Oxygen migration on the graphene surface. 2. Thermochemistry of basal-plane diffusion (hopping)

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Oxygen migration on the graphene surface. 2. Thermochemistry of basal-plane diffusion (hopping) Ljubisa R. Radovic a b c

a,b,* ,

Alejandro Suarez c, Fernando Vallejos-Burgos b, Jorge O. Sofo

c

Department of Energy and Mineral Engineering, Penn State University, University Park, PA 16802, USA Department of Chemical Engineering, University of Concepcio´n, Concepcio´n, Chile Department of Physics and Materials Research Institute, Penn State University, University Park, PA 16802, USA

A R T I C L E I N F O

A B S T R A C T

Article history:

Thermodynamic affinities, activation energies and diffusion coefficients for oxygen mobil-

Received 12 March 2011

ity on the graphene surface are calculated using density functional theory (DFT). We report

Accepted 20 May 2011

and discuss the effects of geometry, charge distribution and heteroatom substitution on

Available online 25 May 2011

the migration of epoxy oxygen on the basal plane: both the driving force and the ease of surface hopping are very sensitive to their variations. A significant decrease in the hopping energy barrier is observed when graphene contains free edge sites and oxygen functionalities, as well as upon an increase in electron density; conversely, the barrier increases as a consequence of electron removal, and the propensity for graphene ‘unzipping’ also increases. There is a correlation between the hopping barrier and the C–O bond strength of the leaving epoxide group. Under the most favorable conditions investigated, oxygen mobility is quite high, of the same order as that of gas-phase O2 in micropores (ca. 109 m2/s). This is consistent with the increasingly acknowledged role of basal-plane oxygen as a protagonist (e.g., reaction intermediate), instead of a spectator, in the wide variety of adsorption and reaction processes involving sp2-hybridized carbon materials.  2011 Elsevier Ltd. All rights reserved.

1.

Introduction

Since graphene’s discovery [1,2], the study of adatoms on its surface [3] has been of interest for their profound effects on graphene’s physical properties [4–10]. In particular, oxidation [11,12] and functionalization [4,13–17] of carbon materials are crucially related to the fate of adsorbed oxygen, known to be present both at graphene edges and on the basal plane [11,18,19]. Indeed, with the rebirth of interest in graphite oxide [20–23], as an intermediate in the formation of ‘‘reduced graphene oxide’’, as well as of graphene, the presence of oxygen on the graphene basal plane has become a very popular issue. (According to ISI’s Web of Knowledge, there are now close to 500 papers with ‘‘graphene oxide’’ in their title.) Thus, for example, Chen et al. [24] claimed recently that it is ‘‘well known [that graphite oxide] is composed of hydroxyl and

aether groups on both sides and carboxyl ones on the edge’’. Unless demonstrated to the contrary, however, intuition suggests that in the gas phase, where the abundance of O2 is much greater than that of OH radicals, it is the epoxy-type oxygen whose origin, characteristics and fate require a much better understanding than is currently available. A discussion of the former issue has been presented in the first part of this study [25]: it was concluded that the presence of epoxide groups is a result of O spillover subsequent to O2 adsorption on carbene-type zigzag edge sites. Here we analyze the mobility of such epoxide groups and how it is affected by the geometric and electronic properties of the corresponding graphenes. The literature on this issue, especially in terms of comparisons between theory and experiment, is quite limited. Indeed, the key details of surface diffusion of oxygen have not

* Corresponding author at: Department of Energy and Mineral Engineering, Penn State University, University Park, PA 16802, USA. E-mail address: [email protected] (L.R. Radovic). 0008-6223/$ - see front matter  2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2011.05.037

