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Chemical functionalization of graphene ∗ D. W. Boukhvalov and M. I. Katsnelson Institute for Molecules and Materials, Radboud University of Nijmegen, NL-6525 ED Nijmegen, the Netherlands (Dated: January 5, 2009) Experimentalandtheoretical resultsonchemicalfunctionalization ofgraphenearereviewed. Us- ing hydrogenated graphene as a model system, general principles of the chemical functionalization are formulated and discussed. It is shown that, as a rule, 100% coverage of graphene by complex functional groups (in contrast with hydrogen and fluorine) is unreachable. A possible destruction of graphene nanoribbons by fluorine is considered. The functionalization of infinite graphene and 9 graphenenanoribbons by oxygen and by hydrofluoricacid is simulated step by step. 0 0 PACSnumbers: 73.20.Hb,61.46.Np,71.15.Nc,81.05.Uw 2 n a I. INTRODUCTION layer compounds, such as graphite, hexagonal boron ni- J tride and MoS , due to error cancellation85. 2 5 Chemicalfunctionalziationisoneofthemainmethods Sometimes,thechemicalfunctionalziationingraphene to manipulate the physical and chemical properties of is related to the ionic chemical bond. There are i] nanoobjects1,2,3,4,5,6,7,8,9,10 and to study mechanisms of the cases of graphene layers in graphite interca- c interaction of the nanoobjects with their environment lated compounds86,87 and graphene layers at metal -s (e.g., to investigate the stability of desired properties surfaces35,88,89,91,92,93,94,95,96,97,98,100. This type of func- rl with respectto oxidation,hydrogenation,etc.). Initially, tionalizationisimportanttostudypossiblesuperconduc- mt graphenewas used by theoreticians as a simple model to tivity in graphene, by analogy with the superconducting describe properties of nanotubes11,12,13,14,15,16,17. After intercalates CaC6 and YbC6101,102. t. thediscoveryofgraphene18 andofitsextraordinaryelec- Here we restrict ourselves only by the case of cova- a m tronic properties19,20,21,22 the chemical functionalization lent functionalization of graphene. We will start with ofgraphenebecameafocusofespecialinterestincontem- the hydrogenation of graphene, as a prototype of chem- d- porary chemical physics. The main motivations of these ical functionazliation (Section 3). In Section 4, other n studies are (i) modification of electronic properties via examples will be considered, including realistic models o openingtheenergygapintheelectronspectrumofsingle- of the functionalization by diatomic molecules, such as c and bilayer graphene23,24,25,26,27,28,29; (ii) potential use O2 and HF. In Section 5 we will discuss effects of finite [ of graphene for hydrogen storage23,24,31,32,33,34,99; (iii) width on the functionalization of the graphene nanorib- 2 decoration of various defects in graphene11,36,37,38,39,40; bons (GNR). We will give a resume of the work and dis- v (iv) a way to make graphene magnetic for poten- cuss some perspectives in Section 5. 7 tial use in spintronics24,40,41,42,43,44; (v) search for 5 ways to produce “cheap graphene” by chemical re- 2 duction of graphite oxide and manipulation of its II. COMPUTATIONAL METHOD 5 . electronic45,46,47 and mechanical48,49,50 properties; 9 (vi) the functionalization of graphene edges in graphene Our calculations have been performed with the 0 nanoribbons51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69 SIESTA code103,104,105,106 using the generalized gra- 8 and their protection40; (vii) oxidation and cracking of dient approximation (GGA)84 to DFT and Troullier- 0 : graphene70 as tools to create graphene nanostructures Martins107 pseudopotentials. We used energy mesh v of a given shape71,72,73. cutoff 400 Ry, and k-point mesh in Monkhorst-Park i X Therearetwomaintypesoffunctionalization,namely, scheme108. During the optimization, the electronic r a covalent one, with the covalent bond formation, and groundstates wasfound self-consistentlyby using norm- a non-covalent,duetothevanderWaalsforcesonly. Most conservingpseudopotentialstocoresandadouble-ζ plus oftheworksdealwiththecovalentfunctionalization,and polarizationbasisoflocalizedorbitalsforcarbon,oxygen only few of them26,27,75,76,77,78,79 treat the non-covalent and fluorine, and double-ζ one for hydrogen. Optimiza- one which is, of course, not surprising. First, the cova- tionofthebondlengthsandtotalenergieswasperformed lent functionalziation results in much stronger modifica- with an accuracy 0.04 eV /˚A and 1 meV, respectively. tion of geometric and electronic structures of graphene. In our study of geometric distortions induced by the Second, the most of the density functional codes used