Stabilization of Graphene Sheets by a Structured Benzene/Hexafluorobenzene Mixed SolventAndrew J. Oyer,† Jan-Michael Y. Carrillo,†,‡ Chetan C. Hire,† Hannes C. Schniepp,∥

Alexandru D. Asandei,†,¶ Andrey V. Dobrynin,†,‡ and Douglas H. Adamson*,†,¶

†Institute of Materials Science, Polymer Program, University of Connecticut, Storrs, Connecticut 06269, United States‡Physics Department and ¶Chemistry Department, University of Connecticut, Storrs, Connecticut 06269, United States∥Department of Applied Science, The College of William and Mary, Williamsburg, Virginia 23185, United States

*S Supporting Information

ABSTRACT: Applications requiring pristine graphenederived from graphite demand a solution stabilizationmethod that utilizes an easily removable media. Using acombination of molecular dynamics simulations andexperimental techniques, we investigate the solubliza-tion/suspension of pristine graphene sheets by anequimolar mixture of benzene and hexafluorobenzene(C6H6/C6F6) that is known to form an ordered structuresolidifying at 23.7 °C. Our simulations show that thegraphene surface templates the self-assembly of themixture into periodic layers extending up to 30 Å fromboth sides of the graphene sheet. The solvent structuring isdriven by quadrupolar interactions and consists of stacks ofalternating C6H6/C6F6 molecules rising from the surface ofthe graphene. These stacks result in density oscillationswith a period of about 3.4 Å. The high affinity of the 1:1C6H6/C6F6 mixture with graphene is consistent withobserved hysteresis in Wilhelmy plate measurements usinghighly ordered pyrolytic graphite (HOPG). AFM, SEM,and TEM techniques verify the state of the suspendedmaterial after sonication. As an example of the utility ofthis mixture, graphene suspensions are freeze-dried atroom temperature to produce a sponge-like morphologythat reflects the structure of the graphene sheets insolution.

The promise of graphene for material applications comesfrom its impressive electrical, thermal, and mechanical

properties.1−4 Thermal conductivities as high as ∼5,000 W/mK,5 Young’s modulus values of up to ∼1.0 TPa,6 and breakingstrengths of ∼40 N/m have been reported.6 Practicalapplications utilizing these impressive properties, however, arelimited.1 One reason for this is the challenge of producingstable suspensions of graphene without introducing hard toremove stabilizers such as surfactants, polymers, high-boilingsolvents, salts, or super acids.1,7−10 Currently, the mostcommonly used approach involves the oxidation of graphiteto graphite oxide (GO), followed by stabilization in waterdriven by sonication. This is often followed by chemicalreduction, but the resultant graphene sheets contain high levelsof defects.2,11 For many applications, however, pristine sheetsare required. Toward this end, advances have been made in the

production of low defect density graphene sheets by controlledvapor deposition (CVD), an energy intensive process that islikely too costly for many applications.7 Obtaining graphenefrom natural sources would appear to be a less expensivealternative.In this communication we present a method for obtaining

high-concentration suspensions of graphene material from bothnatural flake graphite and highly ordered pyrolytic graphite(HOPG). The solvents we use are low-molecular weight withlow boiling temperatures, easily removable by simpleevaporation. This solvent system, an equimolar of solution ofbenzene (C6H6) and hexafluorobenzene (C6F6), solidifies at23.7 °C, with its solid structure consisting of alternating C6H6/C6F6 columns.12 The boiling point of the mixture isapproximately 78 °C, nearly the same as that of the puresolvents,13 and is easily removed at moderate temperatures.14

While independently both benzene and hexafluorobenzenehave been shown to be less than optimal solvents for graphenesolution stabilization,15 their equimolar mixture provides astructured solvent fundamentally different than either solventseparately.Equimolar solutions of C6H6/C6F6 were first studied and

characterized in the 1960s,14 and their structure has beenexplained by quadrupolar interactions.16−18 Simulations of thecharge densities of C6H6 and C6F6 indicate that they arecomplementary, with C6F6 having a localized, independentcharge density on each F atom.19 These charge densities giverise to interactions that have been successfully exploited insupramolecular20,21 and polymer22−24 chemistry and in thestabilization of liquid crystalline phases.25 In this communica-tion, we show that the ordering resulting from theseinteractions can be nucleated by graphene, inducing orderingabove the bulk melting temperature, and we utilize this processfor graphene stabilization.Molecular dynamics simulations are used to highlight the

unique properties of this mixed solvent. We perform moleculardynamics simulations of a graphene sheet immersed in water,C6H6, xylenes, heptane, C6F6, and various C6H6/C6F6 mixtures.The simulations are done using the NPT ensemble at T = 300K and P = 1 atm, with details given in the SupportingInformation (SI). Figure 1 shows the solvent density

