Electronic Properties of Cycloaddition-Functionalized Graphene

Published: February 09, 2011

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

ARTICLE

pubs.acs.org/JPCC

Electronic Properties of Cycloaddition-Functionalized GrapheneKelvin 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 ofcovalently functionalized graphene by nitrene chemistry usingfirst-principles density functional calculations. The perfluoro-phenylazide functionalization leads to a band-gap opening ingraphene and transition from a semimetallic to a semiconduct-ing state. The [2þ 1] cycloaddition-induced gap is shown to beattributed to the modification of the π conjugation that dependson the concentration of aziridine adducts. The implications oftailoring the band structure of functionalized graphene for fu-ture graphene-based device applications are discussed.

’ INTRODUCTION

Graphene is a one-layer sheet of carbon arranged in a honey-comb lattice. Graphene has attracted a great deal of attention due toits remarkable properties and promising potential applications.1-5

The effective application of graphene transistors, integrated circuits,and biosensors, requires an improved understanding and control ofthe structural and electronic properties of graphene. Because of thegapless character of the graphene band structure, the future ofgraphene electronics depends on developing routes to engineer aband gap.

A gap can be formed in epitaxial graphene grown on a lattice-matched substrate.6,7 Although the approach involving lattice-matched substrates is straightforward, combining it with electronictransport remains a challenging task. Another promisingmethod forgap engineering relies on spatial confinement, such as patterninggraphene into nanoribbons.8,9 The gap obtained by such amethodcan be tuned by varying the spatial width of graphene ribbons.However, the approaches relying on spatial confinement are proneto rough edges and defects. Moreover, although graphene nanor-ibbon field-effect transistors have been shown to exhibit excellentproperties,8,10 mass production of graphene nanoribbon-baseddevices is beyond the capability of current lithography techno-logy.6 Recently, there has also been a number of studies on gene-rating a band gap in the gapless bilayer graphene with a perpendi-cularly applied electric field.11-14 In bilayer graphene, the Bernalstacking can be lifted by asymmetric chemical doping or electricalgating,4 leading to a gap opening.

On the other hand, a wealth of approaches has been developedfor noncovalently and covalently functionalized graphene.10,15-23

Graphene contains a paucity of functional moieties and limiteddispersibility in solvents, seriously hindering the realization of itsgreat potential.16,21-23 As a result, developing chemical methodsin order to tune the materials properties has become one of themost critical issues in exploring graphene technologies. Variouschemical modification techniques have been shown to not onlyenhance its solubilities and processabilities but also render suitable

properties for graphene-based nanoelectronic and nanophotonicdevices.

Modification of graphene's electronic properties has beencarried out by well-established chemical functionalization tech-niques, in which groups, such as H, OH, or F, bind covalently tocarbon atoms, transforming the trigonal sp2 orbital to the tetra-gonal sp3 state.15,24-28 Such transformations drastically modifythe local electronic properties.

Recent experimental studies have demonstrated an efficientmethod to covalently functionalize pristine graphene with the useof nitrene chemistry, in which a perfluorophenylazide (PFPA)undergoes cycloaddition with C-C double bonds, forming anaziridine-ring linkage (see Figure 1).23 A wide range of aryl azidederivatives are available and can be further functionalized with anarray of polymeric functional groups. The aziridino-ring reactioncan be carried out by thermal and photochemical activation, whichresults in graphene being soluble in organic solvents and water.The advancement of graphene-aryl-aziridine adduct nanocom-posites brings with it the need to understand their impact on theelectrical properties of graphene. In lieu of the increasing amountof experimental and theoretical studies of chemically functiona-lized graphene, a better understanding of how covalent functio-nalization impacts the morphology and electron/hole transport ingraphene becomes pivotal for its future application in nano-electronics.

Experimental advances have motivated our study of electronicstructure characteristics of PFPA-functionalized graphene. Here-in, we report on comprehensive results based on first-principlesdensity functional calculations. PFPA-functionalized grapheneperturbs the π conjugation of graphene, and the correspondingelectronic properties change from metallic to semiconducting.We show that, with the increase of aziridine adducts, the resultant

Received: December 7, 2010Revised: January 11, 2011

3314 dx.doi.org/10.1021/jp111637b |J. Phys. Chem. C 2011, 115, 3313–3317

The Journal of Physical Chemistry C ARTICLE

energy gap can be tuned. Our work thus asserts the uniqueopportunity of tailoring the band gap of graphene with varyingchemisorption compositions.

’RESULTS AND DISCUSSION

Covalent functionalization of graphene with polymers isadvantageous in that long polymer chains facilitate solubilizinggraphene into a wide range of solvents, even at a low degree offunctionalization.16,21-23 The soluble graphene can further un-dergo in situ polymerizations with the immobilized functionalgroups. Although important for solubility, the side chains ofPFPA are not crucial to the electronic properties of this nano-composite.29 As such, we replaced the side chains of PFPA withmethyl (-CH3) groups in order to simplify electronic structurecalculations.

