Interplay between Oxidized Monovacancy and Nitrogen Doping in

Article pubs.acs.org/JPCC

Interplay between Oxidized Monovacancy and Nitrogen Doping in Graphene Zhufeng Hou,*,†,‡ Da-Jun Shu,†,‡ Guo-Liang Chai,† Takashi Ikeda,§ and Kiyoyuki Terakura†,∥ †

Department of Organic and Polymeric Materials, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 I6-31, Ookayama, Tokyo, 152-8552, Japan ‡ National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China § Condensed Matter Science Unit, Quantum Beam Science Center, Japan Atomic Energy Agency (JAEA), Hyogo 679-5148, Japan ∥ Research Center for Simulation Science, Japan Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan S Supporting Information *

ABSTRACT: In most of the N-doped graphene (N-graphene) which attracts strong attention in the context of precious-metal free catalysts and nanoelectronics, the oxygen content is generally higher than or at least comparable to the nitrogen content. In order to understand the effect of oxygen-containing chemical groups (OmHn) on N doping in defective graphene sheets, we perform density functional theory calculations to study the interplay of oxidized monovacancy (MV) and the nitrogen doping, motivated by the fact that MV is more frequently observed and more chemically active than divacancy and Stone−Wales defect. We determine the phase diagrams of undoped and nitrogen-doped oxidized MVs as a function of temperature and partial pressure of O2 and H2 gases. The modification of the electronic structure of MV by oxidation and N doping is studied. Our results show that the ether group (−O− in plane) is a common component in stable configurations of oxidized MVs. Most of the stable configurations of oxidized MVs do not induce any carriers. The stabilization of pyridinic N, pyridinium-like N, and graphitic N at MV depends on the oxidation degree of MV. Our results also suggest that pyridinic N and pyridinium-like N at clean MV do not facilitate the oxygen-reduction reaction.

1. INTRODUCTION Nitrogen-doped graphene (N-graphene) has attracted much attention because of its highly promising applications in the energy conversion/storage and in the nanoelectronic device.1−4 N-Graphene can be synthesized by using the bottom-up method from the N-containing precursors or through the posttreatment of graphene and graphite oxide (GO).5,6 Oxygenrelated chemical groups cannot be removed completely in both methods. In most cases, the oxygen content is generally higher than or at least comparable to nitrogen content.7 Therefore, it is important to study the role of oxygen-containing chemical groups in N doping in graphene and to understand the related modification of electronic structures of N-graphene. During the synthesis process of N-graphene via posttreatment method, N doping is likely to induce a non-negligible amount of defects and bond disorders.8−12 For example, nitrogen ion bombardment or electron beam irradiation of graphite or graphene can create a pyridinic N at monovacancy (MV).13,14 In our previous study based on density functional theory (DFT) calculations,15 we found that the doped N and the native point defects interact attractively and display a cooperative effect. Among several structural defects, such as MV, divacancy (DV), Stone−Wales (SW) defect, and edges, the attractive interaction is strongest for MV. We also found that MV in graphene has dangling π and σ states just below the © 2014 American Chemical Society

Fermi level and that it is more chemically active than DV and SW defect.16 This together with the calculated formation energy15,17,18 would make MV thermodynamically unfavorable compared with DV and SW defect. Nevertheless, for graphene under irradiation condition, MV can be easily created and frequently observed in experiment by transmission electron microscope (TEM)19−21 and scanning tunneling microscope (STM).13,14,22−24 Therefore, MV is an important defect in Ngraphene. However, only the clean and monohydrogenated MVs were considered in our previous studies.15,16 The stability of oxidized MVs has not been well understood in literature, as only limited configurations of oxidized MVs have been studied so far.25,26 To this end, we make the phase diagram of oxidized MVs. Moreover, we study the interplay between the oxidized MVs and the nitrogen doping. For comparison, the oxygencontaining chemical groups on perfect graphene are also studied in the present work. N-Graphene is one of the basic structure components in the carbon alloy catalyst27 for the oxygen reduction reaction (ORR) in a polymer electrolyte membrane fuel cell (PEMFC). If the oxidation of the carbon alloy catalyst happens during the Received: May 1, 2014 Revised: July 30, 2014 Published: August 5, 2014 19795