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been thoroughly analyzed for either graphene or the wide variety of sp2-hybridized carbon materials (e.g., graphite, nanotubes, carbon blacks, cokes and chars). In a pioneering study, Yang and Wong [26] used etch-decoration transmission electron microscopy to obtain direct evidence for surface diffusion of oxygen on graphite and an estimate of 35 kcal/mol for the activation energy of site-to-site hopping. In contrast, detailed proposals and observations are available for silicon surfaces. Thus, for example, Tsong and coworkers [27] used scanning tunneling microscopy to study site hopping of adsorbed O2 molecules on a Si(111) surface and reported activation energies of 2.0–2.3 eV (46–53 kcal/mol), depending upon the configuration of dangling bonds at the surface. In a subsequent study [28], they observed single oxygen atoms on the same surface and reported activation energies in the range 1.8–2.0 eV (42–46 kcal/mol); for hydrogen atoms the measured activation energy was only slightly lower, 1.7–1.9 eV (39– 44 kcal/mol) [29]. More recently, Ghaderi and Peressi [30] have used DFT to show that both the adsorption energy and the diffusion barrier for atomic oxygen and OH groups are very sensitive to the geometry and chemistry of the graphene surface (e.g., presence of vacancies or Thrower–Stone–Wales defects). Among the most important issues of relevance here is the role of epoxide-type surface oxygen in the formation of CO2 (vs. CO) during carbon oxidation [31,32]. It is well known that molecular oxygen chemisorbs only at graphene edges, which typically contain both free edge sites and functional groups (e.g., carboxyl, hydroxyl, quinone); O2 adsorption on carbene-type edge sites does account for the ‘direct’ CO2 formation path [31]. But there is also an ‘indirect’ CO2 formation path, requiring the existence of mobile basal-plane oxygen [25,31] – neither in the role of a ‘spectator’ [33] nor in that of a classical reaction intermediate [31] – and consistent with the experimental facts that (i) O2 does not chemisorb or dissociate on the graphene basal plane [16,33] and (ii) there is more oxygen on many carbon surfaces than can be accounted for by the number of edge carbon sites [18,34]. Therefore, mobile

[35] surface oxygen atoms – e.g., of the epoxy type [36–39] – are implicated in CO2 formation, e.g., by surface diffusion and insertion to form a seven-member ring at a graphene edge containing a quinone-type oxygen [31,39] (see molecular-level illustration below), in essential agreement with the intuitive expectations of Yang and Wong [26]. This mechanism is postulated to be applicable for the entire range of sp2-hybridized carbons, the only difference being the size of the basal plane (graphene sheet) over which oxygen diffusion takes place in a specific polycrystalline carbon material. O

O O

O

This elementary process is similar to the ‘unzipping’ of graphene or of carbon nanotubes [9,40–43] and it hinges upon the feasibility of epoxy oxygen migration. Another issue of practical interest is the phenomenon of spillover [44,45] of oxygen, which is at the heart of many catalytic applications of carbon materials [46]. It is well documented that H atoms ‘jump’ through the gas phase [47–49]; a similar spillover mechanism has been invoked for oxygen atoms, although the evidence for it is much less compelling [50,51]. A comparison of the fate of oxygen atoms as they change their location on the graphene surface is thus of great interest. In order to emphasize the undisputed importance of edges and thus of graphene geometry and surface chemistry (e.g., in graphene nanoribbons, as well as in the ubiquitous less ordered carbon materials such as soot, carbon blacks, coke and chars), the results for prototypical two-dimensional clusters (or molecules) of different size and shape are compared here with those obtained using periodic boundary

Fig. 1 – A possible, but thermodynamically unfavorable pathway to epoxy-type oxygen formation on the graphene basal plane. The energy difference (DE) and activation energy (Eact) here and in subsequent figures are given in kcal/mol, and selfconsistent-field energies (E) in hartrees. (Here and in subsequent figures: GS = ground state; TS = transition state.).

