Atomic Hydrogen Diffusion on Doped and Chemically Modified

To explore hydrogen mobility on graphene, density functional calculations are used to determine the magnitude of binding energy versus the diffusion b...
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Atomic Hydrogen Diffusion on Doped and Chemically Modified Graphene Angela D. Lueking,*,†,‡ George Psofogiannakis,† and George E. Froudakis*,† †

Department of Chemistry, University of Crete, P.O. Box 2208, Voutes, Heraklion, Greece 71003 Department of Energy & Mineral Engineering, Department of Chemical Engineering, and EMS Energy Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, United States

‡

S Supporting Information *

ABSTRACT: To explore hydrogen mobility on graphene, density functional calculations are used to determine the magnitude of binding energy versus the diffusion barrier for graphene, considering the effects of hole and electron doping, B and N substitutional dopants, and oxygen heteroatoms. Although C−H binding energy and the barrier for chemical diffusion are not correlated, the binding energy of H in the lowest energy site on top of a C atom correlates with the binding energy of H over a “bridge” C−C bond, which is the transition state for chemical diffusion. Using this framework, we demonstrate that both B substitutionally doped graphene and hydoxylated graphene have the potential to simultaneously meet thermodynamic and kinetic constraints for reversible room-temperature hydrogenation. The constraints demonstrate that reversible room-temperature hydrogenation is possible only when H diffuses in a chemically bound state.

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with immobile deuterium clusters implanted on HOPG.2,5,6 In contrast, gravimetric uptake20 of the oxidized surface, combined with disappearance of the C−H wag after ambient temperature evacuation,11 demonstrated high H mobility to/from an active catalyst. As hole doping reduces the H chemical diffusion barrier,25 shifts observed in the carbon doping level (perhaps upon surface hydroxylation) in the Raman studies pointed to facilitated H chemical diffusion.11 The results were inconsistent with propositions that H will desorb into a weakly bound physisorbed state, in which it can freely diffuse,19,28 as OH groups increase the H BE to adjacent Cs.19 Increased BE is necessary to account for C−H bond formation from gas-phase H26,11−16 but is generally thought to increase the barrier for chemical diffusion, as demonstrated for H clusters on graphene.17,18 Here, we utilize density functional (DFT) calculations to revisit the mechanism for hydrogen mobility via the spillover process, considering the role of heteroatoms. It has been previously shown that electronic29,30 and substitutional dopants31 may lower the H diffusion barrier relative to a highly pristine graphene surface, and we compare their effects to those of oxygen heteroatoms by developing a framework to consider BE and activation energy (EA) of diffusion. Although defects and dislocations,32 as well as mechanical deformations,33−35 may also affect graphene hydrogenation, we limit our consideration to dopants and heteroatoms. Our goal is to

INTRODUCTION Diffusion of atomic H on a carbon surface is a fundamental problem in surface science, with applications extending to novel materials,1,2 electronics (graphene to graphane),3,4 astrophysics,5−8 catalysis, and hydrogen storage.9,10 Atomic hydrogen may be introduced via either a “hot” hydrogen atom beam2,5,6 or catalytic nanoparticles that dissociate H2 via the hydrogen spillover mechanism.11 A chemisorbed H atom will rehybridize the carbon to which it is attached, leading to disruption of the π-aromatic network and surface restructuring. Thus, clustered H atoms have significantly increased binding energies compared to isolated H,6,12−16 and deuterium clusters implanted on HOPG are stationary at room temperature.5,6 Calculations confirm H clusters are significantly less mobile17,18 than isolated H atoms.19 This leads to a seeming paradox in the hydrogen spillover literature: reports of significant catalytic adsorption of H29,10,20−22 presuppose high binding energy (BE) and significant mobility. Combined with significant potential error in H2 adsorption measurements23−25 and poor reproducibility between laboratories,26,27 such reports are highly controversial. Recently, in situ, high-pressure Raman spectroscopy was used to track ambient temperature hydrogenation of three carbon surfaces (graphene, activated carbon, and oxidized activated carbon) patterned with Pt nanoparticles, to probe the hydrogen spillover mechanism.11 A C−H wag mode was indicative of partial surface hydrogenation for all three carbons, independent of morphology, surface chemistry, or catalyst size. For graphene and activated carbon, low gravimetric uptake suggested hydrogenation was localized around the catalyst, consistent © 2013 American Chemical Society

