Fracturing graphene by chlorination: a theoretical viewpoint

1.4 MB·English

by  M. Ijäs

Fracturing graphene by chlorination: a theoretical viewpoint
M. Ij¨as,∗ P. Havu, and A. Harju
Department of Applied Physics and Helsinki Institute of Physics,
Aalto University School of Science, Espoo, Finland
(Dated: January 17, 2012)
Motivatedbytherecentphotochlorinationexperiment[B.Lietal.,ACSNano5,5957(2011)],we
study theoretically the interaction of chlorine with graphene. In previous theoretical studies, cova-
lent binding between chlorine and carbon atoms has been elusive upon adsorption to the graphene
basal plane. Interestingly, in their recent experiment, Li et al. interpreted their data in terms of
chemical bonding of chlorine on top of the graphene plane, associated with a change from sp2 to
2 sp3 incarbonhybridizationandformationofgraphenenanodomains. Westudythehypothesisthat
1 these domains are actually fractured graphene with chlorinated edges, and compare the energetics
0 of chlorine-containing graphene edge terminations, both in zigzag and armchair directions, to chlo-
2 rine adsorption onto infinite graphene. Our results indicate that edge chlorination is favored over
adsorption in the experimental conditions with radical atomic chlorine and that edge chlorination
n
a withsp3-hybridizededgecarbonsisstablealsoinambientconditions. Anabinitiothermodynamical
J analysisshowsthatthepresenceofchlorineisabletobreakthepristinegraphenelayer. Finally,we
discuss the possible effects of the silicon dioxide substrate on the chlorination of graphene.
3
1

] I. INTRODUCTION sorption of both isolated heavier halogen atoms21,24 and
l halogen molecules23 on graphene have predicted no co-
l
a valentbondingbetweenthehalogenatomsandgraphene
h Graphene, the two-dimensional allotrope of carbon,
carbons. Forgraphenenanoribbons(GNRs),somestruc-
- has been a topic of intense study ever since its experi-
s tures with halogen-carbon binding at the edges of a
mental discovery in 2004. As the properties of pristine
e zigzag GNR (ZGNR) at low edge coverage have been
m graphenearebecomingincreasinglywellunderstood, the
reported.22
research community has turned its attention toward the
.
t modification of graphene properties. Graphene is a zero Recently, Liet al.25 studiedgraphene-chlorineinterac-
a
m bandgapmaterialthathasalineardispersioninthechi- tions by using radiation to break Cl2 molecules to reac-
ral electronic bands near the Fermi level, which causes tive chlorine radicals. Based on XPS and Raman spec-
-
d someofitsextraordinarypropertiessuchashighelectron tra, they report graphene basal plane chlorination as-
n mobility. Thelackofabandgapinbulkgrapheneposes, sociated with sp3 hybridized carbon atoms, the forma-
o however,limitationsforitsuseinsomeapplications,such tion of graphene nanodomains that are approximately
c asingraphene-basedtransistors.1 Cuttinggrapheneinto 30-50 nm in lateral dimension, the appearance of a band
[
narrow ribbons introduces a band gap.2 An alternative gapgreaterthan45meV,andestimatethedegreeofchlo-

1 way of introducing a gap is chemical modification that rination to 8 atom-%. In another recent experimental
v occurs either at graphene edges, or through adsorption report, Wu et al.26 report two different reaction regimes
5 or chemical binding to the carbon plane. For instance, for graphene exposed to Cl2 plasma. For short exposure
3
through hydrogen3–5 or fluorine6–8 attachment onto the times, the conductivity of graphene is increased related
9
2 basalplaneofgrapheneabandgapcanbeinduced. Fur- to p-doping, only a weak defect-related Raman peak is
. thermore,thepropertiesofgraphenenanoribbonscanbe seen, and pristine graphene is recovered upon annealing.
1
modified through edge-terminating groups9–13 and even Forlongexposure,anirreversiblechangeinthegraphene
0
half-metallicitycanenterthroughinequivalentedges.14,15 propertiesisreported,associatedwithformationofchlo-
2
rine binding defect patches as seen in transmission elec-
1 This far, only the lightest one of the halogen atoms,
: fluorine, has been extensively studied in the context of tron microscopy images. Thus, in both of these experi-
v
i interaction with graphene, both theoretically16–23 and ments,changesinthestructureofgrapheneareobserved
X experimentally.6–8 The structures of fully fluorinated upon chlorination.
r grapheneandhydrogenatedgraphenearesimilar;inboth The differences in these experiments may be due to
a
the covalently bound heteroatoms changing the carbon different chlorination procedure and graphene quality.
hybridization from sp2 to sp3 and strongly corrugating The purpose of this study is to address this discrep-
the graphene layer.3–5 Instead, calculations with heav- ancy between the binding of Cl on graphene in the
ier halogens (Cl, Br, and I) on graphene with all car- photochlorination experiment25 and previous theoretical
bon atoms halogenated have predicted ionic binding to calculations,19–21,24 commenting also the very recent ex-
graphene with no change in the carbon hybridization, perimentalobservationsbyWuet al. inRef.26. Wepro-
retaining the planarity of the carbon network, and no pose that the presence of atomic chlorine can lead to the
induced band gap.19,20 The carbon-halogen distances for formationofedgesingraphene,sothatthenanodomains
these structures are around 4 ˚A, much higher than typ- observed by Li et al.25 could actually be chlorine-edged
ical covalent bond lengths. Additionally, studies on ad- nanostructures,andcomparethechlorinatededgeforma-
2
TABLE I. Chlorine binding energies [Eq. (1), in eV per Cl atom] and chlorine equilibrium distance from the carbon plane
for different supercell sizes and initial positions of the chlorine atom. The calculations starting from the hollow position that
converge to top positions are excluded from the table.
