Relative Stability of Graphene Nanoflakes Under Environmentally

Article pubs.acs.org/JPCC

Relative Stability of Graphene Nanoflakes Under Environmentally Relevant Conditions Hongqing Shi,†,‡ Lin Lai,† Ian K. Snook,‡ and Amanda S. Barnard*,† †

CSIRO Materials Science & Engineering, Parkville, Australia Applied Physics, RMIT University, Melbourne, Australia

‡

S Supporting Information *

ABSTRACT: The stability of finite-sized graphene nanostructures under different conditions is contingent on the stability of the highly reactive undercoordinated atoms around the circumference. Chemical passivation is a convenient way of stabilizing the edges and corners, provided the conditions support adsorption. In this paper we examine the stabilities of hydrogen, oxygen, hydroxyl, and water functionalization of the edges of graphene nanoflakes using a combination of ab initio thermodynamics and self-consistent charge density functional tight-binding simulations. We find that the adsorption of hydrogen and oxygen on graphene nanoflakes is selective and sensitive to the edge and corner structure and the local environment. Under hydrogen-rich conditions (or in vacuo), we find that armchair edges are preferred, whereas under oxygen-rich conditions the stability of the zigzag edge is enhanced. In addition to this, we find that the types of corners play an important role, and the presence of acute 60° corners is thermodynamically preferred, particularly under humid conditions. In each case, the adsorption efficiency is related to the temperature and the pressure, which may be used to stabilize one type of structure or another.

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INTRODUCTION Since the successful isolation in 2004,1 graphene has been the focus of intense research, and cost-effective methods to manufacture bulk quantities for commercial applications are already being developed. Graphene has extremely high carrier mobility and capacity, high electron transfer rate, excellent ability to quench fluorescence, high thermal conductivity, maximal surface-to-volume ratio, and outstanding robustness and flexibility. On the basis of these desirable properties, and despite its short history, graphene has already demonstrated great potentials in various novel sensor applications, such as physical sensors for detection of photons, magnetic fields, mass, and strain. However, graphene has one severe limitation from the point of view of electronics applications: it has no band gap and a vanishingly small density of states at the Fermi level, making it a semimetal.2,3 Decreasing the dimensionality is one of the methods to modify graphene4 and can open a band gap and tune it to broaden the range of applications, and in many cases this involves restricting the in-plane dimension and/or introducing undercoordinated atoms. The introduction of reactive undercoordinated atoms around the circumference of finite-sized graphene nanostructures is also critical to the development of sensing applications. Graphene has already been used as electrochemical sensors, electronic sensors, optical sensors, and nanopore sensors for biological or chemical detection, all of which draw upon graphene’s extraordinary electrical, optical, and chemical properties.5 In the latter case, knowledge of the interactions of graphene with the local chemical environment is imperative, and controlling these interactions is the topic of much research. Published 2013 by the American Chemical Society

For example, oxidation of carbon is one of the most common chemical reactions when hydrophobic graphene is exposed to ambient conditions, but the controlled oxidation of carbon to add functional O-groups is one way of tuning the chemical activity.6 When taken to the extreme, a new material (graphene oxide) is formed, which is hydrophilic.7−9 Graphene oxide formed by oxidizing crystalline graphite is similar to a graphene sheet with the in-plane carbon atoms being directly functionalized with oxygen-containing groups (such as carboxyl, hydroxyl, ketone, and ether).10−12 Graphene oxide is an insulator but has applications in transparent conductive films, paper-like and composite materials, energyrelated materials, and biological and medical applications. Reduction of graphite oxide is also a practical way to synthesize graphene sheets directly.13 Experimental data have shown that some hydroxyl functional groups exist also at reduced graphene sheets,14 but the configuration at higher coverage, where epoxy and hydroxyl groups coexist at the graphene surface,15 is not fully known. However, circumferential O-functionalized graphene is not the same as graphene oxide, as in the former case it is only the edges and corners that are decorated with Ogroups, whereas the latter also involves planar adsorption. Oxygen is also present to some degree in the vast majority of graphene synthesis methods.16 In contrast, the hydrogenated graphene has great potential in other kinds of applications, due to different characteristic Received: April 28, 2013 Revised: June 12, 2013 Published: July 11, 2013 15375