dx.doi.org/10.1021/jp504298p | J. Phys. Chem. C 2014, 118, 19795−19805

The Journal of Physical Chemistry C

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process of ORR, it may modify (or even poison) the catalytically active site, alter the pathway of ORR, or even lead to the degradation of catalyst. Because pyridinic N possesses one lone pair of σ electrons in addition to the one electron donated to the conjugated π bond in nanostructures of carbon alloy, it has been expected to facilitate the ORR in PEMFC.28−32 Pyridinic N may exist at vacancies or edges of graphene. Our previous study showed that pyridinic N at zigzag edges of graphene does not display any catalytic activity because of unfavorable adsorption of O2 molecule.33,34 In various reaction paths for the complete reduction of O2 into H2O, the elementary steps involve the adsorption of the reaction intermediate species such as *O, *OH, and *OOH.35,36 In this work, we study ORR intermediate species on pyridinic N at MV to explore its possibility of catalytic activity toward ORR. The remainder of this paper is organized as follows. In section 2, we introduce computational methods for calculations of oxidized MV in graphene and N-graphene. The results for the phase diagram and electronic structures of undoped and Ndoped oxidized MVs are presented in section 3. The conclusions are given in section 4.

ΔEf (OmH n) = Et(host + x N + OmHn) − Et(host) x m − Et(N2) + xEt(g) − Et (O2 ) 2 2 n − Et(H 2) 2

(1)

where x is the number of doped N atoms. Et(host + xN + OmHn) is the total energy of undoped (x = 0) and N-doped (x > 0, in the present work we mainly discuss the case of x = 1) oxidized MV in graphene. Et(host) is the total energy of a clean MV in graphene. Et(g) is the total energy per atom of perfect graphene. Et(X2) is the total energy of an isolated X2 (X = N, O, and H) molecule.41 All of the above total energies are obtained by performing the DFT calculations at 0 K. To consider the influence of temperature and pressure on the stability of oxygen-containing chemical groups at MV, we have calculated the Gibbs free energy for their functionalization according to the following approximated equation: x m n Gf (OmHn) = ΔEf (OmH n) − μ N − μO − μH 2 2 2 2 2 2 (2)

where the temperature and pressure influences on MV in graphene are neglected. μX2 is the chemical potential of X2 molecule and can be evaluated by the ideal-gas approximation according to the tabulated experimental data:42

2. METHOD AND COMPUTATIONAL DETAILS DFT calculations are performed with the PWSCF code of the Quantum ESPRESSO suite37 in a plane-wave ultrasoftpseudopotential38 approach. The exchange-correlation functional is treated by the generalized gradient approximation (GGA) after Perdew, Burke, and Ernzerhof.39 The spinpolarization is taken into account if it exists. Further, the spinpolarization energy (ESP) is estimated by the total energy difference between the atomic structures optimized separately by the spin-polarized and nonspin-polarized calculations. The kinetic energy cutoffs for wave function and charge are set to 35 and 350 Ry, respectively. A 9 × 9 hexagonal supercell of graphene sheet with a lattice constant of 22.167 Å (see Figure S1 in the Supporting Information), which is constructed from the primitive unit cell of graphene with the calculated lattice constant of 2.463 Å, is employed to study the oxidation of MV and the substitution of carbon by nitrogen. The results of the convergence test on the supercell size as presented in our previous papers15,16 show that the use of a 9 × 9 supercell is large enough to give accurate results for N-graphene. Oxidation of MV is simulated by functionalizing carbon atoms next to vacancy site with different oxygen-containing chemical groups, such as the epoxy group (/O\), the ether group (−O−), the ketone or carbonyl group (O), and the hydroxyl group (−OH). We denote them as OmHn (m = 1−3 and n = 0−2). To avoid the spurious interaction between graphene layers, the vacuum thickness in the supercell is set to 12.0 Å. A 3 × 3 × 1 k-point grid in the Monkhorst−Pack scheme40 is employed to sample the Brillouin zone (BZ) of the 9 × 9 supercell. The results of the convergence test on the size of the k-point grid (see Figure S2 in the Supporting Information) show the above setup is sufficient to ensure the accuracy in the present study. During geometry optimization, all atoms are fully relaxed until residual forces on constituent atoms are smaller than 0.01 eV/ Å. To assess the energetic stabilities of OmHn at undoped and N-doped MV, we have calculated their formation energies as