chemisorption of single hydrogen atom which will be now do not allow to include the effects of the van der described below (Section 3) a supercell containing 128 Waals interactions80,81,82 playing a crucial role in the carbon atoms with k-point 4×4×1 mesh is used. For non-covalent functionalization. In those cases the lo- the cases of maximal coverage of graphene by various cal density approximation (LDA)83 is mostly used, in- chemicalspecies(Section4)thestandardelementarycell stead of the standard generalized gradient approxima- of graphene with two carbon atoms is used, similar to tion(GGA)84 whichgivesusuallyrathergoodresultsfor the case of full hydrogenation24, with k-point 20×20×2 2 mesh. To simulate interaction of bulk graphene with hydrofluoric acid the supercell with 8 carbon atoms is used, similar to our previous works24,25,45 with k-point 11×11×1 mesh. To investigate chemical functionalization of graphene nanoribbons (Section 5) zigzag stripes with the width 22and66 carbonatomsare used,similar to Ref.40, with 1×13×1 k-mesh. Foreachstepofthe functionalization, its energyis de- fined asEchemn = En - En−1 - Eads, where En andEn−1 are the total energies of the system for n-th and n-1- th steps and Eads is the total energy of the adsorbed molecule. In contrastwith the standarddefinition of the chemisorption which we used in the previous works,this definition allows to evaluate energy favor or disfavor of eachstepseparately. WechooseEads asatotalenergyof the correspondingmoleculeingaseousphase. Thisisthe most natural choice to estimate stability of chemically modified graphene. This is the crucial issue, for example,forthecaseofgraphiteoxidewherethedesorptionof hydroxy groups in the main obstacle to derive a “cheap graphene”45. Note that molecular oxygen exists in both triplet (spin-polarized) and singlet (non-spin-polarized) states, the former being more energetically favorable by FIG. 1: (color online) Optimized geometric structure of 0.98 eV (we have found for this energy difference the C60H2 value1.12eV).Wewillusehere,aswellasintheprevious work45 the energy of singlet O ; to obtain the data with 2 respect to magnetic oxygenone needs merely to shift up This can be realized only for odd numbers of hydro- the presentedenergies by 1.12 eV. When considering ox- genatoms perbuckyball119. Unfortunately, these hydro- idation of nanotubes both energy of singlet109,110,111,112 genated fullerenes are unstable and observed only as in- and triplet111,112,113 oxygen are used. termediateproductsofsomechemicalreactions;foreven numbersofthehydrogenatomsmagnetismdoesnotsur- vive and disappears with a time120. It is worth to note III. HYDROGEN ON GRAPHENE thatthehydrogenatedfullerenesthemselvesarequitesta- ble chemicallyanddonotloosehydrogenevenunder the Hydrogenation of carbon nanoobjects is a sub- action of high pressures121. ject of special interest starting from the discovery of The discovery of single-wall carbon nanotubes122,123 fullerenes114, due to potential relevance of this issue for (further we will discuss only this kind of the nan- the hydrogen storage problem and a general scientific otubes) and successful attempts of their reversible importance for chemistry. Soon after the synthesis of hydrogenation124,125, which makes the nanotubes the first fullerenes theoretical115,116 and experimental117 more prospective materials for hydrogen storage than works appeared on the minimal hydrogenated fullerene, fullerenes, have inspired numerous theoretical models of C H . Itwasshownintheseworksthatthe moststable the nanotube hydrogenation. Geometric structure ofthe 60 2 configuration of hydrogen on the fullerene corresponds nanotubes differs essentially from that of the fullerenes. to the functionalizationofthe neighboringcarbonatoms Single-wall carbon nanotubes can be represented as a (1,2,accordingtochemicalterminology,seeFig. 1). Fur- graphene scroll of length up to few microns and width ther investigations result in discovery of numerous sys- 1-1.5 nm. tems with larger contents of hydrogen, up to C H 118. Importantly,armchairandzigzagnanotubesexistwith 60 36 Further hydrogenation of the fullerenes turns out to be different structure of the honeycomb net on their sur- impossible, due to their specific geometric structure. It face, and the nanotubes can be chiral which is essen- is important that all known stable compounds C60Hx tial for their chemical functionalization4. To avoid these contain even numbers of the hydrogen atoms. Together complications, graphene is frequently used to simulate with other known facts2,3 it allowed to formulate the chemical functionalization of the nanotubes11,12,13,14,15. main