dx.doi.org/10.1021/jp404200r | J. Phys. Chem. C 2013, 117, 15375−15382

The Journal of Physical Chemistry C

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properties. For example, patterning H atoms on graphene in a one-dimensional (1-D) manner leads to so-called graphene nanoroads, which have properties similar to graphene nanoribbons.17 Two-dimensional hydrogenation was found both theoretically and experimentally to be an effective way to convert graphene from a gapless semimetal to a semiconductor with a tunable band gap,18−20 and partial hydrogenation may induce interesting magnetic states that have potential applications in spintronics.21 Hydrogenation is usually a deliberate process, during which the absorption and diffusion of H atoms on graphene are of great importance to determine the hydrogenation pattern and related electronic properties. Hydrogen is also the most common terminal group used in computational modeling of graphene.22 Chemical reactions are even more complicated when we consider the zero-dimensional (0-D) form, known as graphene nanoflakes (GNFs) or graphene quantum dots (GQDs).23 The bottom-up synthesis of graphene using chemical methods often produces GNFs and GQDs, and there are already ways of producing GNFs from the top down. Substrate-free synthesis has been reported,24−26 which makes GNFs (and GQDs) a viable candidate for integration into future devices. The advantage of using these materials is that they have many more structural degrees of freedom than graphene membranes or graphene nanoribbons. They possess edge states and corner states and can range in size from molecular to semi-infinite 2-D structures.27 They can also be engineered with different geometries, each with unique (and potentially tunable) properties. Since GNFs may be cut into a much larger variety of different shapes,28−31 we have previously established a categorical scheme based on the geometric complexity.23 Class 1 of 0-D graphene is characterized by a single type of edges (arm-chair or zigzag), where the edges and corners are of the same type. Class 2 of 0-D graphene is also characterized by a single type of edge but with the opposite types of corners. Class 3 of 0-D graphene nanostructures is characterized by a combination of arm-chair- and zigzag-edges, and any may have both arm-chair- and zigzag-corners. In this paper, we have investigated the stability of the circumferential oxygen, hydrogen, and hydroxyl termination of Class 1, Class 2, and Class 3 GNFs with respect to varied temperatures and different O- and/or H-rich environments using a combination of ab initio thermodynamics and computer simulations based on the density functional tight-binding theory. Our results show that the thermostabilities of the O-, H-, and OH-passivation of GNFs are highly dependent upon the surrounding temperature and/or the chemical environment, as well as the geometric category of the shape. The O- and Hpassivation is more stable than the OH-passivation, unless the supersaturations of O and H are simultaneously high (humid conditions). We also find that the thermodynamically preferred edge type depends on the chemical environment and that since the adsorption efficiency is related to the temperature and the pressure these may be used along with chemical functionalization to support one type of structure or another. There has been some seemingly contradictory evidence in the literature as to which type of edges (armchair or zigzag) are most likely,32,33 and our results suggest that both types of edges may be stable, depending on the local conditions. These results are compared with recent experimental findings where available.