Received: November 30, 2011Published: March 13, 2012

Communication

pubs.acs.org/JACS

© 2012 American Chemical Society 5018 dx.doi.org/10.1021/ja211225p | J. Am. Chem. Soc. 2012, 134, 5018−5021

distribution along the z-axis with the graphene sheet located inthe xy-plane. Here we only show the density distribution alongpositive z-direction, but the density profile is symmetric andspans both sides of the graphene sheet. It is apparent that thegraphene sheet induces a layered structure in the C6H6/C6F6mixture, which is observed as density oscillations with a periodof about 3.4 Å. This corresponds to the van der Waals diameterof the carbon atom. Some degree of ordering is also observed inC6F6 and heptane systems, but it is not as well pronounced asin the 1:1 C6H6/C6F6 mixture, where one can clearly identify atleast eight peaks spanning up to 30 Å from the graphenesurface. This long-range ordering is due to quadrupolarinteractions between C6H6 and C6F6 molecules within stacksof alternating molecules.Within the layers, molecules are oriented parallel to the

graphene sheet. This can be seen in the lower panel of Figure 1,where the distribution of the orientational order parameter

φ= ⟨ ⟩ −S z

z( )

(3 cos ( ( )) 1)2

2

(1)

is shown, with φ(z) being the angle between the z-axis andnormal to the plane of the carbon ring of the aromatic solventmolecule. Averaging over all orientations of solvent moleculeswith the center of mass located at distance z from a graphenesurface is performed during the last stages of the simulationruns. Close to the graphene surface the value of the orderparameter S approaches one. This value of the order parametercorresponds to a parallel alignment of the solvent moleculesand graphene sheet. This is also clearly seen in the snapshot ofthe first-layer structure, shown in Figure 2.The negative values of the order parameter S correspond to

perpendicular orientations of the solvent molecules andgraphene sheet (Figure 2). As in the case of the densitydistribution (Figure 1), the 1:1 C6H6/C6F6 mixture shows the

longest orientational correlations between solvent moleculesand the graphene sheet. While a high degree of orientationaland translational order in the z-direction in the C6H6/C6F6mixture is present, the snapshots of the first-layer structure (seeFigure 2) do not show a high degree of lateral order. This iswhat one would expect for liquid crystalline ordering inmixtures of disklike molecules.We also perform simulations during which a potential of the

mean force between a large graphene sheet and a smallgraphene flake is calculated (details in SI).26 In thesesimulations, a graphene flake is modeled by a G8 coronene-like molecule (C384H48). The simulations are performed atconstant system temperature and volume, thus providinginformation about the change in the Helmholtz free energyof the system as a function of separation between the graphenesheet and graphene flake.Simulations have shown qualitatively different graphene

solubility in the 1:1 C6H6/C6F6 mixture and pure hexafluor-obenzene as compared with that in benzene. In a 1:1 C6H6/C6F6 mixture and in pure hexafluorobenzene, the solvatedgraphene state has a lower Helmholtz free energy than does thelayered graphene state. Thus, having both sides of a graphenesheet covered with solvent is more thermodynamicallyfavorable than having two sheets in contact with each other.This is manifested in a positive change in the Helmholtz freeenergy upon graphene aggregation (or restacking), with ΔF =838 kcal/mol for the 1:1 C6H6/C6F6 mixture and ΔF = 672kcal/mol for hexafluorobenzene. The opposite trend isobserved in benzene, with ΔF = −89 kcal/mol. Benzene isthus a poor solvent for graphene. The larger positive value ofΔF obtained for the 1:1 C6H6/C6F6 mixture confirms that themixture is a better solvent for graphene than is the purehexafluorobenzene or pure benzene, and that the mixed solventis not simply a weighted average of the two. It is important topoint out that one can still see a suspension of graphene inbenzene after sonication. This is due to an energy barrierseparating solvated and layered graphene states (see SI fordetails). Such suspensions are kinetically stable, and it will takesome time for graphene sheets to aggregate and settle.To confirm unique properties of 1:1 C6H6/C6F6 mixture

experimentally, we employ a Wilhelmy plate method in orderto observe the interaction of the solvent mixture with graphenesurfaces. In this method, an HOPG sample is suspended fromthe beam of a balance, and a solvent is raised to the HOPG at aset rate (see SI for details). In the case of solvents that wet theHOPG surface, a wicking event occurs and is observed as anincrease in the weight of the HOPG just before it enters thesolvent and buoyant forces begin decreasing the observedweight (advancing). As the solvent is then removed from theHOPG (receding), the observed weight increases as thebuoyant forces decrease, until the distance between the solvent

Figure 1. (Top) Solvent density distributions obtained from moleculardynamics simulations of a graphene sheet immersed into differentsolvents. (Bottom) Solvent orientational order parameter distributionin aromatic solvents. aHexafluorobenzene. bEquimolar mixture ofhexafluorobenzene and benzene.

Figure 2. Snapshot of the first-layer structure relative to the graphenesheet for benzene (left), C6F6 (right), and the 1:1 molar mixture(center), with C6F6 molecule in blue and C6H6 in red.

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and the HOPG is zero and only the wicked solvent remains. Asthe HOPG moves above the solvent, the wicking ceases, andthe weight decreases. The results of these weight vsdistance27,28 measurements show hysteresis, with the advancingweight being lower than the receding weight. The hysteresis ispresented as the difference in the weights divided by theadvancing weight, and is presented in Table 1.