Received: January 23, 2013 Revised: February 22, 2013 Published: February 25, 2013 6312

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Figure 1. Carbon cluster models. Heteroatoms were placed on the central rings of the C42 cluster in either the “x”, “xy”, or “xz” positions. With the exception of structures labeled C16, all clusters included 42 C atoms, but for brevity, only the central rings are shown here. External oxygen functionalities (OH or COOH) were placed on C42 and C16 at the C positions shaded in black. H diffusion was considered along the central bond, with one exception: for C42−OH*, H was placed at the position marked by * and moved horizontally to the left along this bond.

establish that the cluster calculations do not induce any artifacts in the calculations due to the finite size, and the checks were limited to graphene and B- and N-doped graphene. Two different periodic cell sizes were used in the periodic calculations. These were the 2 × 2 and the 4 × 4 supercells of graphene (henceforth called supercells for all structures), containing 8 and 32 surface atoms, respectively (Scheme S1, Supporting Information). Only one heteroatom per cell was used in each calculation, so that the two periodic cells correspond to different atomic fractions of the heteroatoms, and it is thus presumed that the larger unit cell should approach the cluster calculation models containing only a single heteroatom more accurately. The larger 4 × 4 periodic cell was used for an estimation of binding energies reported below, whereas activation energies are based on the 2 × 2 cell at the BP86/6-31G** level of theory. Further validation of these model parameters is provided in the Supporting Information.

provide a framework to understand the seeming paradox mentioned above.

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THEORETICAL METHODS DFT calculations were performed with Turbomole36 using the BP86 exchange and correlation functionals,37,38 the resolutionof-the-identity (RI) approximation,39 and def2-TZVP basis sets for all atoms.40 We explore the effect of carbon geometry, boundary conditions, charge, and number, type, and placement of heteroatoms. The C42 “base case” is a 14-ring, 42-atom carbon cluster (see Figure 1 for all structures). B and/or N substitutional dopants were inserted into the C42 cluster at the “x”, “xy”, or “xz” configuration. External oxygen functional groups (either OH or COOH) were placed on C42 (or a 4ring, 16-atom, C16) clusters at the positions marked by black, to arrive at an oxygen content of ∼10 wt %. In most cases, heteroatoms (including H) were placed in pairs to maintain symmetry for diffusion of an additional H. Internal hydrogen adatoms or hydroxyl groups were placed on the same side of the carbon plane in the “xy” configuration; the third H atom was placed either on the same (s) or opposite side (o) of the carbon plane. An additional same-sided case with OH groups placed at the “xz” configuration was also studied. gOpenMol41 was used for qualitative visualization using total electron density (TED), electron density difference plots, and contour plots. Density difference plots are relative to a structure with the exact same atom position, but with C replacing any heteroatoms. Use of the term TED below refers to total electron density, unless otherwise specified. Periodic DFT calculations were performed with Gaussian0342 and the atom-centered Gaussian basis sets 3-21G* and 6-31G**43 and the density-fitting approximation.44 The BP86 exchange-correlation functional was used to facilitate comparison with the 14-ring cluster Turbomole calculations performed with the BP86 functional. The intention was to

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THEORY

BE is defined as the difference in electronic energies of a graphenic structure with chemisorbed H (“HX”) versus the sum of the energies of the clean surface (“X”) and free H prior to chemisorption (“H”), when H is located on the lowest energy “on top” C site BE = E HX − E H − E X

(1)

To estimate the diffusion energy barrier, complete internal reaction coordinate scans were performed by constraining one C−H bond distance and relaxing all other coordinates. BE† is the corresponding energy difference when H is at the maximum energy position along this path, which occurs above a CC bridge site BE† = E HX † − E H − E X 6313

(2)