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Fig. 2 – Mulliken population analysis for (a) graphene C16H10O with epoxy oxygen at three different surface locations, and (b) graphene C42H16 and C42H16O (H atoms and epoxy O not included). Inserts show the range of negative charge densities at the three types of edge sites (armchair, zigzag and zigzag cusp), as well as the atom identification scheme (the numbers outside the ring system refer to H atoms and the numbers inside the ring system refer to C atoms). The unit of atomic charge density here and in subsequent figures is the fractional electron number (positive if electron-deficient).

conditions; the former are to be distinguished from polycyclic aromatic hydrocarbon (PAH) molecules by virtue of their unique edge chemistry [25,31,34,52–54].

2.

Computational methods

Periodic graphene calculations were carried out using the VASP plane-wave density functional theory (DFT) code. The

projector augmented wave (PAW) method [55,56] with a plane wave energy cutoff of 300 eV was used for electron–ion interactions [57,58]. To describe exchange and correlation, the Perdew, Burke and Ernzerhof implementation of the generalized gradient approximation (GGA-PBE) [59,60] was used. A Monkhorst–Pack k-point grid was applied, with a k-point spacing of ˚ 1. Self-consistent electronic iterations were run until 0.019 A energy differences between iterations fell below <105 eV.

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Fig. 3 – Oxygen surface diffusion on the basal plane of pyrene, as a model compound for graphene.

Fig. 4 – Optimized geometries of C42H16O graphene involved in oxygen surface diffusion.

Fig. 5 – Optimized geometries of C30H14O graphene involved in oxygen surface diffusion. Singlet is the ground state in both cases: (a) epoxy C–C = 0.155 nm, C–O = 0.144 nm, C–O–C = 65.2o; (b) epoxy C–C = 0.213 nm, C–O = 0.137 nm, C–O–C = 102o.

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Atomic relaxations were run until all forces fell below ˚ . In all calculations, the graphene supercell was 102 eV/A sized such that C–C distances were the same as in graphite ˚ ). Transition states were found using the VTST [61,62] (1.42 A implementation of the Nudged Elastic Band (NEB) method [63] with 9 images. Spring constants between images were ˚ 2. set to 5.0 eV/A For graphene clusters (or ‘‘model compounds’’) we used DFT at the B3LYP/6–31G(d) level, widely acknowledged to represent a judicious compromise between physical reality and computational expediency and as implemented in the commercially available Gaussian 03 software [64]. Because comparative effects and qualitative trends are of primary interest, results were obtained using the classical Mulliken population analysis. Special care was taken to explore the effects of the number of unpaired electrons (spin multiplicity, M) on the stability and charge distribution of representative graphene molecules. The self-consistent-field (SCF) energies of singlet or triplet ground states (GS) and transition states (TS) were determined and are reported in kcal/mol (1 eV = 23.06 kcal/mol, 1 hartree = 627.5095 kcal/mol). Geometry optimization and vibrational frequency calculations were carried out in all cases. For transition states, the existence of imaginary frequencies of vibrations connecting reactants and products was verified; intrinsic reaction coordinate (IRC) analyses were performed as well. In most cases we report driving forces and barriers in terms of self-consistent-field energies (ESCF); trends were essentially the same when Gibbs free energy (DG) values were considered. Oxygen diffusivity was determined using the standard fundamental equation [65], 1 2 D ¼ d v expðEact =kTÞ 4 where d is the jump length (0.123 nm, the distance between epoxy sites), Eact is the activation energy, and v is the hopping

attempt frequency, calculated using the vibrational modes of the equilibrium and transition states in the harmonic approximation [66].

3.

Results and discussion

3.1.