Article

COMPUTATIONAL METHODOLOGY

As mentioned above, this study uses the density functional based tight-binding method with self-consistent charges (SCCDFTB).34,35 In this approach, the Kohn−Sham density functional is expanded to second order around a reference electron density, which is obtained from self-consistent density functional calculations of weakly confined neutral atoms within the generalized gradient approximation (GGA). The confinement potential is optimized to anticipate the charge density and effective potential in molecules and solids and unrelated to charge transfer. A short-range element-specific diatomic repulsive potential accounts for double counting terms in the Coulomb and exchange-correlation contributions as well as the internuclear repulsion. A minimal valence basis is established, and one- and two-center tight-binding matrix elements are explicitly calculated within DFT. The PBC set of parameters developed by Köhler and Frauenheim36 is used to describe the contributions from diatomic interactions of hydrogen, oxygen, and carbon. The Fermi level is smeared by 300 K, which leads to the electronic temperature of 1 meV. Self-consistency is converged within 0.01 meV at the level of Mulliken charges.35 All structures were fully relaxed first with the final forces on the atoms being less than 0.5 meV/Å. DFTB is a highly transferable method that overcomes the main limitation of density functional theory (DFT) at the reduced computational cost of standard tight binding; a detailed comparison of DFTB with DFT, for graphene systems, is provided in ref 37. This approach has also proven successful in studying the electronic properties of GNFs in the past.23,28−31,38−40 In this study all calculations include spin polarization and full noncollinear spin relaxation, to ensure that each structure is relaxed with respect to the magnetic moment. Both ferromagnetic and ferrimagnetic initial spin states were tested to ensure that the spin relaxation converged, and the final magnetic configuration was independent of the starting configuration. A comparison with simple, self-consistent, ionic, and electronic relaxations (that included only spin polarization) confirmed that the thermodynamic results are largely unchanged with the addition of magnetic effects, as the energy difference falls within the uncertainties of the method. Nevertheless, they have been included for completeness and will be reported elsewhere as part of a large and detailed comparison of the size , shape, and chemical dependence of the magnetic properties of GNFs. To evaluate the stability of O-, H-, and OH-functionalized GNFs, we have used a standard thermodynamic formalism where the formation energy per atom, Ef, is defined as Ef = (μC,X − nCμC − nX μ X )/Nt

(1)

where μC,X denotes the chemical potential of each GNF combined with adsorbate (X), which is equivalent to its static total energy. The nC represents the number of C atoms; nX represents the number of adsorbed X atoms, molecules, or groups; and Nt represents the total number of atoms in the passivated GNF. The chemical potential of the carbon atom, μC, is equal to the total energy per C atom in the fully relaxed unterminated (radical) version of each structure. This means that we are calculating the relative formation energy of each system, to evaluate the stability of a particular combination, rather than a total formation energy (where the structures are 15376



Article total where Etotal O2 and EH2 are the total energy of a free, isolated O2 and H2 molecule at T = 0 K, and hvO2/2 and hvH2/2 are the vibrational energy of an O2 and H2 molecule. This thermodynamic formalism is well established and routinely used throughout ab initio thermodynamics to study the environmental stability of materials and surfaces.43−54 As mentioned above, a detailed comparison of the computational method (with density functional theory) is provided, for graphene, in ref 37. On the basis of this combination of methodologies, it is estimated that the uncertainties in the following simulations are on the order of 0.05 eV.

products of synthetic reactions). It is worth pointing out that this definition of the formation energy has been published in work elsewhere and that the absolute value of the atomic energy cancels out.41,42 One can also easily include a comparison to an infinite graphene membrane by simply subtracting the constant bulk-graphene free energy (or any other frame-of-reference containing carbon, such as graphene, graphite, diamond, amorphous carbon, or a carbide), and this will not alter the relative stability of the different nanoflakes. It should be pointed out, however, that to obtain the correct absolute stability one should select the correct bulk frame-ofreference from the phase diagram of carbon, which will be graphite or diamond (depending on the pressure and temperature) and not graphene at all. The formation energy Ef is linked to the environmental conditions (such as temperature, pressure, and chemistry) via the chemical potential of adsorbates μX. The chemical potential μX can be derived in a standard way from the combination of chemical potentials of gaseous molecules at chemical equilibrium. Since we assume a gaseous chemical reservoir, the chemical potential of any kind of molecule can be defined as μX = E X +

⎛ pV ⎞ hνX + kBT ln⎜ X ⎟ 2 ⎝ kBT ⎠

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RESULTS AND DISCUSSION The fully relaxed structures of unsaturated GNFs are presented in Figure 1, with representative structures from Classes 1, 2,

(2)