The source of hysteresis in such measurements has beenthought in the past to arise from several possible sources:surface roughness, chemical nature of the surface, adhesion,rearrangement of the surface when in contact with the liquid,and chemical heterogeneity of the surface that causes pinning ofthe advancing or receding contact line.27,29−34 As all of ourmeasurements use the same HOPG sample, the condition ofthe surface cannot explain the hysteresis differences. Addition-ally, the structure of the HOPG surface is chemicallyhomogeneous and will not rearrange, as is sometimes observedwith polymeric surfaces. Therefore, the differences in hysteresisare attributed to differences in the adhesion of the varioussolvents to the graphene surface. While the average hysteresisfor heptane, NMP, benzene, and xylenes is 0.142 ± 17%, forC6F6 it is 0.075 (47% lower than average), and for the C6H6/C6F6 mixture it is 0.303 (113% higher than average).These differences are explained as resulting from the

quadrupolar ordering observed in our simulations. Since bothC6F6 and C6H6 associate with graphene via van der Waalsinteractions, the smaller van der Waals size of H as compared toF results in a larger adsorption energy for hydrogenatedsolvents as compared to C6F6. This is manifested in the smallerhysteresis of C6F6 in comparison with C6H6 or the othersolvents. The monolayer closest to the graphene surface in themixture, however, (see Figure 2), consists of both C6H6 andC6F6 molecules, allowing the next layer to associate withcomplementary quadrupoles. This continues for some distance,resulting in an increased mass of the solvent adhering to thegraphene surface. The other solvents do not associate throughquadrupolar interactions but rather through dispersion forcesthat are weaker than the complementary quadrupolar C6H6/C6F6 interactions. Therefore their hysteresis values lie betweenthe larger retained mass of the mixture and the smaller retainedmass of the poorly interacting C6F6.Stable suspensions derived from the sonication of both

natural flake graphite and HOPG are found to be stable forlong periods of time with typical 50 mg/mL concentrations ofnatural flake graphite showing no signs of settling after sittingfor more than one month. Figure 3 shows suspensions ofnatural flake graphite before and after sonication. After sittingfor over a week, no settling is observed. Similar images of the

component solvents are included in the SI, as is TEM andRaman data. Imaging these dark solutions suggest that theycontain large flakes of pristine graphene rather than simplysmall fragments produced by sonication. Figure 4 shows AFMimages of exfoliated sheets from both natural flake graphite andHOPG.

While exfoliating and suspending graphene sheets is a criticalstep toward many applications, the final material will likely needto be stabilizer free. One way to remove volatile stabilizingsolvents while retaining the dispersed morphology is throughfreeze-drying, which has been shown to produce graphiticmaterials with high surface areas in systems that involve GOsuspended in water,35 or reduced GO in water with polymericstabilizers.36 Proposed applications for these materials includecatalysis, drug release, biotechnology, and electronics.37 In allprevious work, water is used as the solvent, and due to theinsolubility of graphene in water, it has been necessary tooxidize the graphene first, thus introducing defects thatadversely affect the properties of the sheets. High-boilingsolvents such as NMP and DMF are not suitable for freeze-drying due to their low vapor pressures. By contrast, the C6H6/C6F6 mixture combines the capability of suspending graphenewith the ability to remove the solvent by freeze-drying due tothe high vapor pressure and high freezing point of the mixture.Drop casting a liquid C6H6/C6F6 graphene suspension

results in the immediate freezing of the suspension due toevaporative cooling. Solvent sublimation occurs with noadditional cooling or vacuum required. Figure 5 is a fieldemission scanning electron microscope (FESEM) image ofsuch a material. This graphene “sponge” contains nosurfactants, polymer, or solvent residue and is continuousover the entire surface onto which it is cast.Not surprisingly, the graphene sponge is weak mechanically,

as it consists of a combination of multisheet stacks and single

Table 1. Hysteresis of Solvents with Graphene

solventaverage advancingweight gain (mg)

average recedingweight retained (mg) hysteresisc

C6H6 67.5 77.5 0.149xylenes 46.5 53.0 0.140heptane 51.0 57.0 0.118C6F6

a 60.0 64.5 0.075NMP 92.5 107.5 0.162C6H6/C6F6

b 54.5 71.0 0.303aHexafluorobenzene. bEquimolar mixture of hexafluorobenzene andbenzene. cCalculated as the difference of advancing and recedingweight divided by advancing weight.

Figure 3. Natural flake graphite (50 mg/mL) in an equimolar solutionof C6H6/C6F6. The picture on the left is of the mixture beforesonication, the image in the middle is after sonication, and the pictureon the right is the suspension after standing for more than one week.

Figure 4. AFM images of graphene sheets prepared in the C6H6/C6F6solvent mixture. The sheets are in the micrometer range for bothnatural flake graphite (left) as well as HOPG (right).

