Synergistic Amination of Graphene: Molecular Dynamics andThermodynamicsVitaly V. Chaban† and Oleg V. Prezhdo*,‡

†Instituto de Ciencia e Tecnologia, Universidade Federal de Sao Paulo, 12231-280 Sao Jose dos Campos, SP Brazil‡Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

ABSTRACT: Functionalization of graphene using organic moieties constitutes anaffordable way to modulate its physical and chemical properties. Finding an exactstructural formula of functionalized graphene using experimental approaches ischallenging. We studied in detail the thermal stability and thermodynamics of amino-and ethylamino-graphene and found a surprising synergistic effect: more amino groupsstabilize functionalized graphene favoring further amination, whereas a smallconcentration of amino groups is unstable in many cases. The functional groups canbe attached either on the same side or simultaneously on different sides of thegraphene sheet. Deformation of functionalized graphene is proportional to the numberof amino groups. Complete amination leading to formation of the ultimate product,Cx(NH2)x, is hindered sterically. Our study assists in the determination of the structureof chemically modified graphene and makes specific predictions that can be tested andvalidated experimentally.

Graphene (GRA) exhibits many unusual and valuableproperties, stimulating active investigation by chemists

and physicists.1−33 GRA functionalization is of crucialimportance for efficient solubilization and for tuning numerouschemical and physical characteristics.1,9,11−20,22−31,33−37 Certainphysical properties of GRA can be improved further if thegrafted atoms or groups weaken the impact of existingstructural defects. Functionalization facilitates binding of GRAand organic molecules.11,12,18,22,27,33 It also makes GRA an idealplatform for anchoring metallic nanoparticles.13,17 Function-alized graphene (FG) can be obtained by both covalent andnoncovalent modification. The first class of techniques usuallydelivers stronger changes in GRA properties. For instance,electrical conductivity of FG is much smaller than that ofpristine GRA; surface area decreases because of oxidation,chemical reduction, and sonication; and chemical reactivity ofgraphene oxide (GO) appears much different than that of pureGRA or graphite.1 FG can be further processed by solvent-assisted techniques, such as drop-casting, layer-by-layerassembly, spraying, filtration, and spin-coating. Sheets of FGdo not agglomerate in solution, thus maintaining the propertiesof graphene as an isolated two-dimensional layer of carbon witha honeycomb structure.1,2

The most widely spread functionalization of GRA involvessome kind of oxidation with a formation of multiple carbonyl,carboxyl, hydroxyl, epoxide, and diol groups at the surface.3,18,30

Oxidation is actively employed for exfoliation directly fromgraphite. Alternative recipes to obtain FG rely on nucleophilicsubstitution, electrophilic addition, condensation, and otheraddition chemical reactions.1 Nucleophilic substitution mainlytakes place via the epoxy groups of GO. The amine group,−NH2, bearing a lone pair of electrons attacks the epoxy groupreadily at room conditions in the aqueous medium. Aliphatic

and aromatic amines, amino acids, room-temperature ionicliquids, and amine-terminated biomolecules were proven toefficiently functionalize GRA and GO.1 This method exhibits apotential to be used for industrial scale applications.Spontaneous grafting of the aryl diazonium salt to GRA is astraightforward example of an electrophilic substitution.14

Condensation of GRA occurs with isocyanate, diisocyanate,and amine compounds via the formation of amides andcarbamate ester linkages.26 Two or more molecules combine toform a larger molecule in organic addition reactions. Animportant illustration of the addition reactions involving GRAis the 1,3-dipolar cycloaddition of azomethine.12

Different substituted amines were embedded into GO forenergy storage applications, electrocatalytic oxygen reductionreactions, and electrochemical sensors.29,38 An improvedperformance was observed in certain cases. Similarly, theamine functionalization of carbon nanotubes was used toenhance the controlled covalent bonding to polymers andbiological molecules.27 These wide applications inspire researchefforts toward synthesis of amino-FG with a fine control overits structure and properties. Detailed knowledge about amino-FG is required for this purpose.Navaee and Salimi proposed a simple method based on the

Bucherer reaction to attach −NH2 to GO.31 In that method,the reaction of ammonia and GO is catalyzed by sodiumbisulfate. According to the surface analysis and materialcharacterization, the authors establish the presence of multiple−NH2 groups on the GRA surface. An improved electro-