Here, EX represents the static total energy of the molecule obtained from calculations at the level of theory, and with the same computational settings, p, T, kB, h, and νX are the external pressure, temperature, Boltzmann’s constant, Planck’s constant, and sum of vibrational frequencies of the molecule (using experimental data) in the chemical reservoir, respectively. Finally, VX indicates the quantum volume of the molecule ⎛ ⎞3/2 h2 VX = ⎜ ⎟ ⎝ 2πmX kBT ⎠

(3)

where mX is the mass of adsorbate X. It is clearly shown in eq 2 that the chemical potential can be altered by changing the environmental temperature and/or pressure and by choosing suitable chemical reservoirs. At a given temperature, the pressure is the partial pressure (or supersaturation) of H2 (or O2); conversely, at a given supersaturation, the temperature is the surrounding temperature, which contributes to the vibrational entropy. The oxygen and hydrogen chemical potentials (μO and μH) are half of the chemical potential of O2 and H2 molecules, respectively. Most oxygen- and hydrogen-rich conditions can be defined as the point beyond which gaseous O and H would start to condense on the sample. However, in the temperature and pressure range we are interested in, a condensed O2- and H2-solid phase does not exist (the critical temperature of O2 and H2, i.e., above which the gas and liquid phase are in thermodynamic coexistence, is Tc ≈ 150 K and 30 K). Thus, an appropriate and well-defined estimate of the upper limit of the oxygen and hydrogen chemical potentials is !

max[μO(T , p)] = !

max[μH (T , p)] =

hνO2 ⎞ 1 ⎛ total ⎜EO2 + ⎟ 2⎝ 2 ⎠

(4)

hνH2 ⎞ 1 ⎛ total ⎜E H 2 + ⎟ 2⎝ 2 ⎠

(5)

Figure 1. Fully relaxed geometry of Class 1 trigonal GNFs: (a) with AC-edges and 468 C atoms and (b) with ZZ-edges and 481 C atoms; Class 2 rhombic GNFs: (c) with AC-edges and 448 C atoms; and (d) with ZZ-edges and 448 C atoms; Class 2 hexagonal GNFs: (e) with AC-edges and 480 C atoms, and (f) with ZZ-edges and 486 C atoms; and a Class 3 rectangular GNF: (g) with both AC- and ZZ-edges and 448 C atoms.

and 3.23 Class 1 is defined as having edges and corners of the same chirality (either arm-chair or zigzag); Class 2 is defined as having edges and corners of opposing chirality; and Class 3 is defined as having edges (and corners) with both arm-chair and zigzag chirality. We have selected model structures with between four and five hundred atoms, which provides a reasonable comparison while reducing complexity associated with size dependence.23,28,30,31 From a purely geometric perspective, four different shapes are included. The trigonal (Class 1), hexagonal (Class 2), and rhombic (Class 2) GNFs have a unique edge of arm-chair (AC) or zigzag (ZZ), while the rectangular flake (Class 3) has both 15377



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combination of high temperature and/or P ≈ 0 will help to purify the GNFs, by encouraging H desorption. The latter is representative of the majority of electronic structure simulations of graphene reported in the literature, and using the same computational method as described above we have shown that the lowest energy ″radical″ structure is the ACedged Class 2 hexagonal nanoflake.28,30 As we increase the supersaturation of H, in the range μH = −2.91 to −3.08 eV, the ZZ-edged hexagonal (Class 2) GNF gains stability. As we increase the supersaturation of H a little further (μH = −2.86 to −2.91 eV), the ZZ-edged rhombic (Class 2) GNF becomes the most stable configuration. Under H-rich conditions, when μH = −0.11 to −2.86 eV, the ZZedged trigonal (Class 1) GNF with the hydrogen adsorption is the most stable. Across this entire range the ZZ-edge is preferred, but as we increase the hydrogen partial pressure, we see an increased preference for shapes with a higher edge-toplanar ratio (moving from Class 2 to Class 1). When H is fully saturated, or oversaturated (μH > −0.11 eV), the AC-edged trigonal (Class 1) GNF is the most stable configuration. At this point we see a change from ZZ- to ACedges, which again explains the common computational conclusion that AC-edges are most stable, as computational studies traditionally use H as a generic passivant. We can also see some trends associated with the temperature and/or pressure. When the ambient temperature is lower than room temperature (RT), Class 1 AC-edged GNFs are the most stable, with acute 60° corners. When the environmental temperature is close to, or higher than RT, Class 1 ZZ-edged GNFs dominant, which also have acute 60° corners. When the temperature is much higher, Class 1 ZZ-edged GNFs gradually give way to hexagonal Class 2 ZZ-edged GNFs, with obtuse 120° corners, via the rhombic GNF (has both acute and obtuse angles). Oxygen (O) Adsorption. The adsorption of oxygen atom on GNFs has also been studied using ab initio thermodynamics and the structures shown in Figure 1. The relative formation energies of these structures with respect to the oxygen gas reservoir are presented in Figure 3.