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sheets held together by van der Waals forces. While the spongemorphology is related to the structure of the graphenesuspension, the presence of multisheets stacks is not anindication that single sheets do not exist in the suspension.Separated graphene sheets, upon solvent removal, will restack.This is what occurs during freeze-drying, resulting in the jaggedthree-dimensional sponge structure held together by misalignedand interconnecting restacked graphene sheets, shown inFigure 5.In this communication, we have presented a method for the

dispersion of pristine graphene, both from natural flakegraphene and HOPG. This method does not require the useof oxidized materials or materials that have been reduced afteroxidation, meaning that nearly defect-free graphene can berecovered. It also does not require the use of strong (e.g.,chlorosulfonic) acids.38 Unlike the more common solvents suchas DMF or NMP, the mixed solvent presented here is lowboiling and thus easily removed. As an example of its utility, wedescribe the production of a high surface area, three-dimensional graphene sponge with potential applications forcatalysis and electronics.35−37,39−41

■ ASSOCIATED CONTENT*S Supporting InformationExperimental procedures, details of TEM and AFM samplepreparation, and details of the computational study. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authoradamson@uconn.eduNotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported by the Air Force Office of ScientificResearch award number FA9550-10-0462 and by NSF DMR-1004576 and DMR-1111030. Resources of the KeenelandComputing Facility at the Georgia Institute of Technology,which is supported by the National Science Foundation underContract OCI-0910735, were used in this research.

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Figure 5. FESEM images of a three-dimensional graphene structureformed by freeze-drying a suspension of graphene from ahexafluorobenzene/benzene solvent mixture.

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Stabilization of Graphene Sheets by a

Structured Benzene / Hexafluorobenzene

Mixed Solvent

Andrew J. Oyer,† Jan-Michael Y. Carrillo,

†,‡ Chetan C. Hire,

† Hannes C. Schniepp,

∫

Alexandru D. Asandei,†,¶

Andrey V. Dobrynin,†,‡

and Douglas H. Adamson†,¶,*

†Institute of Materials Science, Polymer Program, University of Connecticut, Storrs, CT 06269,

‡Physics

Department, University of Connecticut, Storrs, CT, 06269, ¶Chemistry Department, University of

Connecticut, Storrs, CT 06259, ∫Department of Applied Science, The College of William and Mary,

Williamsburg, VA, 23185

SI 1

Simulation Details and Additional Simulation Results

We have performed molecular dynamics simulations of the adsorption of

water, benzene, hexafluorobenzene (C6F6), xylenes, and heptane on graphene sheets.

The Generalized Amber Force Field (GAFF)(1) parameters were used for atomistic

models of solvents and graphene while water was simulated by using a modified

TIP3P model optimized for simulations with Ewald summation.(2) The partial

charge distributions for the solvents, except water, were obtained by performing ab-

initio calculations using the Gaussian 09 (G09) simulation package(3) with 6-31G(d)

basis set and B3LYP DFT method.

The total potential energy of the system consisted of the bonded, bond angle,

dihedral angle, improper angle and non-bonded interaction potentials. The

interaction parameters for the van der Waals potential between heterogeneous

atomic pairs were calculated as the geometric mean of the interaction parameters

for each atom. The default AMBER force field weighing coefficients for pair-wise

energy and force contributions were used to account for contributions from the van

der Waals and electrostatic interactions.

ji ij

ji

ij

ij

ij

ij

IMPROPER

eq

DIHEDRALS

n

ANGLES

eq

BONDS

eqrTOTAL

R

qq

R

B

R

AKn

V

KrrKU

612

2

22

cos12

(SI.1)

The simulation box was built using Chem3D,(4) G09, Antechamber(5) and

AMBER2LAMMPS python script that is included with LAMMPS.(6) The G09 input file

for the solvent molecule, e.g. benzene, was built in Chem3D, then G09 calculations

SI 2

with geometry optimization using AM1 semi-empirical method were performed.

The Gaussian output from the calculation was used as an input for Antechamber to

determine charges, atom type, bond type, angle and dihedral type assignments.

Figure SI 1 Partial charge distributions used in simulations: water (a), benzene (b), xylene (c), heptane (d) and C6F6 (e). All charges except for water were obtained by using Mulliken population analysis from ab initio calculations with 6-31G(d) basis set and B3LYP DFT method. The water charges were obtained from Price and Brooks.(2)

SI 3

The AMBER topology file was created by using LEAP that was included in the

Antechamber package. The AMBER topology file was converted into a LAMMPS data

file using the python script AMBER2LAMMPS. Using output of the AMBER2LAMMPS

script as a template, the solvent molecule was replicated and distributed in the

simulation box using in-house code. The graphene sheet was modeled as a neutral

xy-periodic “macromolecule” using the GAFF definition of the aromatic carbon for

the van der Waals interaction parameters. The partial charges of the solvents,

except water, were obtained with the Mulliken population analysis from ab initio

calculations using G09 with 6-31G(d) basis set and B3LYP DFT method. The results

are summarized in Figure SI 1.

Figure SI 2 Initial system configuration of equimolar mixture of benzene and C6F6 molecules. The graphene sheet is located at z=0. Hydrogen atoms are shown as green beads, fluorine atoms as yellow beads, aromatic carbon atoms as grey beads, and carbon atoms in the graphene sheet are colored in black.