principle for the hydrogenation of the fullerenes: However, as was discussed in Ref.24, a curvature radius hydrogen atoms can be bonded either with the neigh- of typical nanotubes (1.0 to 1.5 nm) is comparable with boring or with the opposite atoms in carbon hexagons the radiusof geometricdistortions induced by hydrogen. (1,2 or 1,4, in the chemical terminology). Another is- Effects of the curvature of nanotubes on the hydrogena- sue of special interest was magnetism of hydrogenated tion was studied in detail recently126 and appeared to fullerenescausedbyunpairedelectronsonbrokenbonds. be quite essential, the hydrogenation being different in 3 two directions, along and around the nanotubes. Influ- ence of different types of chirality on chemistry of nanotubes and differences with graphene was discussed also in Ref.127,128. Let us discuss briefly the main results of these works. Potential barriers for the cases of adsorption of a single hydrogen atom on graphene and several types of nanotubes, as well as formation of hydrogen chains on graphene and around the nanotubes have been studied in Ref.13. Modification of the electronic structure of perfectgrapheneandgraphenewith the Stone-Walesde- fect at the adsorption of single hydrogen atom was discussed in Ref.11. The authors12 investigated a relation ofmagnetismwithchemisorptionofhydrogenforperfect graphene and for two types of defects, that is, monova- cancy and interlayer carbon atom in graphite. Sluiter FIG. 2: (color online) Band structure of a single graphene and Kawazoe14 used the cluster expansion algorithm to layer. Solid red lines are σ bandsand dotted bluelines areπ find the most stable configuration for complete coverage bands. of graphene by hydrogen,to model the hydrogenationof nanotubes. This configuration corresponds to so called graphanewhichhasbeenstudiedafterwardsbytheDFT principles of hydrogenation of graphene have been for- calculations23,24. Wesselyetal15 simulatedthecorelevel mulated based on calculations for various configurations spectra of carbon for the case of chemisorption of single in a broad range of coverage. hydrogen atom on graphene, to interpret existing exper- Carbonatomsingrapheneareinthesp2 hybridization imental data on hydrogenated nanotubes. state when each carbon atom has three σ and one π or- Graphene was used also to model the hydrogenation bitals (Fig. 2). In contrast with numerous polyaromatic ofgraphite129,130,131,132. After the discoveryof graphene hydrocarbonswith localizedsingle- anddouble bonds π- several works have been carried out on the hydrogena- orbitals in graphene are delocalized and all conjugated tion of graphene itself, to modify its physical properties. chemical bonds are equivalent. Chemisorption of hydro- In Ref.43 the chemisorptionof single hydrogenatomwas genatommeansabreakofoneoftheπ bondsandtrans- studiedinmoredetailthanbefore,aswellasinteractions formation from sp2 to sp3 hybridization. At the same of magnetic moments arising, due to unpaired electrons, time,unpairedelectron,oneofthoseformingtheπ-bond, at the hydrogenation of carbon atoms belonging to the remains at the neighboring carbon atoms. This electron same sublattice (it wasshownthatin this case the inter- is smeared in one of the sublattices (Figs. 4b and 4a) actionturnsouttobeferromagnetic). Atthesametime, and forms a magnetic moment. The distribution of spin according to Ref.43 the combination of three hydrogen density in a radius of 1 nm correlateswith distortions of atoms (two of them belonging to sublattice A and the the crystal lattice (Fig. 4b). However, this situation is third one to sublattice B) remains magnetic which may not robust in a sense that the chemisorption of the next be important in light of discussions of potential mag- hydrogenatombondsthisunpairedelectronandkillsthe netism of carbon systems. magnetic moment24. Sofo and coworkers23 considered theoretically a hypo- Thus, the first principle of the chemical functionaliza- thetic material, graphane, that is, graphite with com- tion is the absence of unpaired electrons, or, in other pletely hydrogenatedcarbonlayers(ineachlayer,allhy- words,ofdangling bands. As a consequence of this prin- drogen atoms coupled with one sublattice are situated ciple,chemisorptionoffunctionalgroupsondifferentsub- above, and with another sublattice - below the layer). lattices are much more energetically favorable than on This structure corresponds to weakly coupled diamond- the same sublattice. like layers, with sp3 hybridization, instead of sp2 in Thenextprincipleisaminimizationofgeometricfrus- graphite. Thischangeofhybridizationresultsinopening trations. One