bridge hollow top
E E d E E d E E d
B,Cl B,Cl2 B,Cl B,Cl2 B,Cl B,Cl2
(eV/Cl) (eV/Cl) (˚A) (eV/Cl) (eV/Cl) (˚A) (eV/Cl) (eV/Cl) (˚A)
4×4 -1.040 0.703 2.93 - - - -1.049 0.695 2.86
6×6 -1.159 0.584 3.10 -1.142 0.601 3.23 -1.161 0.582 3.05
8×8 -1.210 0.533 3.12 -1.196 0.547 3.22 -1.212 0.532 3.08
12×12 -1.244 0.499 3.17 - - - -1.248 0.496 3.12
tion to adsorption onto bulk graphene. By considering a ing energies calculated with respect to atomic chlorine
largenumberofchlorine-containingedgeterminationsin corresponds to reaction conditions, and the molecular to
our density-functional theory calculations, we show that ambient conditions.
chlorine atoms preferably bind to the graphene edges,
rather than onto the basal plane of graphene. Using an
ab initio thermodynamics approach, we find that only III. RESULTS
chlorinated armchair (AC) edges are stable with respect
to pristine graphene, and that in the presence of radical A. Chlorine adsorption on infinite graphene
chlorine, graphene may spontaneously break into struc-
tures with chlorinated armchair edges. Additionally, we
First,westudythebindingofonechlorineatomonthe
discussthepossibleeffectsthataSiO substratecanhave
2 infinitegraphenesheet. Inpreviouscalculations,nocova-
on chlorination.
lentbindingbetweengraphenecarbonandchlorineatoms
thatcouldchangethehybridizationofcarbonatomsfrom
sp3 to sp2 has been found. Instead, the adsorption was
II. COMPUTATIONAL DETAILS of ionic type, associated with charge transfer between
graphene and the adsorbate, that has the lowest-energy
adsorptionpositionsontopofacarbonatom,21 oronthe
Our calculations were performed using the density-
bridge site between two carbon atoms.21,24 The carbon-
functional theory (DFT) with a van der Waals (vdW)
chlorinedistanceswerearound3˚A,24 clearlylongerthan
correction,27 implemented in the all-electron density-
the covalent bond length between carbon and clorine,
functional code, developed at the Fritz-Haber Institute
1.72-1.85 ˚A.30 The adsorption energies in these calcula-
(FHI), called FHI-aims.28 Double numeric plus polariza-
tions were −0.3 eV/Cl24 or −0.80 eV/Cl,21 the chlorine
tion basis set of numerical atom-centered orbital basis
reference state being atomic chlorine.
functions and the PBE29 exchange correlation function-
In our calculations, we consider three initial positions
als were used. The structural relaxation (with the vdW
for chlorine atoms: on top of a carbon atom (t), bridge
correction) was converged until the forces acting on the
betweentwocarbonatoms(b)andinthecenterofacar-
atoms were less than 0.001 eV/˚A and the electronic de-
bon hexagon (h). As periodic supercells are used in the
grees of freedom were converged below 10−6 eV. Unless
calculation, we address the finite size effects by calculat-
otherwisementioned,nospinpolarizationwastakeninto
ing the binding energy for the single Cl atom absorption
account, as in previous calculations chlorine adsorption
to graphene for different supercell sizes. The binding en-
has not been shown to induce spin polarization.24
ergy is given by
The optimized lattice constant, 1.42 ˚A, of an infinite
graphenesheetwasusedinallcalculationsintheabsence E =E −E −E , (1)
B,Cl Cl−gra gra Cl
of a substrate. In order to avoid interaction between the
periodic images, a vacuum layer of 15 ˚A was placed be- where E is the total energy of the graphene su-
Cl−gra
tween the graphene layers. The Brillouin zone sampling percell with a single chlorine atom, E the energy of
gra
was adjusted to the supercell size, corresponding to a pristinegrapheneinasupercellofthesamesize,andE
Cl
48×48 k-point mesh for the graphene primitive unit cell. theenergyofachlorineatom. Whenmolecularreference
Inthecalculationofbindingenergies, thereferencestate for chlorine is used, E is substituted by E /2.
Cl Cl2
for carbon was chosen as the infinite pristine graphene Table I shows our results for the atomic chlorine bind-
sheet, and for hydrogen a hydrogen molecule in the gas ing energy and the equilibrium distance for different su-
phase. For chlorine, both molecular and atomic refer- percell sizes, ranging from a 4×4 supercell (32 carbon
ence states were used, as in the photoclorination experi- atoms) also used in Ref. 21, to a 12×12 supercell (288
mentradiationisusedtobreaktheclorinemoleculesinto carbonatoms). Ourresultsqualitativelyagreewiththose
atomicchlorineradicals.25Thus,theformationandbind- of Ref. 21, giving little difference in adsorption energies
3
(a) (b)
TABLE II. The chlorination of graphene on SiO for dif-
2
ferent substrate terminations in the 2×2 and 4×4 graphene
supercells. The C-Cl bond distance for adsorbed chlorine
(d )andthechlorinebindingenergywithrespecttorad-
C−Cl
ical (E ) and molecular chlorine (E ) are given for all
B,Cl B,Cl2
surface terminations.
termination E E d
B,Cl B,Cl2 C−Cl
(eV/Cl) (eV/Cl) (˚A)
O -0.920 0.530 1.83 EB,Cl =-1.867 eV/Cl EB,Cl = -1.333 eV/Cl
O2×2 0.063 1.513 1.83 EB,Cl2=-0.125 eV/Cl EB,Cl2=0.410 eV/Cl
4×4 (c) (d)
Si -0.901 0.549 1.80
2×2
Si -0.782 0.668 3.08
4×4
OH -1.622 -0.173 1.90
2×2
OH -0.827 0.623 1.90
4×4
E = -1.277 eV/Cl
rec-O2×2 -0.432 1.018 2.93 EB,Cl= -1.335 eV/Cl B,Cl
E =0.466 eV/Cl
rec-O4×4 -0.823 0.625 3.02 EB,Cl2= 0.408 eV/Cl B,Cl2
FIG. 1. (Color online) The geometries for the different two-
chlorine configurations. (a) Cl molecule (b) on the opposite
2
between top and bridge adsorption sites and no covalent sides of the carbon layer, bridge site, bound structure [in-
binding or noticeable distortion of the graphene plane. set: side view] (c) opposite sides of the carbon layer, top
Finite-sizeeffectsareclearlysignificantbothforthebind- site(d)ontheoppositesidesofthecarbonlayer,bridgesite,
adsorbed structure [inset: side view]. Below the structures,
ingenergiesandforthechlorineequilibriumdistancebut
the binding energy in radical and ambient conditions (E
as the energies are converging, we use the values calcu- B,Cl
above E ) is given per chlorine atom. Atom colors:
latedusingthe12×12supercellforcomparisons. Asseen B,Cl2
Brown/gray–chlorine, black–carbon.