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Figure 2. (a) Calculated binding energies for the structures shown in Figure 1. The inset provides the corresponding activation energies. Full numeric data are found in Table S1 (Supporting Information). (b,c) Total electron density plots of select structures in the transition state to demonstrate the relationship between binding energy and electron density.

t ∼ L2 /D

The bridge site is illustrated in Figure 1 and is attached to two adjacent C atoms, whereas the on top site is attached to a single C atom. The shorthand notation H−C and H−CC will be used in subsequent discussion to refer to H found on on top and bridge sites, respectively. The barrier for chemical diffusion (EA) is the difference between energy in the transition state (EHX†) and the lowest energy state (EHX). It is thus related to BE† and BE as follows BE† = BE + EA

To arrive at an upper bound of 0.7 eV, Liu et al. take the diffusion distance to be 20 nm, based on experimental measurement of particle distribution, and take the desired completion time (t) to be ∼1 h. With the exponential dependence of the diffusion coefficient on EA, there is a clear delineation at ∼0.7 eV, as 0.6 and 0.8 eV barriers lead to diffusion times of ∼1 min and ∼40 h, respectively (keeping L at 20 nm). This 0.7 eV limit is not only based on specific experimental parameters but also based on free energy, whereas the energy barriers in this paper are electronic energy and should be corrected for thermal and entropic effects to directly relate the calculated values to experiment. Although these calculations are certainly possible, and have been performed by the authors previously,45 our goal is to provide a “screening” parameter so that multiple surfaces may be considered without time-intensive frequency calculations for each candidate material. To make this tie from experiment to theory, we use the 3 H cluster, which as we discuss below has a calculated electronic energy barrier of 1.25 eV. As significant roomtemperature mobility of H-implanted graphite is not observed,5,6 we take a target upper limit of the electronic diffusion barrier to be 1.25 eV (i.e., EA < 1.25 eV). This value should be considered approximate.

(3) †

As defined, BE and BE are negative for attractive interactions; however, absolute values are discussed below to facilitate discussions of bond strength. Desorption is preferred over chemical diffusion when EA > −BE

(4)

BE† > 0

(5)

where eq 5 is a result of substitution of eq 3 into eq 4. The activation energy for surface diffusion is related to surface mobility. Liu et al.11 state the EA of diffusion should be less than 0.7 eV for diffusion to occur readily at 300 K. This is based on consideration of activated diffusion13 D=

1 2 −E barrier / kT α νee z

(7) 11

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(6)

RESULTS AND DISCUSSION Our analysis hinges on developing a relationship between H surface BE and H mobility, which is determined by EA. The Brönsted−Evans−Polanyi (BEP) rule47,48 suggests a linear relation between BE and EA for elementary steps in a catalytic reaction. As this relationship is semiempirical,49 there is no reason to assume a priori that it applies. Furthermore, the premise of the H spillover process is that (a) H2 dissociation

where D is the diffusion coefficient, and we have used values for graphene for the number of adjacent sites to which the H could hop (z = 3), the jump length (α = 1.5 Å), and the vibrational mode parallel to the surface (experimentally,11 νe = 1180 cm−1; theoretically45 this has been calculated at 1176 cm−1). The diffusion constant can be related to time for adsorption (t) and diffusion length (L) as follows46 6314

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constant diffusion barriers (the C42 diagonal, i.e., EA = 1.25 eV is shown). Deviations above the C42 diagonal correspond to an increase in EA, whereas deviations below the diagonal represent a decrease in EA, relative to the pristine case. As the deviation above/below the diagonal is not constant, this is another way to illustrate the lack of correlation between EA and BE. Given the relationship between bond energy and TED, deviations from the C42 diagonal occur when the heteroatoms influence the HC or HCC bond differently. TED is influenced by structure geometry, in particular, expansions and contractions that occur upon hydrogenation. Charged structures C+ and C− best illustrate this, as geometric effects must have a stronger influence than total number of electrons on binding energies to account for the trends seen in Figure 2a: on top binding is enhanced in both cases (BE is 1.54 for C+ and 1.39 eV for C−). The electron deficiency in C+ is accompanied by less displacement of the C atom out of the plane to which H is attached (Table S3, Supporting Information). The electron excess in C− is partially transferred to the H adatom (Figure 3), dampening the effect on TED in