Epoxy-type surface oxygen

How exactly oxygen atoms arrive at the graphene basal plane – in the absence of gas-phase atomic oxygen, which is the case of greatest practical significance and of interest here – was discussed in Part 1 [25]. Experimental evidence for its presence as epoxide groups in graphite oxide [67–70], or graphene oxide [30,71–74], is by now quite compelling. Of greatest relevance to the present study are the following facts: (i) chemisorption of O2 on the basal plane is thermodynamically highly unfavorable (e.g., 60 kcal/mol for pyrene); (ii) chemisorption of O2 on free edge sites is both barrierless and thermodynamically favorable [31,75]; (iii) oxygen adsorbed at graphene edges is known to be able to ‘‘spill over’’ onto the basal plane [11,26,76–78]. The presence of epoxy-type oxygen on the basal plane is additionally supported by the analysis summarized in Fig. 1: if molecular O2 were present on the basal plane, its dissociation into two epoxy-type O-species would be thermodynamically favorable and the required activation energy (Eact = 24 kcal/mol in the case of pyrene) is not exceedingly large. The distribution of electronic charge in the presence and absence of epoxy oxygen is illustrated in Fig. 2. Apart from clearly distinguishing between edge and basal-plane sites (the latter being electron-deficient), perturbations produced by the presence of epoxy-type surface oxygen at both size levels are predicted to occur in the immediate vicinity of the adsorption site. Thus, for example, both the zigzag sites (C1, C23, C30, C36) and the armchair sites (C18, C19, C33,

Fig. 6 – Oxygen surface diffusion on the basal plane of a more realistic graphene molecule containing free edge site(s) and quinone groups. (See Fig. S6a in Supplementary Information for an additional case study.)

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C34, C37, C39–C42, C44–C46) in C42H16O (Fig. 2b) retain the negative charge (0.30–0.37 and 0.19–0.23, respectively) that they possess in the absence of oxygen; and zigzag cusp sites C2 and C6 (Ca type [75]) are affected much more (Fig. 2a) than the analogous C11 and C14 sites.

3.2.

Surface diffusion of oxygen

For hydrogen adatoms, the transition state for ‘hopping’ from one carbon atom to the next is a completely desorbed state (results not shown). This was confirmed using both finite graphene molecules and periodic boundary conditions; thus, for example, the equilibrated Had-graphene plane distance

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in the case of pyrene (on-top position) is 0.112 nm and in the transition state (bridge position) it is >0.3 nm. This is consistent with the intriguing experimental fact that dissociated hydrogen migrates easily from one carbon particle to another [47,48,79]. In contrast, the thermodynamically favorable oxygen hopping from one epoxy site to the next is a surface diffusion phenomenon. This is illustrated in Fig. 3 for oxygen on the basal plane of pyrene: the associated activation energy is relatively high, but it does exhibit both geometric and electronic dependence, as discussed in detail below. The effects of graphene size on the diffusion barrier are illustrated in Figs. 3–5. In Fig. 4 oxygen hopping is seen to remain thermodynamically favorable but its activation energy

Fig. 7 – Charge (a) and spin density (b) distributions for the graphenes shown in Fig. 6: left, ground state with epoxy O at C4– C7 (Fig. 6, left); middle, transition state with epoxy O at C4 (Fig. 6, middle); right, ground state with epoxy O at C4–C5 (Fig. 6, right).

