induced band gap provide useful guidelines for enabling the flexibility and optimization of graphene-based nanodevices. ’ METHODS The structural and electronic properties were investigated using first-principles density functional calculations.36 Our first-principles

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calculations are based on density functional theory as implemented in the DMol3 package.36 Perdew-Burke-Ernzerhof (PBE) parametrization37 of the generalized gradient approximation (GGA) was used in the calculations. A supercell with a vacuum space of 16 Å normal to the graphene plane was used. A kinetic energy change of 3 10-4 eV in the orbital basis and appropriate Monchorst-Pack k-point grids of 6 6 1 were sufficient to converge the integration of the charge density. The optimization of atomic positions proceeds until the change in energy is less than 1 10-6 eV per cell. Although the GGA approach systematically underestimates the band gaps, we are primarily interested in the mechanism of gap opening. The GGA approach is expected to provide qualitatively correct information and remains the popular choice for investigations of covalent functionalizations.14 To pursue the effect of addend concentration on the electronic structures, we have considered two configurations by adding one or two PFPA polymers onto a 7 7 rhombus cell, respectively. The cell constitutes 98 carbon atoms for graphene, 7 carbon, 4 fluorine, 1 nitrogen, and 3 hydrogen atoms for each PFPA molecule. A transition-state search employing a combination of LST/ QST algorithms36 facilitates the evaluation of energy barriers. For transition-state calculations, we used a graphene flake to model the graphene layer and found that the distortion generated in the transition-state search is not crucial for the extracted energy barrier (error less than 0.2 eV). The assessment was based on examination of hydrogen passivation and the fix of boundary atoms during the calculations.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the National Science Foundation (Grant DMR-0934142), the Army Research Office (Grant W911NF-06-1-0442), and the Air Force Office of Scientific Research (Grant FA9550-10-1-0254). ’ REFERENCES (1) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183. (2) Rao, C. N. R.; Sood, A. K.; Subrahmanyam, K. S.; Govindaraj, A. Angew. Chem., Int. Ed. 2009, 48, 7752. (3) Neto, A. H. C.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. Rev. Mod. Phys. 2009, 81, 109. (4) Allen, M. J.; Tung, V. C.; Kaner, R. B. Chem. Rev. 2010, 110, 132. (5) Oostinga, J. B.; Heersche, H. B.; Liu, X.; Morpurgo, A. F.; Vandersypen, L. M. Nat. Mater. 2008, 7, 151. (6) Berger, C.; Song, Z.; Li, X.; Wu, X.; Brown, N.; Naud, C.; Mayou, D.; Li, T.; Hass, J.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; de Heer, W. A. Science 2006, 312, 1191. (7) Leenaerts, O.; Partoens, B.; Peeters, F. M. Phys. Rev. B 2009, 80, 245422. (8) Li, X.; Wang, X.; Zhang, L.; Lee, S.; Dai, H. Science 2008, 319, 1229. (9) Xia, F.; Farmer, D. B.; Lin, Y.-M.; Avouris, P. Nano Lett. 2010, 10, 715. (10) Wang, X.; Ouyang, Y.; Li, X.; Wang, H.; Guo, J.; Dai, H. Phys. Rev. Lett. 2008, 100, 206803. (11) Castro, E. V.; Novoselov, K. S.; Morozov, S. V.; Peres, N. M. R.; dos Santos, J. M. B. L.; Nilsson, J.; Guinea, F.; Geim, A. K.; Neto, A. H. C. Phys. Rev. Lett. 2007, 99, 216802. (12) Zhang, Y.; Tang, T.-T.; Girit, C.; Hao, Z.; Martin, M. C.; Zettl, A.; Crommie, M. F.; Shen, Y. R.; Wang, F. Nature 2009, 459, 820. 3316



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(13) Mak, K. F.; Lui, C. H.; Shan, J.; Heinz, T. F. Phys. Rev. Lett. 2009, 102, 256405. (14) Samarakoon, D. K.; Wang, X.-Q. ACS Nano 2010, 4, 4126. (15) 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. Science 2009, 323, 610. (16) Liu, L.-H.; Yan, M.-D. Nano Lett. 2009, 9, 3375. (17) Chen, Z.; Nagase, S.; Hirsch, A.; Haddon, R. C.; Thiel, W.; Schleyer, P. v. R. Angew. Chem., Int. Ed. 2004, 4, 1552. (18) Zhao, J.; Chen, Z.; Zhou, Z.; Park, H.; Schleyer, P. v. R.; Lu, J. P. ChemPhysChem 2005, 6, 598. (19) Nduwimana, A.; Wang, X.-Q. ACS Nano 2009, 3, 1995. (20) He, H.; Gao, C. Chem. Mater. 2010, 22, 5054. (21) Quintana, M.; Spyrou, K.; Marek Grzelczak, M.; Browne, W. R.; Rudolf, P.; Prato, M. ACS Nano 2010, 4, 3527. (22) Choi, J.; Kim, K.-J.; Kim, B.; Lee, H.; Kim, S. J. Phys. Chem. C 2009, 113, 9433. (23) Liu, L.-H.; Lerner, M. M.; Yan, M. Nano Lett. 2010, 10, 3754. (24) Partoens, B.; Peeters, F. M. Phys. Rev. B 2006, 74, 075404. (25) Flores, M. Z. S.; Autreto, P. A. S.; Legoas, S. B.; Galvao, D. S. Nanotechnology 2009, 20, 465704. (26) Li, Y.; Zhou, Z.; Shen, P.; Chen, Z. Chem. Commun. 2010, 46, 3672. (27) Li, Y.; Zhou, Z.; Shen, P.; Chen, Z. J. Phys. Chem. C 2009, 113, 15043. (28) Li, Y.; Zhou, Z.; Shen, P.; Chen, Z. ACS Nano 2009, 3, 1952. (29) Samarakoon, D. K.; Wang, X.-Q. ACS Nano 2009, 3, 4017. (30) Lee, Y.-S.; Marzari, N. Phys. Rev. Lett. 2006, 97, 116801. (31) Park, H.; Zhao, J.; Lu, J.-P. Nano Lett. 2006, 6, 916. (32) Ogunro, O. O.; Wang, X.-Q. Nano Lett. 2009, 9, 1034. (33) Ogunro, O. O.; Karunwi, K.; Khan, I. M.; Wang, X.-Q. J. Phys. Chem. Lett. 2010, 1, 704. (34) Suggs, K.; Wang, X.-Q. Nanoscale 2010, 2, 385. (35) Denis, P. A.; Iribarne, F. J. Phys. Chem. C 2010, 115, 195. (36) DMol3; Accelrys Software Inc.: San Diego, CA, 2010. (37) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865.

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Electronic Properties of Cycloaddition-Functionalized Graphene - The

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