occurs on a metal nanoparticle; (b) H is able to diffuse to and (c) along the support; and in general, it is presumed that (d) H2 dissociation directly on the support does not occur. Our goal is to develop a relationship between the BE on the support (the energy difference of reaction (d)) and EA of diffusion on the support (reaction c), and thus the BEP rule is clearly not applicable, as these are two separate steps in a multistep mechanism. Consideration of prior ab initio calculations for H chemisorbed to graphene also demonstrates that the relationship between BE and EA is not linear: the BE of the first added H is less than EA, thus it is easier to desorb H than for H to move to an adjacent site in a chemically bound state.6,28,45,50,51 Collective stabilization of multiple H adatoms increases both BE and EA,6,12−16 but not linearly. Our calculations reproduce this trend and can be used to more definitively demonstrate the breakdown of the BEP rule. The BE is less than EA for the C42 cluster model (0.91 and 1.26 eV, respectively), the C16 cluster (0.72 and 1.21 eV), and periodic graphene (1.03 and 1.30 eV). Adding two additional H to C42 across the central bond (Hxy, Figure 1) leads to a BE of 2.06 (2.32) eV and increases EA to 1.44 (1.30) for same sided (and opposite sided) addition of a third H. Comparing the isolated H to the 3-atom H cluster, the BE is more than doubled, while EA increases by only ∼15%, suggesting these values are not correlated and the BEP rule is not valid. Diffusion of H in larger clusters has been studied previously17,18 and shows similar trends. In all cases, the mobility barrier for surfaces with multiple H is sufficiently high (>∼1.25 eV) that room-temperature diffusion is unlikely, and as discussed above, experimental observations of immobility on deuterated HOPG5,6 serve as a basis for the target upper limit of the EA. There is perfect qualitative agreement and good quantitative agreement between the cluster and periodic models and the varying cluster sizes. (In addition to the model used (i.e., cluster versus periodic), basis-set differences and different functional implementations can account for some quantitative deviations.) Further discussion on periodic versus cluster models and all tabulated data is found in the Supporting Information (Tables S1 and S2). Consideration of a number of graphenic and doped structures (Figure 1) shows there is absolutely no linear correlation between BE and EA (Figure 2a, inset, R2 = 0.036), and the BEP rule is not valid. Rather, there is a strong correlation between BE and BE† (Figure 2a, R2 = 0.75), suggesting a relationship between the electronic environment at the on top lowest energy site and nearby bridge site which is the transition state for chemical diffusion. Unlike EA, BE and BE† correspond to physical positions of H on the material. In hindsight, the relationship between BE and BE† seems somewhat obvious, although we are unaware of prior considerations of BE† to discuss surface mobility. The strength of a given bond is determined by the total electron density (TED) of the bond, and the proximate HC and HCC sites are similarly affected by dopants. To illustrate this further, placing two external electron-withdrawing (C16-OH) or -donating (C16-COOH) groups on the C16 cluster shows a corresponding electron depletion or increase in the TED of the bonding environment (Figure 2b, transition state shown, on top results are similar). Structures with the highest BE† tend to have the greatest vertical component of the TED (Figure 2c), such that the TED may increase the strength of the H−CC bond. Although no correlation between EA and BE is found for multiple surfaces, EA and BE† are linearly related for a single surface (eq 3), and thus diagonal lines in Figure 2a represent

Figure 3. Total electron density plots for the charged cases, C− (top) and C+ (bottom). Left structures are in the lowest energy on top site. Right structures (denoted with †) are in the transition state. Corresponding geometric data are found in the Supporting Information.