can see in Fig. 4b that the chemisorption a gap of order 3 eV in electron energy spectrum, due to of single hydrogen atom results in essential atomic dis- a transformation of π and π∗ orbitals to σ and σ∗ (see placements inside a circle of radius 5 ˚A (two periods of Fig. 2). The cohesive energy was found to be relatively graphene crystal lattice) and in smaller but still notice- small(oforder0.4eVperhydrogenatom)whichallowsto able distortions with a characteristic radius 10 ˚A (Fig. make the process of hydrogenation reversible24. Roman 5). The chemisorption of single hydrogen atom leads to and coworkers41,42 considered different configurations of a strong shift up of the carbon atom bonded with the hydrogenongrapheneforthecaseofone-sidehydrogena- hydrogen and shifts down for two neighboring atoms. It tion and have found that configurations when hydrogen is worth to notice that if one fixes positions of all car- atoms are bonded with different sublattices (similar to bon atoms except nearest and next-nearest neighbors Fig. 3c)arethe moststable. Inourwork24 somegeneral of the central atom135 it changes essentially the pic- 4 FIG. 3: A schematic representation of chemical bonds in (a) pure graphene (dashed lines correspond to delocalized dou- FIG. 4: Charge distribution for unpaired electron as a func- ble bands), (b) graphene with single chemisorbed hydrogen tion of a distance from the central carbon atom where hy- atom (white circle, the black circle corresponds to unpaired drogen is chemisorbed (a) and deviations of carbon atoms electron at the broken bond, it distributes in the sublattice fromflatconfigurationforthecasesofsinglehydrogenatoms shown in red), (c) graphene with chemisorbed pair of hydro- (red solid line) and two atoms chemisorbed on neighboring gen atoms (nonequivalent sublattices are shown in different sites from different side of the graphene sheet (green line) colors). (color online) (b). (color online) ture of atomic displacements. Such a procedure may predictthatinthemoststableconfigurationforhydrogen be reasonable to simulate chemical functionalization for pair on graphene the hydrogen atoms will sit on neigh- constrained systems such as graphene on graphite149, boringcarbonatomsattheoppositesideswithrespectto Ru94,95,97, Ir96 and Pt97 where part of graphene lattice thegraphenesheet. Duetogeometricdistortionsaregion is strongly coupled with the substrate. of radius 5 ˚A around the pair is more chemically active Chemisorption of the next hydrogen atom is more fa- thanpuregraphene,similarto the caseofgraphenewith vorablewhenitresultsinminimaladditionaldistortions. defects12,36,38,39,40 and, thus, next hydrogen atoms will This means that the most energetically stable configu- be chemisorbed near the pair. In the case of graphene ration arises if two hydrogen atoms are chemisorbed by withdefects this processinvolvessomepotentialbarriers neighboring carbon atoms at different sides of graphene whereasforidealinfinitegrapheneitwillproceedwithout sheet. One can see in Fig. 4b that in this case no es- any obstacles, up to complete hydrogenationand forma- sentialadditionalatomicshifts arenecessary. Ifonlyone tion of graphane. sideisavailableforthe chemisorptionthe mostfavorable Infurther works34,135 the results24 onstability ofnon- configurationoftwohydrogenatomsis the bondingwith magnetic pairs of hydrogen on graphene and on the for- carbon atoms in the opposite corners of the hexagon in mation energies have been confirmed, also the case of honeycomb lattice (cites 1,4, or para-position, accord- polyaromatichydrocarbonsC H 34 andC H 135 and 54 18 42 16 ing to the chemical terminology)25. For the case of two C H 136 being considered. Recent paper137 dealing 96 24 moredistanthydrogenatomstheyshouldmigratetothis with adsorption and desorption of biphenyl on graphene optimal position overcoming some potential barriers134 demonstrates importance of step by step simulation of which was observed experimentally for both graphite129 the chemical reaction. and graphene133. It is instructive to compare peculiarities of chemi- These two principles of the chemical functionalization cal functionalization of graphene and carbon nanotubes. 