One of the important chemical reactions is the [2þ 1] cyclo-addition of nitrenes, which has been successfully used to func-tionalize carbon nanomaterials with high efficiency. Shown inFigure 2 is the transition path along with relative energies of thecorresponding [2þ 1] cycloaddition reaction for PFPA-functio-nalized graphene. The reactant constitutes the noninteractingPFPA and graphene, whereas the product is the PFPA-functio-nalized graphene in which the addition of a PFPA saturates adouble bond between two graphene carbon atoms, forming acyclopropane-like three-membered ring. Although the energydifferences between the starting and ending configurations isfairly small (about 0.1 eV), the transition barrier is 1.92 eV, ingood accordance with the experimental estimate of ∼2-3 eV.23

As the predominant contribution to the transition barrier is attri-buted to the breaking of a N-N double bond and the associatedloss of N2, our results are in conformity with the experimental ob-servation that functionalization occurs on the surface of grapheneafter [2 þ 1] cycloaddition of PFPA.

We illustrate in Figure 3 the optimized conformation of PFPA-functionalized graphene. The adduct increases the bond lengthslinking to atoms on graphene. The corresponding bond length

between the C atom on graphene and the N atom of the adduct isaround 1.43 Å, whereas that of the C atom and its nearestneighbors on graphene is around 2.21 Å. The latter C-Cdistance is notably larger than the C-C bond length of 1.42 Åof graphene with sp2 hybridization and indicates bond breaking.The C-C bond lengths in graphene beyond the nearest neigh-bors are found to be little affected by the functionalization.

The graphene-addend interaction in the covalent functiona-lization has direct consequences on the electronic properties ofgraphene. Previous theoretical work investigated the addition offunctional groups as free radicals to graphene.24,25,29 These func-tional groups drastically disrupt the geometries and electronicstructures of graphene by introducing local sp3 hybridizationdefects, which induce an sp3-type “impurity” state near the Fermilevel.14,30,31 In the cases of divalent functionalization, two sp3

states induced by two neighboring functional sites are shiftedaway from the Fermi level due to the rehybridization into bond-ing and antibonding states.31 Therefore, the local bondingconfiguration can significantly affect the electronic structure offunctionalized graphene.

To further pursue this point, it is instructive to recall that, fornitrene-functionalized carbon nanotubes, the cyclopropane ring

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

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

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



structure introduced by [2þ 1] cycloadditions either can remainintact or can lead to cleavage of the sidewall bonds with theincrease of the nanotube curvature, resulting in two valencetautomeric forms that display distinct electronic characteristicsand markedly different transport properties in metallic tubes.30

In those cases, the nitrene chemistry introduces cyclopropanefunctionalities in place of the partial double bonds initially pre-sent in the π-conjugated electronic structure. Each addition satu-rates a conjugated bond and reverts the valence of a pair of car-bon atoms from sp3 to sp2 hybridization.30,31

We depict in Figure 4 the calculated band structures for PFPA-functionalized graphene, along with the pristine graphene forcomparison. It is readily observable that, after the covalent func-tionalization, theπ andπ* linear dispersion of pristine graphene inthe proximity of the Dirac point (K) largely preserves, while thereexists a gap between the π and π* states. These electronic prop-erties of PFPA-functionalized products are in sharp contrast to thesp3 rehybridization and loss of π electrons found upon addition ofmonovalent chemical groups in other functionalization schemes.14,31

The absence of sp3-type “impurity” states in the vicinity of the Diracpoint is also consistent with the rationale that the C-C bond be-tween the two bridgehead atoms is either broken or substantiallyweakened, leading to partial recovery of the π-electron system.

On the other hand, our present results are clearly distinctiveto those of the noncovalent functionalization.14,32,33 For non-covalent functionalization, there is little modification of bandstructures close to the Fermi level, and the corresponding bandstructure constitutes flat and dispersed bands that can be readilyclassified as arising from functional group and pristine graphenecontributions.34 By contrast, the PFPA-functionalized graphenedisplays profound level hybridizations. In particular, the band-gap opening at the Dirac point implies important perturbationsgenerated by the functionalization. All of the band gaps of thePFPA-functionalized graphene appear at the Dirac point. It isworth noting that, although the C atoms on graphene connectingto PFPA retain their sp2 hybridization, the sp2 hybridizationangle is changed. As a result, the electronic structure of grapheneis inevitably affected by PFPA-functionalization.

An important ramification of the [2 þ 1] cycloaddition-induced perturbation is that the alteration in the electronic

structure of graphene increases with incrementing PFPA func-tionalization concentration. We have investigated the functiona-lization of graphene at a higher addend concentration by includ-ing another PFPA functional group in the unit cell (see Figure 3).The results from geometry optimizations indicate that bridge-head C-C bond breaking persists at higher concentrations. Theextracted energy gap is 0.16 and 0.29 eV for one and two PFPAaddends on a graphene unit cell consisting of 98 carbon atoms,respectively.

Closer scrutiny of the band alignments32 and dispersions nearthe Dirac point reveals that the gap opening is primarily attri-buted to the functionalization-induced modifications of the πconjugation. The disruption of the original π conjugation is mani-fested in the level hybridization, as seen in the band structure(Figure 4). Specifically, the highest occupied molecular orbital(HOMO) and the lowest unoccupiedmolecular level (LUMO) ofPFPA line up with the π and π* bands of graphene at about -1and 1 eV, respectively. The band alignment is such that the interac-tion between flat and dispersed bands leads to hybridization-induced level avoided-crossing, which leads to the split ofπ andπ*bands of graphene into two hybridized bands each.