◦ ◦ ) + (H298.15 μ X , PX = (H ◦ − H298.15 − H0◦) − TS◦ 2

2

⎛ PX ⎞ + kBT ln⎜⎜ ◦ 2 ⎟⎟ ⎝ PX 2 ⎠

(3)

where H° and S° are, respectively, the enthalpy and entropy of the gas phase molecule X2 at the standard pressure (P°). Both of them are given as a function of temperature. The subscript of H° in eq 3 indicates the temperature in units of Kelvin. The values of H° − Ho298.15 and S° for X2 molecule can be obtained from the data available at NIST Web site,43 while the value of Ho298.15 − H0° for X2 molecule is obtained from the CODATA table.44

3. RESULTS AND DISCUSSION 3.1. Stability of Oxidized Monovacancy. For a MV in graphene, it is known that the three carbon atoms next to the vacancy site undergo Jahn−Teller (JT) distortion, that is, two of them (labeled C5 and C5′ in Figure 1a) forms a new bond, and the remaining one (labeled C1 in Figure 1a) is dangled, which was predicted by theoretical calculations and confirmed by experiment.16,24,45 To study the oxidation of MV, we have considered functionalization of undoped MV with individual and multiple oxygen-containing chemical groups. Figure 1j presents the formation energies ΔEf(OmHn) of OmHn at MV as a function of (m, n) pair. As the numbers of O and H atoms increase, ΔEf(OmHn) decreases up to (m = 2, n = 2) and the energy difference between the most stable and the metastable configurations for each pair of (m,n) in OmHn tends to decrease. In the cases of O2H1 and O3H0, formation energies of the lowest metastable configurations are higher than those of the most stable ones by about 0.1 eV. We can also see that the conversion from two O2H1 to O2H0 and O2H2 reduces the energy. Therefore, the O2H1 (ether + hydroxyl) configuration does not appear in the phase diagram as shown later. The atomic structures and notations for the most stable 19796



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ether + CH2 and ether + CH + hydroxyl configurations are more stable than water and hydrogen peroxide molecules adsorbed on MV, respectively. We can find that the ether group is a common chemical group in the most stable configurations of oxidized MVs except the case of a single oxygen atom at MV. We analyze first the cases of MV oxidized without the presence of hydrogen (i.e., n = 0 in OmHn simplified as mO below). The formation energy of ith O atom in a system containing already (i − 1) O atoms near MV is defined by the following equation: ΔEf (Oi ) = Et(MV + iO) − Et[MV + (i − 1)O] 1 − Et(O2 ) (4) 2 Clearly, ΔEf(Oi) is the finite difference of ΔEf(iO) with respect to i and the following relation holds, m ΔEf (mO) = Et(MV + mO) − Et(host) − Et(O2 ) 2 m

=

∑ ΔEf (Oi ) i=1

(5)

Figure 2a shows ΔEf(Oi) for i ranging from 1 to 3 for the most stable configurations. As i increases from 1 to 3, ΔEf(Oi)

Figure 1. Local atomic structures of (a) the reconstructed MV (O0H0) and (b) the monohydrogenated MV (O0H1). Inequivalent sites for C atoms around vacancy sites are labeled by nonzero numbers in panel (a). Local atomic structures for the most stable congurations of oxidized MVs: (c) 3-fold oxygen (O1H0), (d) ether + CH (O1H1), (e) ether + CH2 (O1H2), (f) ether + ketone (O2H0), (g) ether + hydroxyl (O2H1), (h) ether + CH + hydroxyl (O2H2), and (i) ether + ketone + epoxy (O3H0). Gray, red, and white balls represent C, O, and H atoms, respectively. (j) Formation energies [ΔEf(OmHn)] for the most stable and metastable congurations of oxidized MVs. Green and yellow solid circles represent the results of water and hydrogen peroxide molecules adsorbed on MV, respectively. Note that two O2H1 are unstable against the conversion to O2H0 plus O2H2.