from the binding energies (Table I), chlorine physisorp-
tion on all sites is energetically feasible in radical chlo-
rine conditions (E ), whereas adsorption does not oc-
B,Cl
curwhenrecombinationtomolecularchlorineispossible and higher in energy than our result for the adsorption
(E ), and metastable adsorbed structures are prone energy of a single chlorine atom, −1.25 eV/Cl.
B,Cl2
to Cl desorption. The lower values for the adsorption Morecomplicatedadsorptionstructuresare,ofcourse,
2
energy (−1.25 eV for top site adsorption calculated for possible, as well as molecular adsorption that has pre-
the 12×12 supercell) in comparison to Ref. 21 are due viously been studied in more detail by Rudenko et al.
to the inclusion of the additional adhesion-providing van in Ref. 23. We restrict ourselves to a pair of Cl atoms
derWaalscorrection. Usingthesamesupercellsizeasin placed in the 8x8 graphene supercell. We note that if
Ref. 21 and excluding the van der Waals correction, we the distance between two chlorine atoms is initially less
√
getthechlorineadsorptionenergyE =−0.76eV/Cl, than 7 times the carbon-carbon distance in graphene,
B,Cl
agreeingwiththevalue−0.80eV/ClthatWehlingetal.21 they attract each other and spontaneously form chlorine
reported. molecules during the relaxation. Our results for the ad-
Wu et al.26 studied one-sided graphene chlorination sorption energy with respect to molecular chlorine and
also theoretically by calculating the chlorine binding en- equilibrium distance of a Cl2 molecule agree well with
ergy on pristine graphene at different coverages. Us- the results of Rudenko et al.,23 giving an equilibrium
ing atomic chlorine as the reference state, they find distance of 3.49 ˚A and binding energy −0.250 eV/Cl2,
that binding is energetically stable, indicated by nega- compared to 3.58 ˚A and −0.259 eV/Cl2 by Rudenko et
tive binding energies. We test this by calculating the al. in Ref. 23. The final adsorption position for a chlo-
binding energy for the structure corresponding to their rine molecule is shown in Fig. 1(a). Instead, for initial
calculation, using both atomic and molecular reference configurations where t√he distance between the chlorine
for chlorine. For 1/4 monolayer coverage, our result atoms is longer than 7 times the carbon-carbon dis-
for the binding energy with respect to atomic chlorine tance, the mutual repulsion between the Cl atoms leads
is with (without) vdW correction −0.44 (−0.29) eV/Cl, to maximum interatomic distance between the chlorine
agreeing well with approximately −0.25 eV reported by atoms within the finite supercell.
Wu et al. in Fig. 4(a) of Ref. 26. Using a molecular In the photochlorination experiment by Li et al.25,
referencestate, however, thebindingenergiesincreaseto grapheneandchlorographeneweredepositedontheSiO
2
1.01(1.16)eV/Clandtheadsorbedstructureisunstable, substrate. In the case of graphene hydrogenation, the
4
substrate may affect the stability of adsorbed struc- to the chair configuration of graphane. The Si surface
tures, as recently reported for hydrogenated graphene, is more inert and unable to provide this stabilization at
graphane, on SiO .31 In order to take this possibility low coverage. On the other hand, graphene on the rec-
2
into account, we calculated the chlorine binding ener- O surface without chemical bonding between substrate
gies on the α-phase SiO surface. As SiO is amor- atomsandthecarbonsresemblesafreestandinggraphene
2 2
phous, we considered four different surface termina- membrane with adsorbates. Like for the freestanding
tions: oxygen-terminated (O), silicon-terminated (Si), graphene,thereisarepulsionbetweenthechlorineatoms
hydroxyl-terminated(OH)andreconstructedoxygenter- in neighboring periodic images,33 and increasing the dis-
minated (rec-O) surface, for which the initial geome- tancebetweentheadsorbatesstabilizesthestructure. At
try was taken from Ref. 32. The lattice mismatch be- thislowercoverage,chlorinatedgrapheneisnolongersta-
tween the optimized substrate and graphene was only ble on any of the surfaces and the discrepancy between
1.3% when a 2×2 supercell formed from graphene prim- the experiment and theoretical calculations can not be
itive unit cells with the optimized lattice constant cor- simply explained by substrate effects. We exclude the
responding to freestanding graphene was used. Three study of chlorine adsorption on defected graphene from
SiO unit cells were used in the slab, corresponding to a this study.