kinds of edges. As mentioned above, oxygen, hydrogen, and hydroxyl adsorption were considered with a complete circumferential monolayer (termed: 1 ML) with all the undercoordinated carbon atoms functionalized. In total, we have investigated 21 functionalized GNFs, and all the relaxed configurations with functionalization can be found in the Supporting Information. We also attempted to passivate the circumference with H2O and confirmed that water will not passivate the circumference of graphene in the range of temperatures under investigation, which is consistent with the fact that graphene is hydrophobic. During these simulations, in most cases, the H2O desorbed or deprotonated, neither of which resulted in stable H2O passivation. The final (unstable) structures are included in the Supporting Information. This property is useful in the application of graphene for a possible nanofiltration system (with water playing the role of a carrier).60 In contrast, an aqueous dispersion of chemically converted graphene (CCG) can be readily prepared by controlled reduction of graphene oxide in water.60 Compared to ″pristine″ graphene, CCG is more susceptible to corrugation due to the presence of some sp3 hybridized carbon atoms and topological defects. The amplitude of corrugation of CCG sheets in water can be readily controlled by hydrothermal treatment, leading to a new class of permeation-tunable nanofiltration membranes. Hydrogen (H) Adsorption. Using eq 1 the adsorption of the hydrogen atom on GNFs has been calculated for each of the 14 structure/chemical/coverage combinations (see Supporting Information). The formation energies of these structures with respect to the hydrogen gas reservoir are presented in Figure 2. We can see from Figure 2 when the chemical potential of H is low (H-poor conditions) the unterminated ZZ-edged Class 2 GNF is the most stable configuration. This indicates that a

Figure 2. Relative formation energies of hydrogen adsorption on Class 1, 2, and 3 GNFs. The dashed vertical lines indicate the upper limitation of the hydrogen chemical potential, μH(T,p), using half of Etotal H2 + (hvH2/2) as zero reference. The corresponding temperatures are given for two selected pressures: one corresponding to ultrahigh vacuum (UHV) conditions and the other to atmospheric pressure. The results are labeled in order of increasing stability at 1 ML hydrogen coverage: (A) AC-edged hexagonal (Class 2), (B) ZZ-edged hexagonal (Class 2), (C) AC-edged rhombic (Class 2), (D) ZZ-edged rhombic (Class 2), (E) AC/ZZ-edged rectangle (Class 3), (F) ACedged trigonal (Class 1), and (G) ZZ-edged trigonal (Class 1). The unterminated graphene reference system is represented by a solid horizonal line, which is set to zero, and the solid vertical lines highlight changes in the relative stability of different structures.