Figure 2. (a) Formation energy of ith oxygen atom [ΔEf(Oi)] in a system containing already (i − 1) oxygen atoms near MV for i in the range from 1 to 3. The dotted line indicates the formation energy of an epoxy group on perfect graphene. (b) Gibbs free energy of multiple O atoms [Gf (mO)] at MV in graphene as a function of the chemical potential of O2 molecule (μO2).

increases monotonously and it tends to approach the adsorption energy of an expoxy-like oxygen atom on the perfect graphene surface. This indicates that oxygen atoms tend to be adsorbed at the vacancy site rather than the bulk region of graphene. If more than one MV exists in graphene, oxygen atoms would be preferentially adsorbed at the clean MV rather than aggregate at a single MV. To examine the relative stability of 3-fold oxygen, ether + ketone, and ether + ketone + epoxy configurations of oxidized MVs, we present their Gibbs free energies Gf(mO) as a function of μO2 in Figure 2b. Our results show that under the oxygenrich condition the ether + ketone configuration is the most stable one, rather than the ether + ketone + epoxy configuration. Indeed, the ether + ketone configuration of oxidized MV has been proposed in the initial stage of defectinduced oxidation on graphitic surface.46,47 Under the oxygenpoor condition, that is, μO2 < −5.76 eV, the 3-fold oxygen

configurations of oxidized MVs are presented in Figure 1b−i. For one, two, and three oxygen atoms (i.e., n = 0 and m = 1−3, respectively) at MV, the most stable configurations contain a three-fold oxygen (i.e., an oxygen substitution for carbon shown in Figure 1c), an ether group plus a ketone group, and an ether group plus a ketone group plus an epoxy group, respectively. For MV oxidized in the presence of hydrogen, two of carbon atoms (i.e., C5 and C5′, as shown in Figure 1a) next to the vacancy site are favorable to be bound with oxygen to form an ether group, and the remaining one (i.e., C1) is terminated by a monohydrogen (CH), a dihydrogen (CH2), a hydroxyl group, or a monohydrogen plus a hydroxyl group. It is noted that the 19797



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Figure 3. (a) Phase diagram of different oxidized MVs (their atomic structures are shown in Figure 1) in graphene as a function of chemical potentials of H2 and O2 molecules. (b) Chemical potential of H2 molecule μH2 as a function of partial pressure PH2 and temperature. (c) Chemical potential of O2 molecule μO2 as a function of partial pressure PO2 and temperature.

configuration becomes stable. However, this value of oxygen chemical potential corresponds to an extremely low partial pressure of O2 molecule gas (about 3.4 × 10−97 atm) at room temperature. It suggests that an oxygen substitution for carbon in graphene is unlikely to be realized in the standard ambient condition and, thus, rarely detected in experiment. According to the calculated Gibbs free energies of MVs oxidized with and without hydrogen, we plot the phase diagram of oxidized MVs as the functions of μH2 and μO2 in Figure 3a. Meanwhile, μH2 and μO2 as the functions of the partial pressures of H2 and O2 molecule gases and temperature are presented in Figure 3b and c, respectively. As it was pointed out, the ether + hydroxyl configuration is unstable and only five configurations are stable in the phase diagram. The ether + ketone configuration is stable in quite wide ranges of μH2 and μO2, for example, at the standard atmospheric pressure with the temperature higher than about 380 K, or at the room temperature with the partial pressure of H2 gas less than 10−2 atm. 3.2. Electronic Structures of Oxidized Monovacancy. To understand the stability of oxidized MVs, we have examined electronic structures of the most stable configurations for each pair of (m,n) in OmHn at MV. The band structures for graphene with oxidized MVs are presented in Figure 4. Our previous study16 showed that clean MV in graphene acts as a hole dopant. Clean MV can also induce magnetism due to spin polarization of the σ state in graphene.16,48,49 Now we explore how electronic structure and magnetic property of MV are modified by the oxidation with different oxygen-containing chemical groups. For the configuration of oxidized MV consisting of a 3-fold oxygen, our calculations predict that the neighboring carbon atoms of the 3-fold oxygen move outward, resulting in O−C bond length of 1.49 Å versus 1.42 Å for C−C bond. The defect σ state of MV and the 2px,y states of O atom are hybridized and merged into the bulk σ band. A remarkable feature is that a flat π band appears just below the EF. This flat band is basically the

Figure 4. Band structures obtained by using a 9 × 9 supercell for graphene without and with different congurations of oxidized MVs: (a) perfect graphene, (b) three-fold oxygen, (c) ether + CH, (d) ether + hydroxyl, (e) ether + ketone, (f) ether + CH2, (g) ether + CH + hydroxyl, and (h) ether + ketone + epoxy, respectively. The corresponding atomic structures of oxidized MVs are shown in Figure 1. Green solid points indicate fat bands derived from O [3-fold oxygen in panel (a) and ether in other panels] 2pz state. Note that the original Dirac points (i.e., K and K′ points) in irreducible Brillouin zone (IBZ) of primitive unit cell of graphene are folded into the Brillouin zone center (i.e., Γ point) of IBZ of 9 × 9 supercell. The zero of energy is set at Fermi energy.