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is reduced and becomes closer to the values observed for periodic graphene (see below). It is important to note the absence of ‘unzipping’ [9,41,43] in this process: the underlying C–C bond in the epoxy group remains at ca. 0.15 nm, the C–O–C angle remains <65, and the distance of O from the basal plane is 0.141 nm in the transition state. This compares favorably with the results obtained for periodic graphene (see below). And it is to be contrasted with the graphene shown in Fig. 5 which illustrates that the unzipping process is quite sensitive to graphene geometry: the underlying C–C bond in Fig. 5b is 0.213 nm, the epoxy angle is 100 and the oxygen is only 0.102 nm away from the basal plane. The influences of surface chemistry and charge distribution on the unzipping of graphene and the oxygen diffusion barrier are illustrated in Figs. 6 and 7. It is now well established that in graphene not all the edge sites are saturated with H atoms [31,34,53,54]: some are free, duly stabilized (as zigzag carbene-type and armchair carbyne-type sites), and others (notably those exposed to room-temperature air) contain oxygen functionalities. It is interesting to note that in such cases the oxygen diffusion barrier can decrease significantly (compare Figs. 3 and 6). As expected based on arguments presented above, unzipping does not occur during such more ‘facile’ surface diffusion process: the relevant C– C bond distances and epoxy group angles for the peripheral (Fig. 6, left) and central position (Fig. 6, right) are 0.155 and 0.154 nm and 65.1 and 64.8, respectively. The potential energy surface around the intuitively appealing transition state shown in Fig. 6 was also explored, by placing the oxygen atom not above the central carbon atom (e.g., C4 in Fig. 2) but at several positions toward the center of the hexagon: only higher-energy transition states were found in all cases, in agreement with the results obtained for periodic graphene. Analysis of charge and spin density distributions (Fig. 7) provides an additional clue regarding the ease of O-hopping: drastic changes are predicted to occur as a consequence of electron localization at the C16 carbene site (Fig. 7b) and charge density differences between edge and basal-plane sites (Fig. 7a) are not as pronounced (compare with Fig. 2a).

Table 1 summarizes the optimized geometry characteristics of prototypical graphenes and their oxygen diffusion barriers. Apart from the intuitively appealing fact that graphene unzipping is associated with a high barrier, it is interesting to observe the existence of a good correlation (R2 = 0.989) between the surface diffusion activation energy and the C1–O bond distance: the weaker this bond is, the more facile is the hopping of oxygen on the graphene basal plane. Essentially the same result was obtained by analyzing graphene with periodic boundary conditions [80]. In the absence of epoxy oxygen, both types of calculations (periodic boundary conditions and finite clusters) yield the correct C–C bond distance of ca. 0.142 nm for sp2-hybridized carbons. Whether or not the diffusion barrier is also related to the exact location of the epoxy oxygen in the transition state (above the C2 atom), as suggested by the relative values of angles C1–C2–O vs. C3– C2–O, would require a more detailed analysis. A straightforward means of altering the electron density distribution is functionalization, e.g., by introducing electron-withdrawing or electron-donating functionalities at graphene edges. In Fig. 8 we summarize the effects of the presence of ubiquitous carboxyl and phenolic groups. The activation energy for oxygen surface diffusion increases in the former case (from 35 to 45 kcal/mol) and decreases in the latter (to 29 kcal/mol). This is in agreement with the results obtained using periodic boundary conditions [80]: when one electron for every 50 carbon atoms was added to graphene, the O-hopping energy barrier was reduced from 0.73 to 0.15 eV (17 to 3.5 kcal/mol); and upon its removal, the barrier increased to 0.89 eV (21 kcal/mol). As expected, the increase is larger for the carboxyl groups, whose inductive and resonance effect reinforce each other; in the OH-group case, the resonance effect (electron-donating) is more influential than the inductive effect (electron-withdrawing), the latter being clearly manifested in Fig. 8b and c. The corresponding C1–O bond lengths are 0.1398 and 0.1442 nm, in reasonable agreement with the correlation established above (see Table 1); indeed, unzipping by the epoxy oxygen occurs when the electron-withdrawing COOH groups decorate the graphene edges and it is ’suppressed’ in the presence of electron-donat-

Table 1 – Geometries (distances in nm, angles in degrees) and O-hopping characteristics of prototypical graphenes. (C1 and C2 are the carbon atoms forming the epoxy bond at the start (a) and C2 and C3 at the end (b) of the O-hopping process.) Molecule

C16H10O (Fig. 3)

C1–O

C2–O(a) C2–O(b)

0.1430 0.1425 0.1382 C42H16O (Fig. 4) 0.1441 0.1438 0.1450 C16H8O2 (Fig. 6) 0.1453 0.1437 0.1425 C16H8O3 (Fig. S6a) 0.1461 0.1443 0.1443 Grapheneb 0.149 0.149 0.149

C3–O

C1–C2 C2–C3 C1–O–C2 C2–O–C3

0.1382 0.1609 0.2120 68.6 100 0.1450 0.1550 0.1510 65.1 62.7 0.1448 0.1554 0.1540 65.1 64.8 0.1443 0.1524 0.1506 63.3 62.9 0.149 0.151 0.151 61.2 61.2

a at 923 K, assuming a constant hopping distance of 0.123 nm. b using periodic boundary conditions.