Figure 3. Relative formation energies of oxygen adsorption on GNFs with different shapes and edges. The dashed vertical lines indicate the upper limitation of the oxygen chemical potential, μO(T,p), using half of Etotal O2 + (hvO2/2) as zero reference. The corresponding temperatures are given for two selected pressures: one corresponding to ultrahigh vacuum (UHV) conditions and the other to atmospheric pressure. The results are labeled using the same method as in Figure 2. 15378



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We can see from Figure 3 that at low oxygen partial pressure (under anaerobic conditions) oxygen dissociates from the circumference of GNFs, and clean ″radical structure″ is preferred. The corresponding transition temperature for this reaction is very high (even in vacuo), which is consistent with the known stability of graphene oxide at room temperature and supports the application of O-terminated graphene under the same conditions. For higher oxygen supersaturation, up to O-rich aerobic conditions (μO > −3.81 eV), we find that Class 1 ZZ-edged GNFs are the most stable configuration. Once again, we find that acute 60° corners (characteristic of Class 1 structures) are the most preferred, which suggests that acute corners influence the chemical activity of GNFs under saturated conditions. Recently graphene single crystals were grown using lowpressure chemical vapor deposition in copper-foil enclosures using methane as a precursor,61 and scanning electron microscopy (SEM) revealed the graphene domains tended to have high ″edge roughness″, with numerous acute corners. Hydroxyl (OH) Adsorption. The relative formation energy for GNFs terminated with hydroxyl was also investigated and is provided as a function of hydroxyl chemical potential as given in Figure 4, with respect to a gaseous O2 + H2 reservoir. In

Figure 5. Thermochemical mapping for the GNFs with hydrogen, oxygen, hydroxyl, and water adsorption in ″constrained equilibrium″ with a H2 and O2 environment on the left. The formation energy of water vapor is indicated by a black solid line.

most stable structure is an AC-edged radical (unterminated) graphene nanoflake of Class 2. Under anaerobic conditions (low oxygen and high hydrogen chemical potential) the most stable structures are the Class 1 AC-edged trigonal GNF with complete edge hydrogenation (1 ML coverage). Under aerobic conditions (high oxygen and low hydrogen chemical potential) the most stable structures are the Class 1 ZZ-edged trigonal GNF with complete edge oxidation (1 ML coverage). Finally, under humid conditions, with high hydrogen and high oxygen chemical potentials, the preferred GNFs are Class 1 AC-edged structures, with complete circumferential passivation. However, under the majority of environmentally relevant conditions, we expect that ZZ-edges and acute corners will prevail. Although not discussed in detail here, we also found that (in addition to the role that the environmental conditions play in the thermodynamic stability of different configurations) the complexity of the gaseous environment can affect the mechanical stability of the (most stable) GNFs. Both of the OH-functionalized configurations (including the energetically preferred Class 1 AC/OH combination) developed out-ofplane distortions during relaxation (as shown in the Supporting Information), which was necessary to accommodate and stabilize the steric effects between neighboring OH groups. Recently experiments have efficiently produced hydroxylfunctionalized graphene from exfoliation of graphite powder by ball milling the presence of potassium hydroxide (KOH).62 The participation of hydroxyl groups was confirmed by Fourier transform infrared (FTIR), nuclear magnetic resonance analysis (NMR), and Raman and X-ray photoelectron spectroscopic (XPS) measurements, and graphene sheets were imaged by atomic force microscopy (AFM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and UV−vis spectroscopy. These structures were produced at room temperature and show good hydrophilicity, excellent electroactivity, and biocompatibility with human RPE cells, which is consistent with an environment rich in OH or H2O and supported by the present results. Our results are also consistent with a recent study exploring the influence of reactive edges

Figure 4. Relative formation energies of hydroxyl adsorption on GNFs with different shapes and edges. The dashed vertical lines indicate the upper limitation of the hydroxyl chemical potential, μOH(T,p), using Etotal OH + (hvOH2/2) as zero reference. The corresponding temperatures are given for two selected pressures: one corresponding to ultrahigh vacuum (UHV) conditions and the other to atmospheric pressure. The results are labeled using the same method as in Figure 2.