Received: October 4, 2015Accepted: October 21, 2015Published: October 21, 2015

Letter

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catalytic activity of the product was recorded. Alkylamino-FGwith oxygen-containing groups was reported to exhibit a gooddispersion in organic solvents and a relatively strong interfacialinteraction with organic polymers.39 Despite the experimentalsuccesses, the structural formula of amino-FG remains largelyunknown.A number of theoretical papers focused on FG and its

properties. Tetsuka et al. used amino groups to tune opticalproperties of GRA quantum dots,38 while Chakraborti and Palexplored amino-GRA flakes for application as anode material inLi-ion batteries.40 Multiple papers investigated hydrogen-ated41−43 and fluorinated35,37,44 GRA. More complex aspectsof GRA chemistry, such as oxygen reduction45 and Diels−Alderreaction,46 were studied.In this letter, we employ ab initio gas-phase thermochemistry

and long-scale finite-temperature electronic-structure-basedmolecular dynamics (MD) to characterize in detail thecomposition and structure of amino-FG. We address thefollowing and related questions: What is the maximumtheoretically stable concentration of amino groups? Canamino groups be grafted in ortho and meta positions in viewof steric conditions? Can −NH2 exist both above and below theGRA plane simultaneously? How does the formation freeenergy depend on the number and location of −NH2 groups?We discover, quite surprisingly, a strong synergistic effect.

The presence of multiple amino groups stabilizes FG and favorsfurther amination. At the same time, a small concentration ofamino groups leads, in many cases, to unstable products. Thegroups can be attached on one or both sides of the graphenesheet. Steric hindrances play an important role in preventingcomplete GRA amination. The reported results can be verifiedexperimentally, complementing the experimental efforts aimedat characterization of FG.Figure 1 depicts simulated models of amino- and ethylamino-

FG, whereas Table 1 provides a full list of the consideredsystems. We investigated a variety of structures involvingdifferent attachment and substitution positionssuch as ortho(1,2); meta (1,3); para (1,4); neighboring rings (2,7); differentarrangements of three, four, and six (ethyl)amino groups persingle 6-membered carbon ringusing a small model sheet(graphene quantum dot). According to our previous (un-published) benchmark studies, dependence of functionalization

on the hybridization state and chemical environment is muchstronger than on the size of the model.Thermodynamic data are provided for the last stage of

amination, i.e., GRA + °NH2 ↔ GRA-NH2 or GRA-H + °NH2↔ GRA-NH2 + °H at 298.15 K and 1.0 bar. We do notconsider °NH2 liberation reactions, which depend on aparticular method of synthesis, employed catalysts, andavailable nitrogen source. Those reactions were well-studiedupon derivation of each particular method. If the last stage ofamination exhibits a sufficiently positive Gibbs free energy, sucha reaction is, most likely, impossible. According to Table 1, all

Figure 1. Amino- and alkylamino-FG models: (a) numbering of the considered attachment sites, (b) 1,4-diaminographene, and (c) 1,4-diethylaminographene. The functionalization at the “edge” position involves substitution of the terminating hydrogen atom of the functional group.

Table 1. Considered Configurations of Amino- andAlkylamino-FG and Their Key Characteristics

no. group positionsa stabilitybΔGM11

(kJ mol−1)rmax(C−C)c (nm)

1 −NH2 1,2 stable +23 0.1602 −NH2 1,3 stable +67 0.1523 −NH2 1,4 stable −41 0.1524 −NH2 2,7 stable +56 0.1525 −NH2 1,2,3 unstable − −6 −NH2 1,2,4 stable −33 0.1607 −NH2 1,2,4,5 stable −27 0.1608 −NH2 1,2,4,5 (above) stable −85 0.161

3,10 (below)9 −NH2 edge stable +30 0.14310 −NH2 1 stable +13 0.15111 −C2H5NH2 1,2 unstable − −12 −C2H5NH2 1,3 unstable − −13 −C2H5NH2 1,4 stable −34 0.15214 −C2H5NH2 2,7 stable +36 0.15115 −C2H5NH2 1,3,5 unstable − −16 −C2H5NH2 1,4 (above) stable −64 0.154

2,5 (below)17 −C2H5NH2 edge stable +43 0.14518 −C2H5NH2 1 stable −3 0.151

aSee Figure 1 for the site designation. bStability indicates integrity ofthe FG during the 200 ps long PM7-MD simulations at 500 K, asdescribed in the Computational Methods section. cThe length of thelongest carbon−carbon (C−C) bond neighboring the grafted(ethyl)amino group. The longest bond is provided, because it directlyreflects FG stability of FG. The C−C bond is 0.141 nm long in pristineGRA.