C2–O (TS)

C1–C2–O Eact (kcal/mol) Diffusivitya (m2/s) C3–C2–O (TS)

0.1426 111 96.5 0.1406 111 104 0.1410 102 110 0.1410 103 108 0.144 108 99.9

35

4.1 · 1016

23

2.6 · 1013

10

4.8 · 1010

5.3

3.9 · 109

17

1.0 · 1011

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Fig. 8 – Effects of carboxyl and phenolic group substituents on the thermochemistry of O-hopping (a) and on the graphene charge distributions before (b) and after (c) the O-hop. (d) Optimized geometry of the ’reactant’ ground state. (See also Supplementary Information, Fig. S8e,f.) Insert in Fig. 8(b) shows the charge densities of the parent PAH molecule.

ing OH groups (see Fig. 8d and Supplementary Information). In principle, this should be related to the charge density differences documented in Fig. 8b and c. Thus, for example, the charges at edge sites adjacent to the substituent (C2, C6, C14 and C16) are mostly higher than the typical values for Ca zigzag cusp sites (see insert in Fig. 2a), although the values at the epoxy sites themselves (compare with Fig. 2a) are hardly affected; a more detailed interpretation of these trends, including the suitability of the classical Mulliken population analysis, is the subject of our continued research. Heteroatom substitution in the graphene basal plane is another means of influencing the charge densities. The effects of B and N were thus analyzed and the results are summarized in Figs. 9 and 10. In both cases, surprisingly, the energy barrier is lowered with respect to C16H10O and it is essentially identical to that calculated for C42H16O (see Table 1). This is consistent, however, with the finding that no unzipping is

predicted in either case: the epoxide C–C bonds in the ‘reactant’ (C22–C15) and ‘product’ (C15–C14) are 0.1534 and 0.1561 nm for C26H13BO, and 0.1530 and 0.1488 nm for C26H13NO. The charge distributions in the two cases are quite different (see Fig. 9), as expected; there is significant charge localization at N4 and the relative perturbations of charge density are much more pronounced than in the absence of heteroatom substituents (compare with Fig. 2). A more detailed analysis (e.g., using natural bond orbitals or atoms in molecules) will be needed, however, to establish a correlation with either the driving force or the barrier for oxygen diffusion, especially because finding the correct transition states turned out to be particularly challenging here. The results reported are reproducible, in the sense that both standard optimization procedures (QST2 and QST3) [64] produced the same structures; but the epoxy oxygen, while vibrating appropriately across the central C15 atom (at imaginary frequencies

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c

d

Fig 8. (continued)

Fig. 9 – Effects of B and N substitution in graphene on oxygen surface diffusion. For the geometry of transition states, see Supplementary Information, Fig. S9a.

of <300 cm1, significantly lower than most of the others reported here; see Figs. 1, 3 and 4b), does so either parallel or perpendicular to the C22–C15-X4 axis, and not at the more appropriate 45o angle with respect to these axes (which was invariably found throughout the rest of this study). In Table 1 we summarize the comparisons between finite clusters and periodic graphene and present the results of calculations of the surface diffusion coefficients. As a typical illustration, C16H10O (Fig. 3) has 75 degrees of freedom and its vibrational frequencies range from 92.1 to 3207 cm1; the 74 frequencies of the corresponding transition state range from 94.3 to 3210 cm1 and thus the hopping attempt frequency turns out to be 705 cm1 or 2.1 · 1013 s1. The diffusivity value shown for the process depicted in Fig. 3 is in very good agreement with the experimental results of Yang and Wong [26]. It is remarkable, though, how sensitive this parameter is to the details of graphene surface chemistry and