general, we can see that hydroxyl functionalization of the edges and corners is stable under ambient conditions and up to high temperature, but under dry conditions the unterminated ACedged Class 2 nanoflake is thermodynamically preferred. For the μOH in the range of −0.82 and −5.62 eV, the Class 1 ZZ-edged GNF is preferred, and once again we see a change to the Class 1 AC-edged GNF when μOH > −0.82 eV. This can be summarized by saying that ZZ-edges are favored under dry conditions, and AC-edges are favored under humid conditions. Comparison and Map of Chemical Stability. By combining all of these results (above), a map of the chemical stability of different classes of GNFs with hydrogen, oxygen, and hydroxyl adsorption is presented in Figure 5. This mapping technique was also successfully used in ref 54. This map highlights that under UHV (and near UHV) conditions, with both low oxygen and low hydrogen chemical potentials, the 15379



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temperature, pressure, or both. From a practical standpoint, this also means that in a realistic environmental chamber, or when developing graphene nanoflakes for sensor applications, the edge structure could potentially be engineered to provide greater selectivity when screening specific gases within gaseous mixtures, or more complex ″multifunctional″ graphene geometries could be developed that are sensitive to more than one gas at a time.

and defects of substrates for achieving a complete cycle of room-temperature molecular sensing using graphene.55 An important aspect of these results is how sensitively the chemical environment influences edge stability, which has been a topic of some discussion in recent years. It was established that the ZZ-edges are kinetically stable by considering the effect of ejecting an atom at the edge for each chirality under electron irradiation at this energy,32 but the influence of thermodynamics remained a point of contention. ZZ-edges have some intrinsic advantages as there are antibonding π-electron states (edge states) localized along edges in the ZZ direction but not in the AC direction.33,56,57 Since the antibonding edge states encourage chemical adsorption, a graphene gas sensor with ZZedges may be more sensitive to gaseous environments. In contrast, the AC-edges are well-known to be thermodynamically stable,28,30,57 due to the energetically favorable reconstructions involving sp1 bonds, and do not possess magnetic edge states.58 This can be rationalized with Clar’s Rule59 and is significant because a preference for one type of edge over another will have important implications for the electronic and magnetic properties. At this point it should be highlighted that, like any nanoscale material, kinetics will also play an important role in determining the structure of graphene nanoflakes under different conditions. The present work is restricted to thermodynamic considerations, and so we cannot speculate as to the kinetics; however, we can see that reversible functionalization will require a change in the thermodynamics environment to be thermodynamically driven, or to lower a kinetic energy barrier as required. In situations where the crossing points in the freeenergy diagrams are shallow, we expect kinetics to be important, as (within uncertainties) we approach a state of mutual thermodynamic coexistence between the competing structures. Although not discussed here, defects (such as vacancies with different shapes and sizes) can also impact the stability of GNFs under these conditions.40 The chemical activity of unsaturated carbon atoms along the boundary of a defect will be comparable to the carbon atoms around the circumference and can therefore be mapped in a similar way. There are far more configurations to be examined when we combine defects with the current geometric classes, but since this issue will have a profound impact on the application of graphene for gas sensing,55 this will be a topic of future work.

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ASSOCIATED CONTENT

S Supporting Information *

Schematic representations of all of the fully relaxed, H, O, OH, and H2O terminated graphene nanoflake structures included in this study. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research has been supported by the Australian Research Council under Discovery Grant DP110101362. Computational resources for this project have been supplied by the National Computing Infrastructure (NCI) national facility under MAS Grant e74. The authors would like to thank Hongxin Yang for useful discussions. This paper is dedicated to the memory of Ian Snook.

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REFERENCES

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CONCLUSION In this paper we have used ab initio thermodynamics and selfconsistent charge density functional based tight-binding simulations to investigate the relative stability of GNF functionalization by hydrogen, oxygen, and hydroxyl. We find that the geometry (Class) and angle subtended at the corners play an important role in determining the stability, particularly when the partial pressure of H or O is low (in vacuo). In contrast, when the partial pressures are high, the relative stability depends on the types of edges, or (alternatively) the stability of different edges is moderated by the environment. Zigzag edges are preferred under a wider range of conditions, but a H-rich environment is necessary to support AC-edge stability. Since the surrounding environment affects the stability of H-, O-, and OH-adsorption on GNFs so dramatically, it may be possible to use this knowledge to probe the structure of samples of graphene nanostructure by simply adjusting the 15380



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