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amination reactions bring modest changes in the free energy. Incomparison, formation of most covalent bonds brings ca.1000 kJ mol−1. Many of the considered amination positionsappear thermodynamically forbidden, e.g., the ortho and metapositions, the edge position, etc. However, the para position isallowed, irrespective of the substituent. Grafting the ethylaminogroups is generally more energetically favorable. For instance,attachment of the lone amino group to a central atom of GRAcosts 13 kJ mol−1, whereas attachment of the lone ethylaminogroup at the same position brings 3 kJ mol−1. All presentedvalues (Tables 1 and 2) were normalized per mole of −NH2.Substitution of °H by °NH2 or °C2H5−NH2 at the rim carbonatom without a catalyst is forbidden in line with the knownamination of arenes.

A clear synergistic effect is seen upon amination. While loneamino groups at the surface of GRA are unstable, addition ofmore −NH2 stabilizes the product. Two, three, and four groupslead to systematically more favorable FG. Six amino groups perring, four above the GRA plane and two below the GRA plane,constitute an unexpectedly favorable FG sample, −85 kJ mol−1.Note that the free energy is given per number of −NH2. Anatural supposition is that the synergistic stabilization occursbecause of Coulombic attraction between −NH2 and an

electronically polarized GRA surface. This hypothesis issupported by several facts. First, amino-FG is more favorablethan ethylamino-FG, −85 versus −64 kJ mol−1. Second,formation of the ‘2,7’ amino-FG and ethylamino-FG systemsis unfavorable because the distance between these positions issignificant, weakening the stabilizing Coulombic attraction.Many other interesting correlations can be derived from Tables1 and 2.Table 2 decomposes Gibbs free energies of the correspond-

ing reactions into the enthalpic (ΔH) and entropic (−TΔS)components. Entropy of the GRA amination is unfavorable inall cases. The entropic component, 298.15 K × ΔSM11, of thereaction at the rim carbon atom amounts to 16 (amino-FG)and 18 kJ mol−1 (ethylamino-FG). Compare this value to thatfor amination of benzene, 18 kJ mol−1, obtained using the samelevel of theory. Similarity of the entropic components confirmsour earlier supposition that enthalpy (including Coulombicattraction) ultimately determines the direction of the aminationprocess in the considered cases. Note, however, that theabsolute value of the entropy change plays an extremelyimportant role for this reaction at room conditions, constitutingmore than half of the reaction free energy in many cases.Thermal stability was investigated using PM7-MD simu-

lations. The geometries of the constructed systems wereoptimized using PM7 and gradually heated from 0 to 500 K.Trajectories that were 200 ps long were used to derive distancedistributions (Figures 2 and 3) and dihedral distributions(Figure 4). Note that we study thermal stabilities of the FGsamples in vacuum. If any aggressive solvent is present, thereported stabilities may alter drastically. The reported trendsare expected to hold in inert solvents.It was found that the ‘1,2,3’ amino-FG is unstable. This

occurs for steric reasons: amino groups do not have enoughspace on the same side of the GRA plane. An average C−C−Nangle, with both carbon atoms belonging to GRA, is 110° in theortho-FG, 107° in the meta-FG, and 106° in the para-FG. TheC−C−N angle is 106° also in the ‘2,7’ amino-FG system.Geometry analysis also explains the thermodynamic observa-tions (Tables 1 and 2). Note that the ‘1,2’ amino-FG system isperfectly stable over the entire MD run, even though itsformation out of pristine GRA is not thermodynamicallyallowed. A more sophisticated synthetic approach should beused.Steric problems undermine thermal stabilities of the ‘1,2’,

‘1,3’, and ‘1,3,5’ ethylamino-FG systems as well. We anticipatethat longer alkylamino chains deliver new spatial restrictions,because a natural shape of the hydrocarbon chain has to

Table 2. Standard Enthalpic Contribution (ΔH), EntropicContribution (−TΔS), and Entropy (ΔS) for theInvestigated Amination Reactions

positionsΔHM11

(kJ mol−1)−TΔSM11

(kJ mol−1)ΔSM11

(J mol−1 K−1)