2
layerof15.8˚A,thatwaseithersymmetricallychlorinated It could, in principle, be possible that some chlorine
from both sides, or terminated with an ideal graphene- intercalates between the graphene layer and the sub-
substrate interface. The chlorine atom, graphene, and strate through cracks and boundaries in the graphene
the three uppermost atom layers of the substrate were layer, thus enabling chlorine attachment to graphene
relaxed until forces acting on atoms were less than 0.01 from both sides of the carbon network. Returning to
eV/˚A. The convergence criterion for the electronic de- graphene in the absence of a substrate, we probe this by
grees of freedom was 10−6 eV and a k-point mesh of placing two chlorine atoms on the opposite sides of the
6×6×1 was used to sample the Brillouin zone. graphene layer, either on top of a single carbon atom,
For chlorine adsorption above the graphene plane, we on neighbouring carbon atoms or symmetrically on both
find that in the radical chlorine environment, binding sides of a bridge site. Chlorine atoms initially placed
to the surface is energetically feasible on all surface ter- on the top of neighboring carbons on both sides of the
minations for the 1/8 monolayer chlorine coverage (2×2 graphene layer relax to a bridge position. The corre-
graphene supercell). In contrast to adsorption onto free- spondingtwo-chlorinegeometriesareshowninFigs.1(b),
standinggraphene,wefindcovalentbondingbetweenthe 1(c),and1(d)thatalsogivethebindingenergyperchlo-
chlorineatomandgrapheneonallsurfacesapartfromthe rineatominradicalandambientconditions(EB,Cl above
rec-Osurface,asseeninthecarbon-chlorinebondlengths EB,Cl2, respectively). The lowest-energy configuration
shown in Table II. The absorption onto the OH surface corresponds to double-sided top position [1(c)], with a
is energetically most favored, as in the case of hydrogen shorter equilibrium distance than for a single adsorbed
adsorption.31 Intheambientenvironment,usingmolecu- chlorine atom (≈ 2.5 ˚A compared to ≈ 3.1 ˚A). The
lar chlorine as the reference state, the adsorption energy double-sidedbridgeadsorptionpositionwithaslightdis-
perchlorineatomisnegativeonlyfortheOH-terminated tortion of the graphene layer [Fig. 1(b)] is very close in
surface, the adsorption energy being −0.17 eV/Cl. This, energy, the difference in EB,Cl being only few meV. In-
however, requires an ideally flat, crystalline SiO surface stead, bridge adsorption that retains graphene planarity
2
and the effect of surface roughness is beyond the scope [Fig. 1(d)] lies approximately 0.05 eV higher in energy.
of this article. The binding energies per chlorine atom for the Cl2
molecules in ambient conditions (Fig. 1 below the struc-
Atlowercoverages,modeledbyincreasingthesupercell
tures), indicate that apart from molecular adsorption, in
size to correspond to 4×4 graphene unit cells (and 2×2
ambient conditions chlorine binding in pairs on pristine
SiO unit cells), scaling the k-point mesh correspond-
2 graphene is not feasible and should be prone to desorp-
ingly, we notice that on those surfaces (O and OH) that
tion processes. Being unable to explain the experimen-
form bonds with chlorinated graphene, the absorption
tal observations by chlorine adsorption and binding onto
energies increase as the distance between the adsorbates
the graphene basal plane with bond formation of chlo-
increases (Table II) and adsorption becomes less favor-
rine with sp3-hybridized carbon seen in the experiment,
able. On the rec-O surface, on the contrary, the absorp-
we thus turn our attention to the binding of chlorine to
tion energy decreases. On the Si surface, graphene binds
graphene edges.
both to the substrate and to the chlorine atom in the
2×2 supercell but increasing the supercell to 4×4 leads
tochangeinthebindingtophysisorption,seeninTableII
asincreaseintheC-Cldistancefrom1.80˚Ato3.08˚A.As B. Cl in zigzag graphene edges
chlorinebindstographeneontheOandOHsurfaces,the
planarity of the carbon network is disturbed and bind- Asamodelforzigzag-terminated(ZZ)grapheneedges,
ing to the substrate provides additional stabilization. In we consider an eight zigzag rows wide ZGNR (8-ZGNR,
this case, it is beneficial to have adsorbates relatively width ≈15.6 ˚A). For fully hydrogen-terminated ribbons,
close to each other, keeping the carbon backbone similar this corresponds to well converged edge energy with re-
5
0 1/3 1/2 2/3 ambient 1 4/3
Å) 0.4
V/
e
(
EF,Cl2
0
0
chlorination
Cl)
V/
(e −1
B,Cl
E
−2
H−H−H2 H−Cl−H2 H−H−HCl H−H−Cl H−Cl H−Cl−HCl H−H−Cl2 Cl−Cl−H2 H−Cl−Cl Cl−Cl−HCl H−Cl−Cl2 Cl Cl−Cl−Cl2
FIG.2. (Coloronline)TheedgeformationenergyE inambientconditions(upperpanel)andbindingenergyperchlorine
F,Cl2
atom E (lower panel) in radical chlorine environment for the different zigzag terminations. In the upper panel, the dotted
B,Cl
horizontal line shows stability with respect to pristine graphene (E = 0), and in the lower panel, the red dotted line
B,Cl2
shows the adsorption energy of a single chlorine atom on pristine graphene in the absence of substrate (12×12 supercell,
E = −1.25 eV/Cl). The geometrical structures are connected to the graph from below (above) if they are (un)stable in
F,Cl
ambient conditions. Vertical dashed lines separate groups of different degree of chlorination, expressed as chlorine atoms per
edge carbon. Brown/gray: chlorine, black: carbon, white: hydrogen.
spect to the ribbon width.34 We checked this also for the lowest-energy isomer as the representative structure
some of the chlorinated structures, finding that in the for the termination. The stability of the edges is deter-
width range 15–28 ˚A, the formation energies remain es- mined by calculating the edge formation energy per unit
sentially constant. Approximately 20 ˚A of vacuum was length
placedbetweenadjacentribbonstoavoidinteractiondue
to periodic boundary conditions. All atoms in the rib- E = ECl−xGNR−NCEgCraphene− N2HEH2 −NClECl,
bons were relaxed and the Brillouin zone was sampled F,Cl L
onlyinthedirectionalongtheribbonaxis. Comparisons (2)
withsystemsinwhichthecarbonatomsinthemiddleof where ECl−xGNR is the energy of the chlorinated ribbon,
the ribbons were fixed and only carbon atoms belonging Nα thenumberofαatoms,EgCraphene theenergyofasin-
to the edge hexagons were relaxed showed only energy glecarboninpristinegraphene, Eα theenergyofspecies
differences of order 10 meV in total energies. αandLthelengthoftheribbonedge. Ifmolecularchlo-
rine is used as the reference state, N E is replaced by
Cl Cl
We generate a large number of initial chlorinated con- N E /2. A stable structure with respect to pristine
Cl Cl2
figurationsbystartingbothfromthemonohydrogenated graphene should have a negative edge formation energy.