5 FIG. 5: Regions of strong (blue circle) and weak (yellow circle) distortions of graphene lattice at the chemisorption of single hydrogen atom (small red circle). (color online) FIG.6: TopandsideviewofgraphenefunctionalizedbyCH3 groups (optimized atomic positions). Carbon and hydrogen Similar to graphene, in nanotubes the most favorable atoms are shown in green and white, respectively. (color on- place forchemisorptionofthe secondhydrogenatombe- line) longs to the opposite sublattice with respect to the first one126. There is no direct experimental evidences of this structure for the case of hydrogen, however, for another storagesinceitallowstohydrogenateanddehydrogenate functional groups it is known that normally they are at- graphene at realistic temperatures29. At the same time, tached to pairs of neighboring carbon atoms4,9,10. Min- for potential use of graphane in electronics this can be imization of geometric frustrations plays an important considered as a shortcoming. Therefore it is interest- role also in the case of nanotubes. In contrast with flat ing to consider other functional groups to search a com- graphene,aparticularshape ofthe nanotubes makesthe pound with the electronic structure similar to graphane chemisorption from external side more favorable, with but larger cohesive energy. theadsorbedpairssituatedalongthenanotube. Forlarge ThecomputationalresultsarepresentedinTableIand enough groups they are usually attached to the opposite inFig. 6. Basedonthemonecandivideallthefunctional sides of the nanotube cross section4, again, to minimize groups in two classes, (a) with the energy gap of order 3 the carbon net distortions. In contrast with graphene eV and large enough cohesive energy and (b) with much where complete one-side hydrogenation is unfavorable weaker bonding and much smaller energy gap, or with- for the case of nanotubes it turns out to be possible, out a gap at all. This difference can be related with the from external side, as is shown both theoretically13 and lengthofchemicalbondsbetweencarbonatoms(carbon- experimentally124,125. carbon distance). For the substances from the first class it is almost equal to that in diamond, 1.54 ˚A whereas forthesubstancesfromthesecondclassitislarger. This IV. FUNCTIONALIZATION OF GRAPHENE meansthatforthelattercase,duetomutualrepulsionof BY OTHER CHEMICAL SPECIES the functional groups, graphene is destabilized which diminishes the cohesive energy. This situation is observed As discussed above, graphane is not very stable which experimentally in graphite oxide which cannot be com- isactuallyquitegoodfromthepointofviewofhydrogen pletelyfunctionalizedduetointeractionbetweenhydroxy 6 TABLE I: Dependenceofthecarbon-carbonbondlength(d),in˚A,and the electron energy gap (∆E), in eV, on chemical species for thecase of 100% two-side coverage of graphene. Chemical species d ∆E NO 1.622 none NH2 1.711 2.76 CN 1.661 2.11 CCH 1.722 0.83 CH3 1.789 0.84 OH 1.620 1.25 H 1.526 3.82 F 1.559 4.17 H and F 1.538 5.29 H and Cl 1.544 4.62 groups45, in agreement with the XPS data139. As examples of chemical species which can provide, similar to hydrogen, a complete coverage of graphene, we will consider F , HF and HCl. Fluorine seems to be 2 verypromisingforthefunctionalizationofgraphenesince it should produce a very homogeneous structure, with a completecoveragebyatomsofthesamekind. Therefore, this might be a way to create a two-dimensional crystal with rather large energy gap but high electron mobil- ity, due to small degree of disorder. However, fluorine is very toxic and very aggressive which may be a problem for industrial use. Also, fluorine is used for ripping of nanotubes140,141 which means that, potentially, edges and defects of graphene lattice interacting with the fluo- FIG. 7: A sketch illustrating processes and energetics of dif- rinecanbecentersofitsdestruction. Actually,graphene ferent reactions of graphene with hydrofluoric acid. White samples are always rippled142,143,144,145,146,147 or can be andredcirclesarehydrogenandfluorineatoms,respectively, deformed as observed for graphene ribbons73. all energies are in eV. (color online) Let us consider now, step by step, interaction of graphene with inorganicacids HF andHCl. The process of functionalization of graphene by HF starts with the for the first one but still positive, +0.27 eV (Fig. 7d). chemisorption of fluorine and hydrogen atoms at neigh- Startingfromthe fourthmolecule,thechemisorptionen- boring carbon sites at the same side of graphene sheet ergies are negative so further reaction is exothermal. As (Fig. 7). a result, complete coverage of graphene by hydrofluoric As a first step of chemisorption of hydrofluoric acid acid is energetically favorable but requires high enough molecule we consider bonding of hydrogen and fluorine energyforthefirststep. Thismeansthat,themostprob- atoms with the neighboring carbon atoms at the same ably,bulkgraphenewithoutdefectswillbestableenough side ofgraphenesheet(Fig. 7a). Incontrastwithmolec- with respect to reaction with HF, at least, at room tem- ular fluorine where the chemisorption energy