We show in Figure 5 charge densities of the correspondinghybrized bands at the band center (theΓ point). For those states,the charge density distributions display predominant chargeconfinements on PFPA addends for hybridized conduction andvalence bands. This is to be contrasted to the conjugated π andπ* pattern on graphene. As can be seen in Figure 5, the increaseof the addend concentration leads to a proportional increase ofthe change of the π conjugation. This correlates with the asso-ciated increase of the band gap and thus provides support of thesuggested scenario of the functionalization-induced band-gapopening. Careful examination of the charge density distributionsalso indicates the existence of σ and σ* bonds in the hybridizedstates that contribute to the gap formation as well.

A few remarks are in order. (i) The semimetallic graphene ismore sensitive to the π-conjugation changes than the metallicsingle-walled carbon nanotubes. For the latter to open a gap, it isnecessary 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 gra-phene is analogous to the epitaxial graphene in that Stone-Wales defects and the graphene-substrate interaction generateband gaps due to the disruption of π conjugation. (iii) In thiswork, we focus mainly on the electronic structure characteristics,

Figure 4. Calculated band structures for pristine graphene (left panel),one-PFPA-functionalized graphene (middle panel), and two-PFPA-functionalized 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. TheFermi level is shifted to 0 eV (dashed blue line).

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



specifically, the mechanism of band-gap formation for PFPA-functionalized graphene. The issue of solubility of alkyl, ethyleneoxide, and perfluoroalkyl groups can be addressed by alternativetheoretical approaches, such as density functional tight-bindingcalculations. (iv) In addition to the absence of midgap impuritystates, it is worth noting that the gap formationmechanismof PFPA-functionalized graphene is qualitatively distinct from that of NH-functionalized graphene.35 We illustrate in Figure 6 the calculatedband structure. As is readily observable from Figure 6 that, althoughboth schema lead to a gap at theDirac point (K) that is attributed tothe functionalization-induced symmetry breaking,35 NH-functiona-lized graphene generates a crossing in the vicinity of theDirac point.By contrast, the PFPA-functionalized graphene sustains the gapformation. This clearly demonstrates the crucial difference betweenNH-radical and aziridine-ring linkages. (v) The concentrationdependence of the [2þ 1] cycloaddition is investigated with addi-tional PFPA absorption on the same side of the graphene, inaccordance with an experimental study.23 If the absorption is ontwo different sides of graphene, our results indicate that the gap isstill opened, but the value of the gap is almost identical (slightlysmaller) than the single adsorption. This shows that the distortion ofthe π-conjugation network depends sensitively on the adsorptionconfigurations as well.

’CONCLUSIONS

In summary, we have studied the electronic characteristics ofPFPA-functionalized graphene. We have shown that the [2þ 1]cycloaddition preserves the sp2 hybridization network of thecarbons on graphene. However, the π conjugation of graphenenear the Fermi level is greatly disturbed by functionalization,which leads to the opening of a band gap dependent upon theaddend concentration. This contrasts with the free-radical func-tionalization case where an sp3-type band is induced close to theFermi level. Such dependence of the electronic properties on thedegree of functionalization of graphene suggests a novel andcontrollable method for the “band engineering” of graphene. Ourfindings on the nature of a PFPA-functionalization-induced bandgap provide useful guidelines for enabling the flexibility andoptimization of graphene-based nanodevices.

’METHODS

The structural and electronic properties were investigated usingfirst-principles density functional calculations.36 Our first-principles

calculations are based on density functional theory as implemen-ted 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 vacuumspace of 16 Å normal to the graphene plane was used. A kineticenergy change of 3� 10-4 eV in the orbital basis and appropriateMonchorst-Pack k-point grids of 6 � 6 � 1 were sufficient toconverge the integration of the charge density. The optimizationof atomic positions proceeds until the change in energy is lessthan 1� 10-6 eV per cell. Although the GGA approach systema-tically underestimates the band gaps, we are primarily interestedin the mechanism of gap opening. The GGA approach is expect-ed to provide qualitatively correct information and remains thepopular choice for investigations of covalent functionalizations.14

To pursue the effect of addend concentration on the electronicstructures, we have considered two configurations by adding oneor two PFPA polymers onto a 7 � 7 rhombus cell, respectively.The cell constitutes 98 carbon atoms for graphene, 7 carbon, 4fluorine, 1 nitrogen, and 3 hydrogen atoms for each PFPAmolecule.

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 tomodel the graphene layer and found that the distortion generatedin the transition-state search is not crucial for the extractedenergy barrier (error less than 0.2 eV). The assessment was basedon examination of hydrogen passivation and the fix of boundaryatoms 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 (GrantW911NF-06-1-0442), and the Air Force Office of ScientificResearch (Grant FA9550-10-1-0254).

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



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Electronic Properties of Cycloaddition-Functionalized Graphene