(H-H-H)andtheH-H-H edge(inwhicheverythirdedge In order to determine whether chlorine prefers to bind
2
carbon is dihydrogenated) and by substituting some of to the edge instead of adsorbing onto the basal plane of
the hydrogen atoms by chlorine. As all ribbon atoms graphene, we also calculate the chlorine binding energy,
are relaxed, some coupling between the two edges of the
ribbon may remain. In order to take this into account, E = ECl−xGNR−NCEgraphene− N2HEH2 −NClECl,
we also calculate all different isomers (including stereo- B,Cl N
Cl
chemistry) for each edge configuration. The differences (3)
intotal energy betweenthe isomers arealwaysbelow 0.1 and compare it to the lowest binding energy of a single
eV and in many cases they are of order meV, and thus chlorine atom on an infinite graphene sheet, for which
theisomersarereportedasasingletermination,choosing we use the energy corresponding to the top adsorption,
6
interaction of monohydrogenated ZGNRs and molecular
TABLEIII. Theenergeticsfordifferentzigzagedgetermina-
chlorineandfoundsimilarstablestructureswithsomeof
tions: the formation energy per unit length of the edge (E )
F the edge carbon atoms bound to both chlorine and hy-
and the binding energy per chlorine atom (E ), both with
B
drogen at low chlorine coverage of the edge atoms. The
radicalchlorine( )andwithmolecularchlorine( )asthe
,Cl ,Cl2 C-Cl bond lengths give some indication on the nature
referencestate. AlsotheC-Clbondlengthsarereported. The
ordering is based on edge stability with respect to molecular of binding. Although all C-Cl bond lengths agree fairly
chlorine (E ). well with the average literature value for covalent C-Cl
F,Cl2
bondsof1.76˚A,36 twodifferentregimesaretobeseenin
system E E E E d
F,Cl B,Cl F,Cl2 B,Cl2 C−Cl Table III. The chlorine atoms are more strongly bound
(eV/˚A) (eV/Cl) (eV/˚A) (eV/Cl) (˚A) tosp2 hybridizedcarbonatoms, indicatedbytheshorter
H-Cl-HCl -0.487 -1.802 -0.016 -0.059 1.88, 1.74 bond lengths 1.72-1.75 ˚A. The bonds between chlorine
H-Cl-H2 -0.245 -1.810 -0.009 -0.066 1.74 atomsandcarbonatomswithincreasedsp3 characterare
H-H-HCl -0.237 -1.755 -0.002 -0.012 1.88 slightly longer, 1.83-1.88 ˚A. These values are well in line
H-H-Cl2 -0.458 -1.695 0.013 0.049 1.83 withliteraturevaluesforcarbon-chlorinebondlengthsin
different chemical environments.30
H-H-H2 0.013 - 0.013 - -
Cl-Cl-HCl -0.665 -1.640 0.042 0.103 1.74,1.73,1.88
Although we use the GNRs only to model graphene
H-Cl-Cl2 -0.664 -1.638 0.043 0.105 1.73, 1.83 edges, we briefly comment on the band gaps of the chlo-
Cl-Cl-H2 -0.425 -1.571 0.047 0.173 1.74 rinated ribbons. ZGNRs with the H-H-H2 hydrogena-
H-Cl -0.271 -1.335 0.083 0.408 1.73 tion pattern are predicted to have a band gap that is
H-H-Cl -0.144 -1.066 0.092 0.678 1.73 also dependent on the relative arrangement of the H2
H-Cl-Cl -0.324 -1.200 0.147 0.544 1.73 groups across the ribbon edges,34,35 whereas the mono-
hydrogenated ribbons are predicted to be metallic in
Cl-Cl-Cl2 -0.728 -1.346 0.215 0.397 1.72,1.86
the absence of spin polarization. If spin polarization is
Cl -0.162 -0.399 0.545 1.344 1.75
taken into account, an antiferromagnetic spin structure
between the two graphene sublattices emerges, leading
to spin-polarized edge states in the metallic ribbons.34
E =−1.25 eV.
B,Cl IntheterminationscommensuratewiththeH-H-H pat-
2
Table III shows the edge formation and chlorine bind-
tern,theedgecarbonatomsthatbindtotwosubstituents
ingenergies(E andE ,respectively)ofthe
F,Cl/Cl2 B,Cl/Cl2 arenotapartofthegrapheneπelectronnetworkandthe
chlorinated edges, along with the carbon-chlorine bond
spin-polarized edge state is destroyed. The substitution
length (d ). Fig. 2 shows E in radical conditions
C−Cl B,Cl ofedgehydrogensbychlorineatomsdoesnotchangethis
(lower panel) and E in ambient conditions (upper
F,Cl2 picture. The band structures in the absence of spin po-
panel),alongwiththegeometriesofstructuresoftheter-
larizationaremetalliciftheedgecarbonsaremonotermi-
minations, depicting some of the data in Table III pic-
nated, and in the case of a H-H-H modification a band
2
torially. The structures below the horizontal lines are
gap is found. The presence of chlorine does not seem to
stable in their own environments (see the caption for
disturbtheedgestateandmodifiesonlyslightlytheband
details). Similarly with the lowest-energy hydrogenated
gapvalues. Forinstance,thebandgapofa8-ZGNRwith
zigzagedges,35 thelowest-energystructuresarecommen-
H-H-H termination is 0.92 eV whereas for the H-Cl-H
2 2
surate with the H-H-H hydrogenation pattern. In all
2 termination the band gap is 0.91 eV.