is negative perature and normal pressure. It seems to be practi- (see above) the energy of this step turns out to be pos- cally important since hydrofluoric acid is used to sol- itive, +1.46 eV, mainly, due to strong distortions of ini- vateSiO2substratewhenpreparefreelyhangedgraphene tially flat graphene at the one-side functionalization. As membrane149. One can expect in this case a formation the next step, we consider chemisorption of one more ofachemicallymodifiedlayernearedgeswithessentially H-F pair from another side of graphene (fig. 7b). Sim- different electronic structure (see below). ilar to chemisorption of the second hydrogen atom (see Ourcalculationsshowthatthe firststepoffunctional- above) this step is energetically favorable, with the for- izationofgraphenebyhydrochloricacidisessentiallydif- mation energy -1.85 eV. Reconstruction to the structure ferent,duetolargerinteratomicdistance(1.27˚AforHCl shown in Fig. 7c diminishes the total energy by 0.33 eV pair, instead of 0.97 ˚A for HF) which close to carbon- which makesthis a possible third step of the processun- carbon distance in graphene (1.42 ˚A). As a result, there der consideration. After that, the chemisorption energy is nobreakofbonds betweenhydrogenandchlorinebut, of third HF molecule turns out to be much smaller than instead, HCl molecule hangs over graphene layer bond- 7 FIG. 8: Optimized geometric structure for step-by-step adsorption of oxygen molecule on graphene. (color online) ing with it by only weak van-der-Waals bond and there is no chemical reaction. Thus, the hydrocloric acid can be safely used to clean graphene. Let us consider now, using oxygen molecule as an example,achemisorptionofdiatomicmoleculewithdouble chemical bond. In this case, at the first step the double bond will transform into the single one, with formation of single bonds with neighboring carbon atoms (Fig. 8). This reaction requires to overcome some energy barrier whichis,however,ratherlowsinceflexibilityofgraphene allows to minimize the energy costs due to lattice dis- FIG.9: Sketchofchemicalreductionofgrapheneoxide153 for tortions. Bilayer graphene is much less flexible25, due to variousdegreesofitsfunctionalization. AllenergiesareineV. interlayer coupling, which makes the chemisorption en- (color online) ergyhigher,inagreementwiththeexperimentaldata152. If we would calculate chemisorption energy with respect to not singlet but triplet state of O molecules it 2 wouldincreaseallchemisorptionenergiesby1.12eV(see Section 2). The resulting energies are so high that it seems in contradiction with the experimental fact that graphene is relatively easily oxidized already at temperature up to 200 152. Also, “unzipping” process at the oxidation of g‰raphite observed experimentally70,150 Let us consider now another important issue, the sim- will involve energetically unstable states. Graphene ox- ulation of reduction of graphite oxide (GO). We have ide turns out to be also unstable with respect to triplet proposed earlier45 models of this compound with differ- oxygen45,153. Probably these discrepancies mean that ent degrees of its reduction. In ref.153 a process of the formationof singlet oxygenplays some role in these pro- reductionhasbeenstudiedandtheschemeofcorrespond- cesses. This issue requires further investigation. A simi- ing reactions has been proposed. Using our model and lar problem was discussed earlier for nanotubes109. this scheme, we have simulated three possible ways of Oxidation energy for graphene turns out to be lower the chemical reduction of GO depending on degree of than for the case of nanotubes109,110. In the latter case, preliminary reduction and calculated the corresponding π-orbitalsarerotatedonewithrespecttoanother7which energies (Fig. 9). To compare, we have calculated also makesformationofoxygenbridgesbetweencarbonatoms energy costs of direct reduction (e.g., by heating). One more difficult. can see from the Figure that for high degrees of cov- Previous computational results for oxidation of erage of GO (weakly reduced) energy costs of chemical graphene151 are qualitatively similar to ours. However, reactions are smaller than those of the direct reduction the energy of cyclo-addition there is higher than ours. whereas for the case of strongly reduced GO, vice versa, Therearetwopossiblereasonsforthisdifference,theuse direct total reduction turns out to be more energetically ofLDAinRef.151 insteadofGGAinourcalculationand favorable. Similar,otherreactionsofreal46,48 andpoten- the use of relatively small graphene “molecule” (with 64 tialfunctionalizationofGOcanbe simulatedwhichmay atoms)insteadofinfinitesystemwithperiodicconditions be importantto searchwaysofits complete reductionto here. pure graphene. 