the HC bond. In the transition state, C+ is contracted (Table S3, Supporting Information), and there is less displacement of C out of the plane (Table S3, Supporting Information) contributing to both an increase in TED and less of an energy penalty for structural rearrangement. Consequently, the barrier to diffusion is significantly reduced for C+ (EA = 0.57 eV) and increased for C− (EA = 1.7 eV, Figure 4), consistent with previous results29,30 in which the electronic doping level was altered by changing the Fermi level rather than removal/ addition of electrons. Both studies are conceptually equivalent, and both lead to the conclusion that hole doping will facilitate graphene hydrogenation. Single B1 and N1 substitutional doping corresponds conceptually to C+ and C− and shows even more pronounced effects on binding energies (Figure 2a). Like C+, B1 substitution significantly increases both BE (to 2.30 eV to the ortho C and 1.72 to the meta C) and BE† (to 1.47 eV), and 6315

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Figure 4. Energy scans for select structures as H is moved along the central carbon bond. The reaction coordinate, ξ, is defined as the difference between the two HC bond lengths for the meta and ortho carbon (inset). For the asymmetric B1 and N1 case, negative values of ξ are closer to the ortho C, as the binding energy to the ortho C was less than that of the meta carbon. In (a), the OH and H energy scan selected is the “xy” configuration with same-sided attachment. Energies are referenced to the binding energy to the ortho C. Energy scans for the periodic calculations are found in Figure S1 of the Supporting Information.

deviation below the diagonal represents a significant reduction in EA (to 0.83 eV for ortho to meta diffusion and 0.24 eV for metal to ortho, see also Figure 4), consistent with previous results31 and qualitatively similar to the periodic calculations (BE = 2.34 eV (ortho); 1.75 eV (meta); EA = 0.92 eV ortho to meta). A depression in TED about the B heteroatom (purple, Figure 5a, left) leads to a surplus of the TED around the adjacent C (teal) which increases BE and BE†. For on top H binding, there is delocalization of electron density in the plane of the H, and the effect is even more pronounced for binding in the bridge site (Figure 5b, left). In general, electron delocalization in the plane of the bond tends to decrease the strength of the bond (see Supporting Information). When the effect is greater for the HC bond, EA is decreased; when it is greater for the HCC bond, EA is increased. Boron dopants tend to “attract” H adatoms as they move to the depression in TED about the B heteroatom (Figure 5b, Table S3, Supporting Information). In contrast, N1 deviates above the C42 diagonal, and the diffusion barrier adjacent to N is significantly increased (to over 2.5 eV [ortho to meta] in cluster models, Figure 4; and to 2.12 eV in periodic models). In TED plots, N retains a fairly localized and symmetric “bulge” above the heteroatom (Figure 5a, right, teal), and this bulge depletes electrons in the adjacent C (Figure 5a, right, purple). There is a high delocalization in the plane of the H−C bond, whereas the H−CC bond is highly localized with an electron excess about N repelling the H in the transition state (Figure 5b). The effects of B and N on the TED appear to be greater in the plane of the transition state, and thus there are large effects on BE† and EA.

Figure 5. Electron density plots of B1 (left) and N1 (right); the heteroatoms are located in the position shown by purple and teal bulges in the upper row, respectively. (a) Density difference plots, prior to H addition, show an electron deficiency at the B heteroatom location (purple, left) and an electron excess at the N position (teal, right), relative to a C structure. (b) Total electron density plots with H in the on top site (middle row) and H in the transition bridge site (bottom row) show corresponding electron deficiency for B1 and excess for N1. See also Figures S1 and S2 in the Supporting Information.