defect π state of MV hybridized weakly with the 2pz states of O atom, which are located about −8.5 eV from the Fermi level [see the partial density of states in Figures S3(b) and S3(c) in the Supporting Information]. The weight of the wave function 19798



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Table 1. Key Properties of Stable Configurations of Oxidized MVs (Shown in Figure 1c−i)a OmHn in oxidized MVs property chemical groups Figure No. dO−C

O1H0 OC 1c 1.49

O1H1 ether, −CH 1d 1.39

O1H2 ether, −CH2 1e 1.38

δzO

0.027

0.36

0.24b

ΔEmlm Mt

−1.67 0.0

−0.51 0.0

Esp

0.0

0.0

0.0

carrier aromatic?

electrong no

−2.43 0.99 0.93e 0.87f −0.034 −0.022e −0.019f no no

O2H0 ether, ketone 1f 1.38b 1.23c 0.17b 1.04c −1.43 0.0

no yes

no yes

O2H1 ether, −OH 1g 1.39b 1.39c 0.30b 0.88c −0.10 0.97 0.91e 0.87f −0.037 −0.025e −0.020f no no

O2H2 ether, CH, −OH 1h 1.38b 1.45c 0.25b 1.35c −0.49 0.0

O3H0 ether, ketone, epoxy 1i (1.41, 1.38)b 1.23,c (1.49, 1.42)d (0.38, 0.08)b 1.15,c (1.30, 1.16)d −0.11 0.0

0.0

0.0

no yes

no yes

a Monohydrogen, dihydrogen, three-fold oxygen, and hydroxyl chemical groups are denoted as −CH, −CH2, OC, and −OH, respectively. dO−C is the bond length (in Å) between oxygen atom and the nearest neighboring carbon atom. δzO is the protrusion (in Å) of oxygen atom out of graphene sheet and given with respect to the nearest neighboring carbon atom. ΔEmlm is the energy difference (in eV) between the most stable configuration and the lowest metastable one. Mt is the total magnetic moment (in μB per cell) of oxidized MV and ESP is the corresponding spin-polarization energy (in eV). bIn the ether group. cIn the ketone group. dIn the epoxy group. eObtained by the calculations of 12 × 12 graphene supercell. f Obtained by the calculations of 15 × 15 graphene supercell. g3-Fold oxygen in the dilute limit would not contribute to carriers.

of the flat band resides mostly at the surrounding C atoms [see Figures S3(a) and S3(d) in the Supporting Information]. From Figure 4b and the corresponding effective band structure unfolded into the primitive cell of graphene [see Figure S7(a) in the Supporting Information], we can see that the 3-fold oxygen donates a small amount of electrons to conduction π* band. However, the electron donation seems to be partly due to the small bandwidth of the flat band and the bandwidth will be zero in the dilute limit of MV. Therefore, we expect that isolated 3-fold oxygen will not contribute to carriers. By the nature of the flat band, the 3-fold oxygen configuration is chemically active. If an additional adsorbate such as hydrogen atom, oxygen atom, or hydroxyl group adsorbed on one of carbon atoms next to the 3-fold oxygen, it will be energetically favorable to form the ether + CH, ether + ketone, or ether + hydroxyl configurations. In the ether + CH configuration, the C−H bond length is about 1.08 Å and the O−C bond lengths are about 1.39 Å. By adding H to the 3-fold oxygen configuration, the originally unoccupied σ state is pulled down below the Fermi level and accommodates two electrons. Therefore, one electron has to be removed from the flat π band, making it half occupied and spin polarized. The spin split bands hybridize with the substrate π bands. This explains the basic features of Figure 4c for the ether + CH configuration. The Fermi level coincides with the Dirac point and no carrier is produced. The ether + CH configuration has nearly 1.0 μB and the corresponding spin-polarization energy is about −0.034 eV. The spin polarization is attributed to the defect π states with a slight mixture of the σ state of protruded monohydrogenated C1 atom in contrast to the case of clean MV in which spin polarization of σ state is the dominant contribution. Similar features are also found in the ether + hydroxyl configuration (see Figure 4d). However, the π state spin polarization depends strongly on the supercell size.16,50 In fact, although the decrease in spin polarization is small by increasing the supercell size from 9 × 9 to 12 × 12, the spin-polarization energy decreases by more than 30% for the