8 V. FUNCTIONALIZATION OF GRAPHENE NANORIBBONS Polyaromatic hydrocarbons (PAH)171 are quite close to graphene nanoribbons (GNR), and their chemistry, in particular, hydrogenation of their edges, is rather well studied158. Another nanoobjects which can be considered as predecessors of GNR are nanographite and nanographite intercalates which were studied, in particular, in connection with their magnetism154,155. Model calculationsoftheirmagneticpropertiesarepresentedin Refs.154,155 whereas first-principle calculations, using a fragment of graphene sheet as a model of nanographite, havebeen performedin Ref.157. Inthat paper, functionalization of the graphene edges by single hydrogen atom hasbeenconsidered,aswellassuppressionofmagnetism byfluorination,inrelationwiththeexperimentaldata156. Starting from the first work by S. Louie and coworkers51 predicting, on the base of the DFT calculations, half-metallic ferromagnetic state of zigzag graphene edges, this problem attracts a serious attention53,63. Later,thefirstresultshavebeenreconsid- ered by the same groupusing more accurate many-body GW method54. Chemical fucntionalization of GNR is currently one of the most popular subjects in graphene science. O. Hod et al. have considered effects of the shape of semiconducting GNR on their stability and electronic structure56,electronic structure ofgraphenic nanodots57 (similar calculations of magnetism and electronic structure have been presented also in Ref.61), effects of geometry of graphene nanosheets on their electronic structure58 and enhancement of half-metallicity due to partial oxidation of the zigzag edges59. Interesting effects which can arise in graphene nanoflakes are discussed in Ref.52. Usually, it is supposed in these calculations that edges of nanoflakes are passivated by hy- drogenatoms52,57,58,160,161,162 but sometimes pure edges are considered163,163. Real structure of some graphene nanoflakeswasdiscussedin Ref.165. Ingeneral,the state ofrealgrapheneedgesisnotwellunderstoodyetandthis, very important, problem needs further investigations. In Ref.60 effect of vacancies at the edges on the electronic structure of GNR were studied. Influence of chemisorption of different chemical species on the electronic structure of GNR was investigated in Refs.55,62. Ref.64 consideredthe chemisorptionof molecular oxygen on GNR and its effect on their magnetism. Various con- figurationsofhydrogenated68 andself-passivated69 GNR were studied; in both cases nonmagnetic state of the GNRturnedouttobethemoststable. Refs.40,67 demon- FIG.10: Aschemeofstep-by-stepoxydationofGNRofwidth strated suppression of magnetism at the zigzag edges by 2.2nm. AllenergiesareineV(toppanel). Optimizedgeomet- oxidation. Sincethelatterisanaturalprocessatthepro- ric structure for partialy oxidized GNR (lower panel). (color online) ductionofGNR73,74,166 somespecialmeasurestoprotect the magnetism chemically are probably necessary. Thus, works on the functionalization of GNR can be divided into three groups. First, there are investigations ofelectronicstructureandphysicalproperties(especially, 9 magnetism)oftheedgesthemselves. Thisgroupincludes very flexible, and atomic distortions influence strongly mostoftheoreticalworks. Second,thereareworksstudy- on the chemisorption process; (iii) the most stable ing the functionalizationofthe nanoribbonsbetweenthe configurations correspond to 100% coverage for two- edges. It seems that the effect of the edges on the elec- side functionalization24 and 25% coverage for one-side tronic structure of GNR is long-range enough and, as a functionalization25. Based on these principles one consequence,chemistryofGNR canbe essentially differ- can model the functionalization of not only perfect ent from that of bulk graphene. Research in this direc- graphene24,25,45 but also graphene with intrinsic and ex- tion is just starting. Third, there are attempts to find trinsic defects which are centers of chemical activity40. optimal geometric and chemical structure of GNR tak- In Section 4 we have studied chemical functionaliza- ing into account realistic technological processes of their tionofgraphenebyfluorineandhydrofluoricacids. They formation. Preliminary,thereisanimpressionthatsome canprovidecompletecoverageand,thus,semiconducting structuresconsideredtheoreticallybeforecanbeverydif- statewithlargeenoughelectronenergygapandweakdis- ferent from the real ones, so we are, indeed, only in the order. Alternatively, non-covalent functionalization can beginning of the way. On the other hand, a lot of exper- be used to create