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substitutional dopants, cross bond (xy) OH groups having a more pronounced effect than parallel (xz) OH groups and same-sided attachment tend toward lower EA than opposite sided attachment (Figure 2a, Table S1, Supporting Information). Although it is common to think that strongly bound adatoms will have low mobility (arising, perhaps, due to application of the BEP rule), it is clear that the EA of surface mobility does not correlate with BE (R2 = 0.036). Contractions/expansions in the structure and localized effects on the TED have a stronger influence on surface mobility than the number of electrons. Heteroatoms also clearly influence the mechanism for diffusion. As mentioned above, clustering reduces the room-temperature mobility of deuterated HOPG,5,6 whereas oxidation increases room-temperature H mobility of activated carbons.11 Figure 2a is useful to understand these trends. Above the horizontal line (at BE† > 0), the barrier for desorption is less than the barrier for surface diffusion (see eqs 4 and 5) due to the linear relationship of these terms. Single H adsorption to pristine C structures is above this line (C42, C16), and as described previously,28,45the mobility of a single H atom on pristine graphene occurs in a loosely bound physisorbed state. However, H clusters (Hxy) fall below this line, and the increase in BE with clustering means diffusion is now more favorable than desorption; however, the high barrier for chemical diffusion (>1.3 eV, Table S1, Supporting Information) in clustered H is likely too high to be easily overcome at room temperature. Indeed, no room-temperature diffusion is observed experimentally for H implanted on HOPG,5,6 and the onset of H2 recombinative desorption occurs at ∼350 K, although surface coverage influences this temperature.7 Replacing the basal plane H adatoms with hydroxyl groups also favors mobility via diffusion rather than desorption, but now, the EA is reduced (to 0.9−1.0 eV, ∼20−25% relative to the pristine case, Table S1, Supporting Information). The BEs for OH adducts and B substitutional dopants are also close to calculated values for H binding to Pt or Pd catalysts,16,54,55 another prerequisite step for surface hydrogenation via the spillover process. Further consideration of entropic,45 thermal,45 and perhaps quantum56 effects are needed to determine whether each specific barrier may feasibly be traversed at room temperature. Nevertheless, the reduction in EA correlates with the experimental observation of reversible hydrogenation and significant mobility in the presence of surface oxygen groups.11 It is also clear from Figure 2a that any structures that are to meet both thermodynamic and kinetic constraints of hydrogenation via surface diffusion must have H mobility that occurs via diffusion in a chemisorbed state. In other words, the only region for which both EA and BE are simultaneously in the desired range occurs below the horizontal desorption−diffusion line (eq 5). Specifically, for there to be a thermodynamic incentive to dissociate H2 and catalytically hydrogenate graphene (i.e., |BE| > 2.3 eV), H is propagated in a chemisorbed state (BE† < 0) unless the EA exceeds 2.3 eV, a barrier which will not be overcome at room temperature.

Localized effects in the TED clearly affect BE, and thus the position of heteroatoms affects mobility. (By extension, there may be preferential diffusion paths on doped surfaces.) Isoelectronic BNxz and BNxy structures illustrate this point: placement of the heteroatoms on the same ring (xy) allows the B to negate the detrimental effect of N by drawing in the excess electrons, whereas locating the heteroatoms further apart (xz) lessens the effect (Figure 6). Thus, the binding energies of

Figure 6. (a) Density difference and (b) TED plots of BNxz (left) and BNxy (right). All structures are prior to H addition. The heteroatoms are located in the position showing the purple (B) and teal (N) bulges in the upper row. See also Figures S3 and S4 in the Supporting Information.

BNxz are similar to C42, whereas BNxy has a greater shift (Figure 2a). Similar trends are found for isoelectronic B2xz and B2xy structures (Figures S6−7, Supporting Information): two depressions about the diffusion path (xy) push the TED to the diffusion path, leading to a greater normal component (Figure 2c) and higher binding energies relative to the single (xz) isoelectronic disruption. Comparing isoelectronic B4 to B4bc shows that highly localized heteroatoms lead to significant curvature (Figure 2c), less delocalization in the H−C binding plane, and high BE. To examine the effect of oxygen groups, we limit our consideration to the effect of adjacent OH groups (epoxides will be converted to hydroxyls in the presence of H19,52) on the localized C structure and H diffusion path on C. As O groups on carbon are relatively mobile,52,53 and may combine with H to form water,19,52 detailed studies of OH stability versus H2O formation will be discussed in a subsequent paper. OH adducts are placed directly on the basal plane and separately compared to placement of either electron-donating (COOH) or electronwithdrawing (OH) groups at the periphery of the carbon cluster (Figure 1). The effects of external groups on the TED of the C16 cluster were discussed previously as an illustrative example, but the effects on BE are minor (C16, C16−COOH, C16−OH, Figure 2a). As the cluster size is increased to C42 to better approximate graphene, neither group (C−OH, C− COOH, Figure 2a) has any effect on the binding energies, even if H diffusion is considered on the same ring as the external group (COH*, Figure 2a). Electron transfer at the edge is destabilized over large polyaromatic networks. In contrast, internal OH adatoms alter the hybridization state of the C to which they are attached and have a significant effect on the binding energies (OHxy, OHxz, Figure 2a). Deviations found for OH adatoms are greater than H adatoms at comparable positions, and OH adatoms decrease EA while H adatoms increase EA (Figures 2a and 3). As was the case for