ether + CH configuration (see Table 1). The latter fact seems to imply that the spin polarization may not exist in the dilute limit. Anyway, irrespective of the presence of spin polarization, the electronic structures indicate that the ether + CH and ether + hydroxyl configurations are chemically active. Indeed, these two configurations can be exothermically protonated. In the ether + ketone configuration, the ketone group forms a CO double bond with a length of 1.23 Å. The C−O bond length in the ether group is about 1.38 Å. As shown in Figure 4e and the corresponding effective band structure unfolded into the primitive cell of graphene (see Figure S7(b) in the Supporting Information) for the ether + ketone configuration, the Fermi level coincides with the Dirac point and no carrier is produced. As the O atom of ketone protrudes significantly, dangling σ and π orbitals of the C atom forming a C−O bond are passivated: dangling σ states of MV are merged into the bulk σ band and there is no dangling π state near the Fermi level. Similar features are also found in the ether + CH2 and ether + CH + hydroxyl configurations (see Figure 4f and g, respectively). By analyzing the arrangement of Clar sextet and double bonds16,51 around these three configurations (see Figure S5 in the Supporting Information), we find that they satisfy Clar’s aromatic sextet rule (see Table 1). Therefore, these three configurations are aromatic and they are very stable. However, the ether + CH and ether + hydroxyl configurations do not satisfy Clar’s aromatic sextet rule and are nonaromatic [see Figure S4 in the Supporting Information and Table 1], and thus, they are less stable than the ether + ketone configuration. Indeed protonation of the ether + ketone configuration to form the ether + hydroxyl configuration is endothermic (see Figure 1j). As shown in Figure 4h for the ether + ketone + epoxy configuration, the Fermi level coincides with the Dirac point and no carrier is produced. There is no dangling π state close to the Fermi level. From the arrangement of Clar’s sextet and double bonds in the configuration of ether + ketone + epoxy (see Figure S6 in the Supporting Information and Table 1), we 19799



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find that this configuration also satisfies Clar’s aromatic sextet rule. However, the number of Clar’s sextets in the ether + ketone + epoxy configuration is reduced with respect to that in the ether + ketone configuration. Therefore, the former is less stable than the latter. 3.3. Phase Diagram of N-Doped Oxidized Monovacancy. In our previous study,15 we studied the N substitution around clean MV and found that a pyridinic N (denoted as pN and shown in Figure 5a) is energetically more favorable than a graphitic N (denoted as gN). A pN at MV can be exothermically protonated to form a pyridinium-like N (denoted as pNH and shown in Figure 5b). Figure 5j presents the formation energies ΔEf(OmHn) of Ndoped oxidized MVs as a function of (m, n) pair for pN, pNH,