chlorinated edges that modify the H-H-H pattern, the
2
binding energy per chlorine atom in radical environment As the realisticity of spin-polarized edge states in
is lower than the adsorption energy of a chlorine atom ZGNRs has been debated37, we note only briefly that
onto pristine graphene and thus edge binding is favored. the chlorinated, monosubstituted ZGNRs show spin po-
Some of the chlorinated H-H-H modifications are stable larized edge states that are slightly lower in energy than
2
alsoinambientconditions(Fig.2upperpanel),although the nonmagnetic ones. The spin moments on chlorine-
the edge formation energies are very small, of the order bindingcarbonatomsareinmostcasesslightlyenhanced
−10−3 eV/˚A.The degreeof chlorinationofthe edgecar- in comparison to the hydrogen-bound ones. As an ex-
bon atoms is 2/3 in the lowest-energy configuration (H- treme example, in the H-Cl-Cl terminated ribbon the
Cl-HCl). In general, there is only little correspondence spin magnitude at the edge carbons are 0.16 µ and
B
between the degree of chlorination and edge stability, as 0.18 µ for the carbon atoms bound to hydrogen and
B
seen in Fig. 2. chlorine, respectively. An exception is the fully chlori-
Looking at the atomic arrangement of the lowest- natededge(namedCl),wherethemaximalspinmoment
energy structure, H-Cl-HCl (Fig. 2, bottom right), we isonly0.06µ andthespinpolarizationisthusstrongly
B
notice that one of the chlorine atoms binds to a planar suppressedincomparisontothemonohydrogenatededge
sp2 carbon. The carbon atom binding to both hydrogen withmaximalspinmomentsof0.20µ . Thismaybedue
B
and chlorine slightly relaxes upwards towards the chlo- tosignificantchlorinecontributiontothedensityofstates
rineandthechlorineisclosetoatopadsorptionposition andanextradispersiveenergybandneartheFermilevel
for the edge carbon. Previously, Lee et al.22 studied the in this structure (not shown).
7
C. Cl in armchair graphene edges
TABLE IV. The energetics for different armchair edge ter-
minations: formationenergyperunitlengthoftheedge(E )
F
It is surprising that even though the modification of and the binding energy per chlorine atom (E ), both with
B
ZGNRswithdifferentedge-terminatingfunctionalgroups radical chlorine ( ) and with molecular chlorine ( ) as the
Cl Cl2
and the resulting effect on their electronic and mag- reference state. Also the C-Cl bond length is reported. The
netic properties has been a field of intense study (see, ordering is based on edge stability with respect to molecular
eg., Refs. 15, 38, and 39), the edge functionalization of chlorine (EF,Cl2).
armchairgraphenenanoribbons(AGNRs)hascaughtthe
system E E E E d
attention of the scientific community only recently.10–13 F,Cl B,Cl F,Cl2 B,Cl2 C−Cl
(eV/˚A) (eV/Cl) (eV˚A) (eV/Cl) (˚A)
Before that, AGNR ribbons have been assumed to be
HCl(cis) -0.990 -2.113 -0.173 -0.370 1.83
fully planar. Rippling of the AGNR edge in the pres-
ence of non-hydrogen terminating groups has, however, HCl-H2 -0.574 -2.450 -0.165 -0.706 1.85
been predicted in recent theoretical works11,13 and we HCl(trans) -0.978 -2.088 -0.162 -0.345 1.83
take this possibility into account by using a doubled su- H2 -0.091 - -0.091 - -
percellalongtheribbonaxisinourcalculations. Inprin- HCl-Cl2 -1.287 -1.832 -0.062 -0.089 1.80, 1.82
ciple,rippleswithalongerwavelengthcouldalsobepos- H2-H2-Cl2-Cl2 -0.834 -1.781 -0.017 -0.037 1.78, 1.82,1.85
sible,butourchoicewillmostlikelycapturetheessential H2-Cl2 -0.806 -1.721 0.011 0.023 1.86
physics of the system regarding the interaction between
H-Cl -0.342 -1.463 0.066 0.281 1.74
the edges and chlorine. Indeed, for all singly-terminated
Cl-H-H-Cl -0.327 -1.396 0.081 0.348 1.74
ribbons apart from the plain hydrogen termination, we
H-H-Cl-Cl -0.320 -1.368 0.088 0.375 1.73
foundstructureswithedgeripplingtobelowerinenergy
than fully planar structures with the same termination. Cl -0.694 -1.483 0.122 0.260 1.73
Previously, the interaction of chlorine with armchair
edges has been only briefly studied. Lee et al.22 studied
formation energy of the favored AC edge is an order of
theinteractionofchlorinemoleculeswithGNRedgesbut
magnitudelowerthanthatofthefavoredZZtermination,
found only weak adsorption of chlorine molecules near
−0.173 eV/˚A [HCl (cis)] in comparison to −0.016 eV/˚A
the ribbon edge with no covalent binding. Wagner et
al.13 reportripplingofthemonochlorinatededge(theCl [H-Cl-HCl]. Actually, between these twoformation ener-
gies there are four other AC edges that are energetically
edge in our nomenclature) but they do not comment on
more stable than the lowest-energy zigzag edge. We do
its energetic stability.
not find any spin polarization in chlorinated armchair
Inordertostudychlorinatedstructuresofanarmchair-
structures.
terminated graphene edge, we use a 13-AGNR (width ≈
14.8 ˚A) as the model system. The electronic and ener- Thedegreeofchlorinationishigherforthemoststable
AGNR edge (1 Cl/edge carbon), compared to the most
geticpropertiesofAGNRsareknowntooscillatewithre-
specttotheribbonwidth.34,40LikeinthecaseofZGNRs, stableZGNRconfiguration(2/3Cl/edgecarbon). Again,
the low-energy structures modify the H edge and have
weconsideralargenumberofchlorinatededgestructures 2
sp3 hybridizedcarbonatomswiththeC-Clbondlengths
created both from the monohydrogenated and dihydro-
genatedAGNRedges,35 andconsideralsodifferentstruc- 1.83-1.85˚A.Thebondsbetweensp2 carbonsandchlorine
are slightly stronger and thus shorter, the bond length
tural isomers with respect to the two edges, as well as
beingapproximately1.73˚A.Notably,thebindingenergy
stereoisomers. Similar to the zigzag edges, the difference
per chlorine atom in ambient conditions for the lowest-
in total energy between isomers is less than 0.1 eV and
energy structures (Table IV, E ) is not only lower
we consider them to represent a single structure. B,Cl2
than chlorine atom adsorption (0.499 eV/Cl) but also
Theenergeticsofthelowest-energychlorinatedAGNR
lower than the adsorption energy of molecular chlorine
edgesaregiveninTableIV,againintheorderofenergetic
(−0.125 eV/Cl).