−NH2

1,2 −26 +50 −1671,3 +18 +49 −1651,4 −91 +50 −1682,7 +7.0 +49 −1631,2,4 −83 +50 −1681,2,4,5 −78 +51 −1731,2,4,5,3,6 −138 +52 −176edge +14 +16 −54‘1’ −34 +46 −156

−C2H5−NH2

‘1,4’ −88 +54 −180‘2,7’ −19 +55 −185‘1,4,2,5’ −120 +56 −189edge +26 +18 −60‘1’ −56 +53 −178

Figure 2. Distributions of the carbon−nitrogen distances (covalent bond lengths) in the amino-FG in the course of the PM7-MD simulations at500 K in vacuum. See Table 1 for system designation.

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accommodate to the available space. Calculations involvingother groups can be readily performed applying our currentlyestablished methodology.The length of the carbon−nitrogen bond in aminobenzene is

0.144 nm. The corresponding distances in FG are different andslightly dependent on the position (Figure 2). When −NH2gets linked at the “edge” position, the bond length is 0.139 nm.If the attachment occurs at any other position (Table 1), thebond length is ca. 0.150 nm. The ‘1,4’ (para) position allows forC−N bonds that are somewhat shorter than the meta andortho positions. Compare these lengths to the lengths of theC−C bonds in the 6-membered rings (Table 1) for differentpositions of −NH2.Figure 3 characterizes the C−C and C−N distances in the

case of ethylamino-FG. Note that the C−N distancescorrespond to the nitrogen atoms of −NH2 and the closestcarbon atom of GRA. That is, these distances are not covalentbond lengths, unlike the C−C distances, which were calculatedbetween the GRA plane and the closest ethylene group of thelinked −C2H5NH2 moiety. The ethylamino groups are verymobile at 500 K, sampling 0.30−0.45 nm C−N distances to theGRA plane. A larger number of the −C2H5NH2 moieties makeseach of them stiffer (Figure 3, right panel).The grafted −NH2 perturbs planarity of the GRA sheet

considerably. The effect in the case of amino-FG is strongerthan in the case of ethylamino-FG (Figure 4), because thenitrogen−carbon groups are polar. In turn, the carbon−carbonbonds in ethylamino-FG are nearly nonpolar. Importantly, aclear dependence is observed between the number of −NH2groups and nonplanarity of the corresponding 6-memberedring. An improper dihedral of the pristine GRA was also plotted

for comparison (Figure 4). On the average, pristine GRA andGRA with a single −NH2 at the edge are planar. Thermalfluctuations are significant; deviations of ±9° are seen in thepristine system at 500 K. The analogous deviations aresomewhat larger in the edge-amino-FG. Although the ringdeforms very significantly because of functionalization, thestructure is maintained. The distribution of improper dihedralsin the ‘1,2,4,5&3,6’ system is quite narrow, suggesting nearlyharmonic fluctuations from planarity during MD. One canexpect that long-range interactions present between polargroups in large graphene sheets will average out geometryfluctuations, reducing somewhat the nonplanarity observedwith the current systems.Figure 5 depicts an interesting product of amination, which

was obtained during the PM7-MD simulations during the first 5ps. The starting configuration was 1,2-ethylaminegraphene.

Figure 3. Distributions of the carbon−carbon (covalent bond) and carbon−nitrogen distances in the ethylamino-FG during the course of thePM7-MD simulations at 500 K in vacuum. See Table 1 for system designation.

Figure 4. Deviation from planarity of the 6-membered ring due to (left panel) amino- and (right panel) ethylamino-functionalization. The depictedimproper dihedrals were computed using positions 2, 10, 4, and 1 (see Figure 1).

Figure 5. Isomerization product obtained from 1,2-diethylamino-graphene (see Figure 1 for site designation).