SI 4

The NPT ensemble simulations were performed using GPU accelerated

LAMMPS code.(7) The equations of motion were integrated by using the velocity

Verlet algorithm with a time step of 1.0 fs. The system was periodic in the x, y and z

directions. The standard PPPM(8) method with an accuracy of 1.0 × 10-5, and the

near-field cutoff set to 10.0 Å, was used to account for contributions from the long-

range electrostatic interactions. The graphene sheet was placed at z = 0 Å and

spanned the xy-plane. The coordinates of the carbon atoms forming a graphene

sheet were fixed during the entire simulation run. Solvent molecules were

distributed over the volume of the simulations box. Figure SI 2 shows a snapshot of

the initial system configuration. The simulation box sizes and the number of atoms

in a system are given in Table SI 1. The system was equilibrated for 10 ns to achieve

the equilibrium box volume, with an average system pressure of 1 atm and a

temperature of 300 K. A Nose-Hoover thermostat and barostat with relaxation times

of 0.1 ps and 1.0 ps respectively were used to maintain the temperature and

pressure in the system. The Nose-Hoover barostat was applied along the z-direction

only because the size of the simulation box in the x and y-directions was fixed by the

size of the graphene sheet. The data collection was performed during the final 3 ns

of the simulation run (production run). Figure SI 3 shows the evolution of the

simulation box size along the z-axis, Lz, and system density during the entire

simulation run.

SI 5

Figure SI 3 Time dependence of the box size along the z-axis and system density in C6F6/ graphene simulation.

Figure SI 4 Density distribution along z-axis in C6F6/ C6H6 mixtures with different mole fraction of C6F6.

SI 6

Table SI 1

Solvent Lx(Å) Ly(Å) <Lz> (Å)

nCarbon

Graphene

nMolecules

Solvent

nAtoms

Total

Water 116.5 115.3 142.1 0.2 5376 67200 206976

Benzene 116.5 115.3 146.1 0.3 5376 12096 150528

Xylenes 116.5 115.3 200.2 0.3 5376 12096 223104

Heptane 116.5 115.3 170.4 0.3 5376 8736 206304

C6F6 116.5 115.3 173.4 0.2 5376 12096 150528

C6F6/C6H6 (3:1) 116.5 115.3 166.7 0.2 5376 12096 150528

C6F6/C6H6 (1:1) 116.5 115.3 158.7 0.3 5376 12096 150528

C6F6/C6H6 (1:3) 116.5 115.3 154.0 0.3 5376 12096 150528

To elucidate the affinity between different solvent mixtures and graphene,

we have calculated the density distribution function of solvent molecules along the

z-direction. Figure SI 4 shows the density distribution in the different molar

mixtures of C6F6 and benzene. This density distribution was obtained by binning

atom positions along the z-axis with a bin size of =0.1 Å. As in the case with other

solvents (see Figure 1 in main text) the 1:1 mixture of C6F6/C6H6 has the highest

degree of ordering among all C6F6/ C6H6 mixtures. This degree of ordering is due to

the orientation of molecules parallel to the graphene sheet plane. This is clearly seen

in Figure SI 5 showing the distribution of the orientational order parameter:

2

1)(cos3)(

2

zzS

(SI 2)

SI 7

where z is an angle between the z-axis and normal to the carbon ring of the

aromatic solvents, and brackets <…> correspond to the ensemble over all molecule

orientations at distance z from the surface during the production run. The positive

values of the order parameter S(z) correspond to the parallel alignment of

molecules with the graphene sheet while the negative values of the order parameter

correspond to perpendicular orientations of molecules with respect to the graphene

sheet. The high degree of parallel alignment indicates columnar stacking of the C6F6

and benzene molecules.

Figure SI 5 Distribution of the orientational order parameter, S(z), along z-axis for different mole fractions of C6F6 in C6F6/ C6H6 solutions.

SI 8

It is interesting to point out that there is a correlation between density excess

in the adsorbed layer and local charge distribution. This is illustrated in Figure SI 6.

The excess of negative charge correlates with an excess of the local density. The

main contribution to this excess comes from fluorine atoms. Hydrogen atoms, with

the smallest van der Waals radius, generate the positive charge excess observed at

the graphene surface. The shoulders and double peaks seen in the charge

distribution between peaks in the density distribution correspond to positively

charged carbon atoms in C6F6 and positively charged hydrogen atoms in benzene.

Figure SI 6 Charge distribution, Q(z), and excess density distribution, (z)-b in 1:1 mixture of benzene and C6F6, where b is a bulk density.

Figure

SI 9

Figure SI 7 shows snapshots of the structure of first adsorbed layer of

molecules at the graphene surface. For these pictures we used only atoms which are

located within 6 Å from the substrate. As one can see from these pictures, the

number of molecules within these layers decreases with increasing molecular size.

The highest number of molecules is observed for water. In addition, heptane and

xylene molecules show weaker orientational alignment with respect to the

graphene surface as compared with that seen in C6F6, C6F6/ C6H6, and C6H6 solvents

as shown in Figure 2 in the main text.