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CONCLUSIONS This paper is concerned with the effect of heteroatoms and dopants on the binding energy and mobility of hydrogen on graphene, with the goal of exploring conditions under which graphene may be catalytically hydrogenated via surface diffusion. Reports of high room-temperature uptake on graphenic surfaces almost certainly require H surface mobility 6317

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The Journal of Physical Chemistry C away from catalytic sites to obtain the high H:C ratios required to account for the reported uptakes. The activation energy for surface mobility is not correlated to binding energy, as these are two separate steps in the spillover process. Rather, binding energy in the transition state is strongly correlated to binding energy in the lowest energy on top site. Within this framework, we identify candidate materials for reversible room-temperature catalytic hydrogenation, such that (a) the BE exceeds the H2 dissociation energy (i.e., BE > 2.3 eV) to drive gas-phase H2 dissociation; (b) there is a minimal energy difference, relative to H2, to allow for reversibility (i.e., 2.4 < BE < 2.6 eV15), and (c) the barrier for diffusion (EA) can be overcome at room temperature (i.e., EA < ∼1.25 eV). The criteria necessitate that room-temperature diffusion on modified graphene must occur in a chemically bound state. H adsorption on pristine graphene will not meet all three criteria. We identify two candidate materials that meet the constraints: OH adducts and B substitutional dopants. OH basal plane adatoms indeed may facilitate significant hydrogen surface mobility while providing the desired binding energy to facilitate gas-phase hydrogenation, as observed in the experimental Raman study11 that motivates this work. Hole dopants and/or B-substituted surfaces have a similar effect, whereas pristine, electron-doped, and N-substitutionally doped carbon surfaces will not have favorable thermodynamics and kinetics for reversible room-temperature hydrogenation. Although beyond the scope of this work other model chemistries (e.g., mechanical deformation or vacancies57) may also be candidate materials, provided that both the outlined thermodynamic and kinetic constraints are satisfied. A forthcoming paper will consider the stability of hydroxyl groups and the potential effect of carbon vacancies57 on the possible role of hydrogen diffusion on a graphenic surface. Even in the latter case, hydrogen diffusion away from carbon vacancies and N functional groups must be invoked to account for the reported uptake. As “real” carbon materials are comprised of many defects, dislocations, heteroatoms, and after activation, porosity, and all these factors will influence binding energy and mobility, the carbon source material, activation procedure, elemental constituents, and oxygen content must be considered in comparative analysis of overall hydrogen uptake via the spillover process. Apparent discrepancies in surface mobility and/or hydrogen uptake27,57−60 on pristine versus heterogeneous surfaces are thus explained by the relative effect of heteroatoms on binding energy versus the barrier for surface diffusion.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported through a Marie Curie International Incoming Fellowship (AL) and a Marie Curie International Reintegration Fellowship (GP). The ideas for this work were drawn, in part, from AL’s work supported by the U.S. Department of Energy, Basic Energy Sciences Awards DEFG02-09ER466556 and DE-SC0002157. This research has been also cofinanced by the European Union (European Social Fund − ESF) and Greek national funds through the Operational Program ″Education and Lifelong Learning″ of the National Strategic Reference Framework (NSRF) Research Funding Program: THALES.

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ASSOCIATED CONTENT

* Supporting Information S

Full tabulated data corresponding to Figures 2 and 3. Periodic calculations. Further geometry and electron density analysis. Additional energy scans for cluster and periodic models. This material is available free of charge via the Internet at http:// pubs.acs.org.

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*Tel.: (1) 814-863-6256. Fax: (1) 814-865-3248. E-mail: [email protected]. Tel.: (+302810) 545055. Fax: (+302810) 545001. E-mail: [email protected]. Notes

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