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This molecule readily cleaves two hydrogen molecules, formedout of two amino groups, whereas unsaturated nitrogen atomscreate a double bond, thereby closing the ring. The 1,2-diethylamino-FG is, therefore, unstable but gives immediate riseto another stable compound.Following the practice of Adeli and co-workers working with

carbon nanotubes,47 we investigated hydrogen bonds betweenthe nitrogen atom of the amino group and the hydrogenatom(s) of the neighboring amino groups. It was found that asingle hydrogen bond, 2.0−2.2 Å long, was formed when theamino groups were attached to the same carbon ring. Thehydrogen bond in the ortho and para positions is longer,ca. 2.2 Å, than in the meta position, ca. 2.0 Å. The orthoposition is less favorable for hydrogen bonding because of anitrogen−nitrogen electron−core repulsion, with the equili-brium distance of 2.6 Å. In turn, the meta position allows thenitrogen−nitrogen distance to be 2.9 Å, i.e., this distance iscloser to the van der Waals diameter of the nitrogen atom.Hydrogen bonding between the grafted groups makes the freeenergy of the respective configuration more favorable.Figure 6 compares the accuracy of PM7-MD to the accuracy

of the M11 hybrid density functional theory48 (HDFT) Born−

Oppenheimer molecular dynamics (BOMD) for the ‘1,2,4,5’system, i.e., one of the most complicated amino-FG. Thederived pair correlation functions for the carbon−carbon,carbon−nitrogen, and nitrogen−nitrogen atom pairs suggestminimal discrepancies between these methods, while allrelevant peaks are reproduced perfectly.To recapitulate, we used the M11 HDFT electronic-structure

calculations and PM7-MD simulations to unravel regularitiesand peculiarities of structure and thermodynamic properties ofamino- and ethylamino-FG. We discovered an unusual,synergistic amination of GRA and characterized the productsin detail. A large number of amino-groups stabilize function-alized graphene favoring further amination. In contrast, a smallnumber of amino-groups typically leads to unstable products.The functional groups can be attached either on the same sideor on different sides of the GRA plane. Steric hindrances playan important role in preventing complete amination andformation of the ultimate FG, Cx(NH2)x. The aminationreactions bring modest changes in the Gibbs free energy. Many

amination positions are thermodynamically forbidden, includ-ing ortho, meta, and edge positions. The para position isallowed, irrespective of the substituent. Grafting a singleethylamino group is more energetically favorable compared to asingle amino group. Deformation of functionalized GRA isproportional to the number of attached groups. Testableexperimentally, the presented results are particularly useful forstructure determination experiments and assist in new organicsyntheses.

■ COMPUTATIONAL METHODS

Thermodynamic potentials for the selected reactions werederived using molecular partition functions. The wave functionswere calculated at the M11/6-311++G** level (hybrid densityfunctional theory),48 followed by calculation of force constantsand resulting vibrational frequencies. The self-consistent fieldconvergence criterion was set to 10−8 hartree. Prior tofrequency analysis, all molecular geometries were thoroughlyoptimized following evolution of energy gradients. Thereported enthalpy, entropy, and Gibbs free energy correspondto the gas-phase approximation. According to the developers,M11 provides an improved structure and electronic andthermochemical properties, as compared to earlier func-tionals.48

The thermal stabilities of amino- and alkylamino-function-alized graphene were investigated using the PM7-MDsimulations49−53 at 500 K. After an initial geometryoptimization, every system was gradually heated from 0 to500 K with a pace of 0.025 K/fs. Production runs that were 200ps long were used to investigate the dependence of FGstructure and stability on −NH2 positions. The equations ofmotion were propagated with a 0.5 fs time-step using thevelocity Verlet algorithm. The system temperature wasmaintained by means of the Andersen thermostat.54

PM7-MD was successfully applied to a set of problems inchemistry including ion-molecular systems,51 competitivesolvation,52 nanoparticles,50 gas capture,53 etc. The presentcomputations were parallelized using 4 processor cores with aspeed-up factor of 2.4.The M11 HDFT-BOMD simulation48 was used to record a

3.000 ps molecular trajectory. The 6-31G* atom-centered split-valence double-ζ polarized Pople basis set was used. Theconstant temperature, 500 K, was maintained via a simplevelocity rescaling every 50 integration steps to obtain the targettemperature. The trajectory was propagated with a 0.5 fs time-step.The PM7-MD simulations were performed using an in-house

code (developed by V.V.C). Thermochemistry and HDFT-BOMD were calculated by the GAMESS quantum chemistryprogram suite. Visualization of the PDB files was performed byVMD 1.955 and Gabedit 2.4.56

■ AUTHOR INFORMATION

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

V.V.C. is CAPES fellow. O.V.P. acknowledges support of theU.S. Department of Energy Grant DE-SC0014429.

Figure 6. C−C, C−N, and N−N pair correlation functions, computedin the 1,2,4,5-tetraaminographene using PM7-MD and M11-HDFTBOMD.

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