Quantitative information about the affinity of different solvents to graphene

can be obtained from solvent surface excess:

dzzzL

d

b

2/

)(2 (SI.3)

where b is the bulk density and d=2.5 Å. The factor of two accounts for two

graphene surfaces exposed to a solvent. The integration of equation SI.3 was

performed numerically with the integration step =0.1 Å. Table SI 2 summarizes our

results for solvent surface excess.

Figure SI 7 Snapshots of the first layer structure relative to the graphene sheet for water (left), heptane (center), and xylene (right).

SI 10

Table SI 2 Solvent surface excess

Solvent

b

g/cm

b

Water 1.04 0.67 0.65

Benzene 0.82 2.40 2.94

Xylenes 0.80 2.65 3.30

Heptane 0.64 2.43 3.78

C6F6 1.64 2.46 1.5

C6F6/C6H6 (1:1) 1.26 3.98 3.15

C6F6/C6H6 (3:1) 1.46 2.76 1.89

C6F6/C6H6 (1:3) 1.04 3.39 3.27

The largest excess mass per unit area is observed for the 1:1 mixture of C6F6/

C6H6. Note also that this value is larger than an average solvent surface excess of

pure benzene and pure C6F6. This can be a macroscopic manifestation of the solvent

mixture structuring at the graphene surface. The lowest surface excess was

observed for water. The normalized quantity of the surface excess has the largest

value for the 1:3 mixture of C6F6/ C6H6. This is a reflection of two tendencies: the

growth of the density of the solvent mixture and the growth of the solvent surface

excess. However, even for the normalized quantity, the value of the solvent surface

excess for the 1:1 C6F6/ C6H6 mixture is larger than the average quantity for pure

components.

SI 11

To show the superior graphene solubility of the 1:1 C6F6/ C6H6 mixture in

comparison with pure solvents, we used the Weighted Histogram Analysis Method

to calculate the potential of mean force between a graphene sheet and a graphene

flake in different solvents.(9) The graphene flake was modeled by a G8 coronene-

like molecule consisting of eight generations of carbon rings and terminated by

hydrogen (see Figure SI 8). The partial charges of the coronene-like molecule were

obtained with the Mulliken population analysis from ab initio calculations using G09

with 6-31G(d) basis set and B3LYP DFT method without geometry optimization. The

C-C bond is set to 1.387 Å while the C-H bond is set to 1.087 Å. This is consistent

with the bond lengths definition for aromatic carbons and hydrogens in GAFF.

Figure SI 8 Generation eight (G8) coronene-like molecule C384H48. Carbon atoms are shown in black and hydrogen atoms are colored in green.

SI 12

Table SI 3 – Systems used in PMF simulations

System Lx(Å) Ly(Å) Lz (Å)

nCarbon

Graphene

nMolecules

Solvent

nAtoms

Total

C6H6 58.3 57.7 75.7 1344 1512 19920

C6F6/C6H6 (1:1) 58.3 57.7 82.3 1344 1512 19920

C6F6 58.3 57.7 90.5 1344 1512 19920

In these simulations, the graphene sheet was placed parallel to the xy-plane

at z=0 Å and spanned the xy-plane. The positions of the carbon atoms forming a

graphene sheet were fixed during the entire simulation run. Initially a graphene

flake was placed at z= 18.254 Å followed by a solvent being added to the simulation

box. The initial size of the simulation box along the z direction was equal to Lz=

159.9 Å. The periodic boundary conditions were used in the x, y, and z directions.

The number of atoms used in these simulations is given in Table SI 3. The system

was equilibrated for 3 ns to achieve the equilibrium box volume, the average system

pressure (1 atm) and the temperature (300 K). A Nose-Hoover thermostat and

barostat with relaxation times 0.1 ps and 1.0 ps respectively were used to maintain

temperature and pressure in the system. The Nose-Hoover barostat was applied

along the z-direction only because the size of the simulation box in the x and y-

directions was fixed by the size of the graphene sheet.

This was followed by simulation runs where we calculated the potential of

the Mean Force by using WHAM.(9) These simulations were performed at constant

temperature and volume (system sizes are listed in Table SI 3). The constant

SI 13

temperature was maintained by coupling a system to the Nose-Hoover thermostat

with relaxation time 0.1 ps. In these simulations the z-coordinate of the center of

mass of the graphene flake with coordinates (xcm, ycm, zcm) was tethered to (0, 0, z*)

by harmonic springs:

Uspring =K1

2zcm - z*( )

2+K2

2xcm

2 + ycm2( ) (SI.4)

where the values of the spring constants are K1= 250 Kcal/mole/Å2 and K2 = 2000

Kcal/mole/Å2. During these simulation runs we varied the location of the tethering

point z* with the increment z*=0.1 Å, until z*= 3.354 Å was reached. For each

location of the tethered point, the system was equilibrated for 0.1 ns. The

equilibration step was followed by the production run with a duration of 0.3 ns.

During this step, we obtained the distribution of the center of mass locations of the

graphene flake for the potential of mean force WHAM calculations. The simulation

results are shown in Figure SI 9.