stabilitywithrespecttomolecularchlorine(E ),and
F,Cl2
in Fig. 3 that also shows the geometries in the fashion of
Fig. 2. Similar to zigzag edges, all chlorinated edges are
stable in a radical chlorine environment in terms of edge D. Thermodynamic stability
formation energy E , and in this environment, the
F,Cl
chlorine binding energies are comparable for both edge The DFT-calculated energies do not take into account
types. In ambient conditions, however, only some of the theenvironment,forinstancethepressureofthegaseous
AC geometries modifying the dihydrogenated edge are species and the finite temperature. It is intuitively clear
stable,and,ingeneral,theACedgesaremorestablethan that if there is only a very limited amount of a reagent
ZZ edges, having lower binding and formation energies. available, this may have an effect on the favored prod-
In addition, there are a larger number of stable configu- uct. We may take these effects into account using ab
rations and as a matter of fact, even the doubly hydro- initio thermodynamics12,35,41 that allows us to compute
genated AC edge is more stable than the lowest-energy the relative stabilities of different edge terminations as a
chlorinated ZZ edge. In ambient conditions, the edge function of the chemical potential of the gaseous species,
8
0.2
0 1/2 1 ambient 3/2
Å)
eV/ 0
(
Cl2
EF,
−0.2
0
chlorination
Cl)
eV/ −1
(
Cl
B,
E
−2
H2 HCl−H2 H−Cl Cl−H−H−Cl H−H−Cl−Cl HCl(cis) HCl(trans) −H−Cl−Cl222 H−Cl22 Cl HCl−Cl2
H2
FIG.3. (Coloronline)TheedgeformationenergyE inambientconditions(upperpanel)andbindingenergyperchlorine
F,Cl2
atom E (lower panel) in radical chlorine conditions for the different armchair terminations.In the upper panel, the dotted
B,Cl
horizontal line shows stability with respect to pristine graphene (E = 0), and in the lower panel, the red dotted line
B,Cl2
shows the adsorption energy of a single chlorine atom on pristine graphene in the absence of substrate (12×12 supercell,
E = −1.25 eV/Cl). The geometrical structures are connected to the graph from below (above) if they are (un)stable in
F,Cl
ambient conditions. Vertical dashed lines separate groups of different degree of chlorination, expressed as chlorine atoms per
edge carbon. Atom colors as in Fig. 2.
the chlorine and the hydrogen. Although gaseous hy-
(a) (b)
drogen is most likely scarcely available in the reaction 0 −0.4
conditions,25 the resulting phase diagram can be used as
Cl
a qualitative rough guide to the effects of other forms of 2
−1
hydrogen, for instance hydrogen bound to the substrate. −0.6 Cl
The Gibbs energy of the edge formation is given by
ρ ρ −2
∆G=E − Hµ − Clµ (4) −0.8
F,Cl2 2 H2 2 Cl2 V) V)
e e
where the reference state for chlorine is chosen to be µ ( −3 µ (
molecular chlorine, and ρ gives the edge density of −1
i
species i and µ the chemical potential of species i. By
i
using the formation energies calculated with respect to −4 1 bar
atomicchlorineandsubstitutingρClµCl2/2byρClµCl,the 1 mbar −1.2
Gibbs energy with respect to atomic chlorine can be de-
−5 1 µbar
termined. The chemical potential, given by
−1.4
µ (T)=H◦(T)−H◦(0)−TS◦(T)+k T ln(P /P◦), (5) 0 500 1000 −10 −5 0
i i i i B i T (K) log(P) (bar)
whereH◦(S◦)istheenthalpy(entropy)instandardpres-
sure and P the partial pressure of species i, can be can
i
becalculatedusingthermodynamicalreferencedata.35,42 FIG. 4. (Color online) The chemical potential of molecu-
Fig.4showsthechemicalpotentialofgaseousatomicand lar (violet/dark gray) and atomic (green/light gray) chlorine
(a)asafunctionoftemperatureatthreevaluesofP (b)asa
molecular chlorine calculated using Eq. (5) at different
functionofpartialpressureatroomtemperature(T=298K).
temperatures and partial pressures.
9
(a) (b) (c) (d)
0 0 0 0
HCl−Cla HCl−Cla
3 3 3 2 3 2
−0.5 −0.5 −0.5 −0.5
2 2 2 2
−1 −1 −1 −1
µ (eV)Cl−−22101 HCCll−−−CCClll−−HClCl2 H−CHl−−CHlC−lH 2 −−−221..55µ (eV)Cl µ (eV)Cl−−22101 Cl HClH−CHlC lC(lc2−isH)2 −−−221..55µ (eV)Cl µ (eV)Cl−−22101 CHl−aCl−HCCl−lzCHl−−CHl−HCHzCll 2H(zcCli−sa)Ha2−−−221..55µ (eV)Cl µ (eV)Cl−−22101 Cla HHCCll −(Hci2as)a −−−221..55µ (eV)Cl
H−H−Cl H−H−H2 −3 H−Cl H2 −3 H−ClzH−H−ClzH−H−H2z H2a −3 graphene H2a −3
−3 −3 −3 −3
−3 −2 −1 0 −3 −2 −1 0 −3 −2 −1 0 −3 −2 −1 0
µH (eV) µH (eV) µH (eV) µH (eV)
2 2 2 2
FIG. 5. (Color online) The phase stability diagrams showing the thermodynamically favored edge termination (with lowest
∆G) in different hydrogen and chlorine environments, given by the chemical potential of the gaseous species Cl , Cl and H .
2 2
(a) Zigzag edges (b) Armchair edges (c) All edges (d) All edges including pristine graphene.