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Fig. 10 – Charge distributions for the graphenes shown in Fig. 9. Singlet is the ground state in each case: C26H13BO (O at C15– C22), E = 1098.65298 hartrees; C26H13BO (O at C15–C14), E = 1098.65246; C26H13NO (O at C15–C22), E = 1128.54006; C26H13NO (O at C15–C14), E = 1128.53697.

Fig. 11 – Optimized geometries of graphene C16H10O: (a) no-unzipping case (see Fig. 3, left); (b) unzipping case (see Fig. 3, right); (c) O-insertion case (ESCF = 690.94047 hartrees).

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electron density distribution in the basal plane: indeed, under the most favorable conditions it approaches Knudsen diffusivity values (ca. 109 m2/s) for gas-phase molecules in nmsize pores [81]. When periodic boundary conditions are applied [80], the epoxy oxygen atom also equilibrates on the ’bridge’ site, bonding to two carbon atoms; to diffuse to a nearby bridge site, it ‘walks’ to a second bridge site by breaking one C–O bond and reforming it with a neighboring carbon atom, in agreement with the results shown above for graphene molecules. It is instructive to compare the corresponding energy barriers and diffusivities to those reported for related systems; thus the compilation of Seebauer and Allen [65] quotes, respectively, ranges of 14–50 kcal/mol and 1011– 105 m2/s for O/W, and 27–34 kcal/mol and 108–101 m2/s for O/Pt under a wide variety of conditions. While the mobility of oxygen atoms on carbon surfaces (as well as on silicon; see Section 1) may not be as facile as on metallic surfaces, Table 1 shows that this is not because of relatively high Eact values. This analysis provides further evidence for the important role that the mobile (but non-desorbable) epoxy oxygen plays in the indirect path for CO2 formation during the graphene-O2 reaction [31]. In effect, as shown in Fig. 11, if oxygen hops from C3–C4 to C3–C7, instead of from C3–C4 to C4–C8 (see Fig. 3), which is indeed thermodynamically more favorable (33 vs. 12 kcal/mol), O insertion occurs with consequent formation of a seven-member ring analogous to oxepin [31].

4.

Conclusions

Use of density functional theory to analyze both prototypical clusters (molecules) and periodic structures has provided unique insight into the mechanism of diffusion (hopping) of oxygen on the graphene surface. Upon spillover of atomic oxygen from the graphene edge, subsequent to chemisorption of molecular oxygen on carbene-type zigzag sites, epoxy-type oxygen migrates from one bridge site to another with remarkably variable activation energy. A correlation exists between the strength of the leaving epoxide group and the epoxy oxygen hopping barrier. Both geometric and electronic properties of graphene affect this energy barrier, which can result in diffusivities that are as low as that of gas-phase O2 in pores of molecular dimensions. Such high mobility of non-desorbable basal-plane oxygen can account for its active role in carbon reactivity, most notably in the formation of CO2 by graphene ‘unzipping’ and formation of seven-member rings at crystallite edges. Supplementary Information. Figs. S6a, S8e, f and S9a, as well as Cartesian coordinates of all the graphene molecules studied.

Acknowledgments This work was supported by CONICYT-Chile (projects #1080334 and PFB-27 CCTE-UDT), the US–Israel Binational Science Foundation (grant #2006238), the CarbonEARTH program (NSF grant #DGE-0947962) and the Donors of the ACS Petroleum Research Fund. Supercomputing facilities used were funded in part by the Materials Simulation Center, a Penn-State MRSEC/MRI

facility, and through instrumentation funded by the National Science Foundation (grant OCI-0821527).

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.carbon.2011.05.037.

R E F E R E N C E S

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