The potential of the mean force calculations do not give the absolute value of

the system Helmholtz free energy but provide information about the change in the

system Helmholtz free energy as the graphene flake approaches the larger graphene

sheet. The largest positive change in the Helmholtz free energy is observed for the

1:1 C6F6/C6H6 mixture. The positive change indicates that the mixture is a good

solvent for graphene. In good solvents, a solvated state, with both sides of graphene

covered with solvent, has a lower free energy than the aggregated (stacked) state,

when the graphene sheets come into contact. Similar trend is observed for pure

hexafluorobenzene. However, these values of F are smaller than in the mixed

SI 14

solvent, with the maximum values of F being achieved at a distance z about 5.2 Å.

At such small separations, the graphene flake experiences large bending

deformations, required for the expulsion of the last layer of the adsorbed molecules

(see Figure SI 10). Note that in the 1:1 C6F6/C6H6 mixture, changes in F occur in a

step-like fashion, reflecting the removal of well-organized layers of solvent

molecules (see Figure SI 5). Steps in F are also seen for pure hexafluorobenzene,

but they are less pronounced, and appear at smaller separations.

The opposite trend is observed for benzene. In this case, F first decreases with

decreasing the distance between graphene sheet and flake. Thus, expelling benzene

Figure SI 9 Dependence of the difference in the Helmholtz free energy F on the distance between graphene sheet and graphene flake. Letters correspond to snapshots of graphene sheet and flake configurations shown in Figure SI 10.

SI 15

from the gallery between the sheet and flake is a thermodynamically favorable

process. The value of F begins to increase at z~7 Å. This increase is due to the

bending of the flake, which occurs prior the expulsion of the last layer of the

benzene molecules located between the graphene sheet and graphene flake (see

Figure SI10). Finally, at z<5.5 Å, the value of F decreases again. The value of F at

contact (see Figure SI10) is negative, supporting the observation that benzene is a

poor solvent for graphene. However, dispersions of a graphene in benzene can be

kinetically stable due to existence of the secondary minimum and a barrier

separating aggregated and solvated states (see Figure SI 9).

SI 16

Experimental Details and Additional Experimental Results

In order to compare the surface interactions of graphene with various

solvents, we utilized a Wilhemy balance. A rectangular, highly ordered pyrolyic

graphite (HOPG) sample suspended from a balance was immersed in solvents of

interest with the results of these measurements being a plot of the weight of the

sample on the y-axis vs. distance on the x-axis. The rate of sample immersion was 80

µm/sec. Figure SI 11 shows a typical plot, in this case for heptane. When the sample

is at distance zero from the solvent, the weight of the sample increases as solvent

wets and climbs the HOPG surface. The weight increases until the sample enters the

solvent, at which time buoyant forces result in a decrease in the weight of the HOPG.

The advancing weight is then taken as the maximum weight (in mg) of the sample as

it nears and enters the solvent. This can be seen on Figure SI 11 at approximately

distance 5 (device scale). This weight, minus the initial weight of the HOPG sample,

A B C D E

F G H I J

C6H6

C6H6:C6F6

C6F6

K L M N O

A B C D EA B C D E

F G H I JF G H I J

C6H6

C6H6:C6F6

C6F6

K L M N OK L M N O

Figure SI 10 Snapshots of the graphene sheet and flake configurations at different separations between their center of mass. Letters corresponds to different separartion distances shown in Figure SI 9.

SI 17

is the weight of the solvent drawn up the surface of the HOPG. As seen in Figure SI

11, the balance is zeroed with the sample above the solvent, so the values on the y

axis represent only the weight gained by the uptake of solvent. After the sample is

immersed further into the solvent, it is then withdrawn. The weight of the sample

then increases as the buoyant forces get smaller.

Figure SI 11 Typical plot of weight vs. distance for hysteresis measurements. Weight increases sharply as solvent is drawn up the HOPG sample as it nears the solvent surface (just before distance 5) until the sample enters the solvent and buoyancy causes a weight decrease. The sample is immersed in the solvent, and then withdrawn. The weight increases as the buoyant forces diminish. As the HOPG is removed from the solvent, the wetting layer drains from the surface and the weight decreases rapidly.

The weight increases until a maximum is reached near distance zero relative

to the solvent surface. Upon further separation of the sample and the solvent, the

weight abruptly decreases back to the initial weight of the HOPG. In Figure SI 11, the

SI 18

weight at the maximum peak height near distance 3 was taken as the receding

weight. Each measurement was taken five times and the results averaged. The

hysteresis value of each solvent was obtained by dividing the difference of the

receding and advancing weights by the value of the advancing weight.

The first measurements taken in each set of five were consistent with the

subsequent measurements, indicating we have no issues with wet vs. dry surfaces.

As all the solvents presented fully wet HOPG with zero contact angle, the work done

by drawing up solvent is a function only of the surface tension of the solvent, not a

function of solvent density.(10) Figure SI 12 plots the literature values of surface

tension vs. the advancing weight gain of the HOPG for each solvent tested. The linear

relationship indicates that our use of a zero contact angle is correct and that the

work done upon wetting is in fact only a function of surface tension. The plots of

weight vs. distance also indicate that the weight loss and gain due to buoyancy is

linear, meaning that the shape of the HOPG sample is regular and does not have

SI 19

thicker or thinner regions (to within the accuracy of the measurement.