As noted in the previous sections, in general the ture of radiated Cl and N so this gives an upper limit
2 2
armchair-type terminations are more stable than their to the chlorine partial pressure. As seen in Fig. 4(b), at
zigzag-type counterparts. Figs. 5(a) and 5(b) show sep- roomtemperaturethiscorrespondstoamaximumchem-
aratelythestabilitydiagramsofthezigzagandarmchair icalpotentialofapproximately−0.45eVthatwouldgive
edges, that is the edge termination with the lowest ∆G, the armchair HCl-Cl as the most stable edge configura-
2
as a function of the hydrogen and atomic chlorine chem- tion and allow its formation from pristine graphene.
icalpotentials. Forcomparison, alsothechemicalpoten-
tial scale corresponding to molecular chlorine is given.
As the chemical potential, and thus the partial pressure, IV. DISCUSSION AND CONCLUSIONS
of chlorine increases, the more densely chlorinated edge
terminations become favored. Fig. 5(c) combines subfig-
We have studied the interaction of chlorine with
ures (a) and (b). Zigzag edges are thermodynamically
graphene using density-functional theory. By comparing
the most stable structures only at low chlorine and hy-
the energetics of different chlorine-containing edge ter-
drogen chemical potentials.
minations, bothforarmchairandzigzaggrapheneedges,
If∆Gofaterminationisnegative,aninfinitegraphene tochlorineadsorptiononpristine, freestandinggraphene
layer can be spontaneously broken into edges.12,35 Thus, as well as graphene on the SiO surface, we showed that
2
the possibility of pristine graphene being the favoured chlorine binds to the edges rather than adsorbs onto the
structure should be taken into account in the stability basal plane. In general, armchair edges are more read-
diagrams. Fig. 5(d) shows a combined armchair-zigzag ily chlorinated and the resulting structures are lower in
stabilitydiagramincludingaregionforpristinegraphene. energy compared with both atomic and molecular chlo-
Atlowhydrogenandchlorinechemicalpotentials,thatis rine adsorption on pristine graphene. In addition, using
at low pressures or concentrations, edge formation is not ab initio thermodynamics, we studied the effect of en-
possible and pristine graphene is preferred. All chlorine- vironment chlorine and hydrogen content on the stabil-
orhydrogen-containingterminationsthatarestablewith ity of different edges and found that pristine graphene
respect to pristine graphene are of armchair type, and may be spontaneously broken into edges in a sufficiently
they are only favored over graphene at higher hydrogen chlorine-rich environment. The presence of the silicon
and chlorine chemical potentials. dioxidesubstratelowerstheadsorptionenergiesontothe
Our approach does not consider chemical kinetics, or basalplaneofgraphenebuteventhenthebindingtothe
reaction barriers between different structures. In a real edges is energetically favored.
environment, metastable states are possible and this In the experiment, Li et al.25 suggest that chlorine
might allow some of the seemingly unstable chlorinated binds covalently to the basal plane of graphene, using
structures also to exist in ambient conditions. It is dif- the increase in the disorder-induced Raman D-peak as
ficult to asses the experimental conditions used by Li et evidence, aswell asXPSspectrashowing covalentbonds
al.25, as they do not estimate their chlorine partial pres- betweensp3hybridizedcarbonatomsandchlorineatoms.
sure. They, however, mention that the reaction is per- Wesuggestthatthenanodomainsobservedintheexper-
formedatroomtemperature,at1atmpressureinamix- iment by Li et al.25 may actually be fractured graphene
10
with chlorine-terminated edges. Our interpretation by substrate-carbondistance. Yetanotherpossibilityisthat
no means contradicts these experimental observations. during the edge formation, the interaction with chlorine
An enhanced reactivity upon chemical modification at leads to upward bending of the edge regions, or partial
graphene edges has previously been reported.43 In addi- overlap between adjacent edges. Cleavage only in the
tion, the Raman D-band is activated also through scat- high-symmetryarmchairandzigzagdirectionsisunlikely
tering from graphene edges.44–46 Carbon atoms that are to occur in the reality, and also bulky chlorinated hy-
sp3-hybridized and bind to chlorine are present in the drocarbongroups[oftype(CH Cl ) CH Cl ]could
x 2−x n y 3−y
lowest-energyedgeterminations. Asseeninourresultsin form at the edges. Even if the Raman maps of the
thepresenceofasubstrate,chlorineattachmentontothe chlorine-reacted graphene do not show spatial variation,
basalplanemaybelocallyfeasibleifadditionalstabiliza- the resolution of the measurement with a beam of 1 µm
tion through the substrate is available. Local substrate- in diameter is much larger than the lateral dimension of
stabilized covalent binding could also explain the cover- the observed domains, 30–50 nm.25
age, 8 atom-%, estimated by Li et al. based on a XPS Our results show that alternative explanations than
measurement that seems quite high to be achieved only thesimplebasalplaneadsorption,suchasacombination
through chlorinated edges. of chlorine-containing graphene edges and substrate ef-
Li et al.25 also found that the average height of the fectsstudiedinthisworkareneededtoexplaingraphene
chlorinatedgrapheneincreasesfrom0.9nmto1.1–1.7nm chlorination in experiments. Additionally, defects are
upon the reaction with chlorine. As the carbon-chlorine likely tobe importantas reactive sites inthe basal plane
bond length is only approximately 0.18-0.35 nm, the ex- but this is a topic of future work.
tremes corresponding to covalent bonds and physisorp-
tion, binding to chlorine alone can not explain the in-
creased height and roughness. It is possible that the for- ACKNOWLEDGMENTS
mation of nanodomains is also related to surface mor-
phology, so that graphene on higher regions or in re- We acknowledge computational resources from CSC-
gionswithacertainsurfaceterminationreactmoreread- IT Center for Science Ltd. and useful discussions with
ily, thus increasing the height variation. Additionally, Andreas Uppstu. M.I. acknowledges the financial sup-
in fractured graphene, chlorine may be able to interca- port from the Finnish Doctoral Programme in Compu-
late between the substrate and graphene, increasing the tational Sciences FICS.
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