the gap. imental and theoretical information is available for related compounds such as arynes167, polyhexacarbens168 The current situation seems to be a bit controversial. and polycyclic aromatic hydrocarbons169 which may be In some papers26,27 an energy gap opening due to ph- also relevant for GNR. ysisorption of various molecules has been found, in con- Itwasshowninourpreviouswork40,usinghydrogenas trastwithotherresults16,17,75,76,77. Itis difficulttocom- anexample,thatthe edgesofGNRarecentersofchemi- parethese worksdirectly since they are,ingeneral,done calactivity andtheir functionalizationcanbe justa first for different chemical species and their concentrations. step to the functionalziation of the whole nanoribbon. However, keeping in mind that in some cases26,76,77 the Here we will consider step by step the oxydationprocess same case of water has been studied one can conclude ofGNR.ThecomputationalresultsarepresentedinFig. that the electronic structure is very sensitive to specific 10. Thus,oxidationofGNRisachainofexothermalpro- concentrationandspecificgeometricconfigurationofwa- cesses. Thisresultmayberelevantalsoforbetterunder- ter on graphene surface. At the same time, one should standing of burning and combustion of carbon systems. keep in mind that a very specific structure of water170 These issues, as well as more detailed results concern- and other hydrogen-bonded substances may be not very ing oxidation and unzipping70 of graphene and related accurately reproduced in the DFT calculations. Prob- compounds will be discussed elsewhere. ably, only combination of the DFT, quantum chemical Let us consider now a reaction of GNR with the hy- calculations and molecular dynamics can clarify the sit- drofluoricacid. Aschemeofthisreactionforthenanorib- uation. bon of width 2.2 nm is shown in Fig. 11a and depen- Anyway, since the cohesive energy at physisorption denceoftheenergyasafunctionofcoverageispresented doesnotexceed20kJ/molthephysisorbedgraphenecan- in Fig. 11b. In contrast with the case of ideal infinite not be veryrobust whichmay resultin some restrictions graphene for narrow enough GNR two steps with posi- of its use in electronics. tive chemisorption energy. This energy cost is so small that the process of hydrofluorination of this nanoribbon WehavedemonstratedusingHFasanexamplethatit can take place even at room temperature. The situation is important to simulate the chemisorption process step isessentiallydifferentforthenanoribbonofwidth6.6nm. by step since it allows to estimate accurately chemisorp- The steps with positive chemisorptionenergy just disap- tionenergiesrelevantforeachstepoftheprocess. Itturns pear, due to larger distance between the regions of the out that for perfect infinite graphene the energy cost of reaction. Thus, the hydrofluorination of a broad enough firststepforthecaseofHFisratherhighwhereasforHCl GNR is easy and complete. this reaction is practically impossible. This means that One can see, that, similar to the case of these acids can be safely used for cleaning of graphene hydrogenation40 (see also the previous section) GNR samples. At the same time, the potential barrier for the are very chemically active which probably means that, oxidation is rather low which makes even moderate an- at least, some of their applications will require an inert nealing of graphene in oxygen-containedatmosphere not atmosphere. very safe procedure. We have shown also, in the last section, that the graphene nanoribbons are chemically active enough to VI. CONCLUSIONS AND PERSPECTIVES be oxidized and to interact with hydrofluoric acid with relativelylowactivationenergy. Itmeansthattoprepare In Section 3 we discussed, using hydrogenation as the graphene nanoribbons with a givenchemical compo- example, three main principles of chemical function- sition alternative ways should be used, e.g., its synthesis alization of graphene: (i) broken bonds are very un- from polyaromatic hydrocarbons165,171 or even use mi- favorable energetically and, therefore, magnetic states croorganismsasitisusedalreadyforbiogenicgrow173,174 on graphene are usually very unstable; (ii) graphene is and cleaning175. 10 Acknowledgements discussions. The work is financially supportedby Sticht- ing voor Fundamenteel Onderzoek der Materie (FOM), We are grateful to A. K. Geim, K. S. Novoselov, E. the Netherlands. Y. Andrei, A. V. Krasheninnikov, A. I. Lichtenstein, T. Wehling, P.A. KhomyakovandO.V. Yazyev for helpful ∗ Electronic address: [email protected] B 76 193409 1 Daniel M-C AstrucD 2004 Chem. Rev. 104 293-346 31 DengW-QXinXuXGoddardWA2004Phys. 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