Figure SI 12 Comparison of the weight of solvent drawn up the HOPG sample vs the literature values of surface tension for the solvents tested.

In typical Wilhemy balance experiments, the value of cosis calculated from

the weight measurements. In order to calculate the angle, it is necessary to know the

weight change of the sample, the value for the perimeter of the sample, and the

surface tension of the solvent at the temperature of the measurement. Rather than

applying the equation for determining coshowever, we use only the weight

measurements and do not preform the subsequent conversions. As the HOPG is

raised and lowered very slowly, and the solvents have low viscosities,(11-13) the

hysteresis does not arise from the more viscous solvents draining from the HOPG

SI 20

more slowly. If that were the case, the hysteresis would scale with solvent viscosity,

and it does not. The hysteresis values of NMP, benzene, xylenes, and heptane are

within 18% of the average value for those solvents, while their viscosity values vary

as much as 95%. Additionally, if viscosity were an issue, the receding weight would

show a slow decrease with time, rather than the abrupt drop that is observed.

A recent paper in Advanced Functional Materials(14) suggests that the ability

of solvents to stabilize graphene suspensions can related to the surface tension of

the solvent. Solvents such as benzene and heptane, with low surface tensions, are

particularly poor solvents for graphene while solvents such as NMP, with much

higher surface tensions, are much better solvents. In the case of our solvent mixture,

its surface tension is lower than benzene and slightly higher than heptane,

approximately 22.1 dynes/cm (benzene is approximately 30 dynes/cm). It thus

appears that for this solvent concentration, surface tension cannot account for the

observed ability of the solvent to stabilize graphene suspensions. In fact, the higher

surface tension benzene is a much poorer solvent than is the mixture.

Sponge samples were prepared by tip sonication of NFG in the equimolar mixture at

a concentration of ~100 mg/mL for 1 hour. SEM samples were prepared from this

mixture by dropping a small amount onto carbon tape on an SEM stub. The mixture

quickly froze and sublimed leaving the remaining structure. SEM images were

generated on a JEOL 6335F FESEM.

TEM and AFM samples were prepared in a similar manner but with a much

lower concentration, generally starting at ~10mg/mL and either centrifuging or

allowing the larger particulates to fall to the bottom. TEM samples were drop cast

SI 21

onto a holey carbon grid and viewed in both transmission and diffraction mode on a

FEI Tecnai T12 STEM. Figure SI 13 shows an image of a graphene sheet obtained

from the solvent mixture. AFM samples were drop cast on a freshly cleaved mica

substrate and imaged under ambient conditions using tapping mode on an Asylum

Research MFP-3D-SA. Raman spectra were obtained on a drop cast sample of

graphene obtained by sonicating natural flake graphite in the 1:1 solvent mixture.

The instrument used was a Renishaw Ranascope System 2000 operating at 514 nm.

Figure SI 13 TEM image of single graphene sheet obtained by sonication of natural flake graphite in an equimolar solution of hexafluorobenzene and benzene.

We have also obtained Ramon spectroscopy data for the suspended sheets.

Figure SI14 contains the Ramon Spectrum of the graphene. The spectra includes the

SI 22

expected D peak at ~1350 cm-1 indicating disordered regions and is likely caused by

sampling the edge of the sheets.(15) The much larger G band is also observed,

occurring at ~ 1580 cm-1. This peak is due to the doubly degenerate E2g mode and

is common to all sp2 carbon systems.

Figure SI 14 Ramon spectrum of graphene obtained from solvent mixture suspension.

Figure 3 in the manuscript presents images of the solvent mixture before

sonicating, immediately after sonicating, and one week after sonication. For reasons

of space, images of the component solvents were not displayed, but are instead

shown here in Figure SI15.

SI 23

Figure SI 15 On the left is a suspension of graphene in benzene after standing for one week following sonication. On the right is a suspension of hexafluorobenzene one week after sonication. While superior to the benzene as a solvent for graphene suspensions ,it is significantly inferior compared to the mixture.

Optical absorbance measurements were obtained for graphene suspensions

obtained by sonication in the 1:1 solvent mixture, pure hexafluorobenzene, and

pure benzene. The results mirror our computational findings and are shown in

Figure SI16. All three samples show a loss of transmittance immediately after

sonication, with benzene slightly less concentrated than the other two. After settling

for a week, the benzene is nearly clear, while both the hexafluorobenzene and the

mixture still show low transmission, with the mixture showing less transmission

than the pure solvent. This further argues against a simple mixing effect of our 1:1

solution.

SI 24

Figure SI 16 uv-vis transmission spectra of benzene, hexafluorobenzene, and a 1:1 mixture. The pure hexafluorobenzene stabilizes the sonication induced graphene suspension much better than does benzene, but not as well as does the mixture.

SI 25

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SI 26

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