and gN. The atomic structures for the most stable configurations of N-doped oxidized MVs are presented in Figures 5c−i. Note that only when all of the three carbon atoms next to vacancy site are passivated by the ether-like and/or ketone-like oxygen atoms, gN becomes more stable than pN and pNH. The resulting configurations are denoted as gN + ether + ketone (see Figure 5f) and gN + 3 ketones (see Figure 5i), respectively. Based on these results, we take two different approaches to construct a phase diagram for N-doping and oxidation for MV. First, we treat single N doping and oxidation at MV on the same footing in the structural optimization. Second approach corresponds to a simulation of ORR process at N doped MV and the position of doped N (either pN or pNH) is assumed not to change in the ORR process. Figure 6a shows the phase diagram of the first approach as the functions of μO2 and μH2. In this case, each phase in the diagram has the lowest free energy under given chemical potentials of O2 and H2. In addition to the unoxidized configurations of pN and pNH, there are six stable configurations in the phase diagram. The configuration of pNH + 2 ketones (O2H1) does not appear in the phase diagram because it decomposes thermodynamically into gN + ether + ketone (O2H0) and pN + ether + water (O2H2), as suggested from Figure 5j. To understand the microscopic mechanism of ORR, it is important to study the adsorption strength and the equilibrium thermodynamics of ORR intermediate species (such as *O, *OH, and *OOH) on N-graphene.35,36 Therefore, in the second approach, the oxidation of pN- and pNH-doped MVs is simulated by considering the equilibrium thermodynamics of adsorption of ORR intermediate species (such as *O, *OH, and *OOH) under the constraint that the doped N position is fixed. This enables us to discuss the catalytic activity of pN and pNH at MV toward ORR. We also consider the adsorption of O2, H2O, and H2O2 molecules upon an unoxidized pN-doped MV. As shown in Figure 5j, the N-doped oxidized MVs (O1H2 and O2H2) are more stable than water and hydrogen peroxide molecules adsorbed on pN-doped MV. For the stable configurations of N-doped oxidized MVs with pN and pNH, as shown in Figure 5, we plot their phase diagram as the functions of μO2 and μH2 in Figure 6b. The adsorption of an O2 molecule and *O species on the pN- and pNH-doped MVs will oxidize the carbon atoms next to vacancy to form the ether and ketone groups, both of which possess strong chemical bonding. The protonation of ether-like oxygen is endothermic and such oxygen thus cannot be electrochemically reduced during the ORR. Although the first protonation of ketone-like oxygen (for example, the configurations shown in Figure 5e,g) is energetically favorable to form hydroxyl groups; the resulting hydroxyl groups cannot be completely reduced by further protonation. That is to say, the configuration of pNH-doped MV is oxidized with the existence of an ether group. *OH and *OOH species adsorbed on pN- and pNH-doped MVs thermodynamically dissociate and lead to the formation of ether and ketone groups. These findings suggest that during the ORR on N-graphene catalyst pN at MV would be protonated into pNH and the carbon atoms around the vacancy site would be oxidized. Both pN and pNH at MV cannot facilitate the ORR. 3.4. Electronic Structures of N-Doped Oxidized Monovacancy. We examine electronic structures of Ndoped oxidized MVs for the stable configurations appearing in the phase digram in Figure 6a. Figure 7 shows band

Figure 5. Local atomic structures of N-doped MVs before and after oxidation: (a) a pyridinic N at clean MV (O0H0), (b) a pyridinium-like N at clean MV (O0H1), (c) pN + ether (O1H0), (d) pNH + ether (O1H1), (e) pNH + CH + ketone (O1H2), (f) gN + ether + ketone (O2H0), (g) pNH + 2 ketones (O2H1), (h) pN + ether + water (O2H2), and (i) gN + 3 ketones (O3H0). Pyridinic N, pyridinium-like N, and graphitic N are denoted as pN, pNH, and gN, respectively. Gray, red, and white balls stand for C, O, and H atoms, respectively. (j) The formation energy [ΔEf(OmHn)] of N-doped oxidized MVs. Green and yellow solid circles represent formation energies of a pyridinic N at MV with adsorbed water and hydrogen peroxide molecules, respectively. 19800



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Figure 6. Phase diagrams for (a) stable N-doped oxidized MVs and (b) simulating the ORR process with pyridinic N doped MVs as a function of the chemical potentials of H2 and O2 molecules. Pyridinic N, pyridinium-like N, and graphitic N are denoted as pN, pNH, and gN, respectively. The corresponding atomic structures are shown in Figure 5.

oxidation degree. For pNH stabilized in the pNH + ether and pNH + 2 ketones configurations, it does not induce any carriers (see Figure 7e,g, as well as Figure S7(d) in the Supporting Information). For pNH stabilized in the pNH + CH + ketone configuration, it acts as a hole dopant (see Figure 7f). As discussed above, we find that the oxidation of MV can stabilize gN at MV. Depending on the oxidation degree of MV, gN acts an electron dopant in the gN + ether + ketone configuration (see Figures 7h and S7(e) in the Supporting Information) or a hole dopant in the gN + 3 ketones configuration (see Figures 7i and S7(f) in the Supporting Information]. 3.5. Interaction between a Single Substitutional N and the Oxygen Functional Groups on Graphene. To quantitatively describe the influence of an additional entity (e.g., oxygen-containing chemical groups, clean MV, oxidized MV, and so on; denoted as entity (A) on a substitutional N (denoted as entity B) in graphene, we calculate their interaction energy Eint by the following definition:15

structures of graphene with these N-doped oxidized MVs obtained by the nonspin-polarized calculations. We comment briefly on the reason for the nonspin-polarized calculations. With the use of the 9 × 9 supercell, we found that the cases of Figure 7b,c,f,h became spin-polarized if spin polarization was allowed. The results of spin polarization and spin-polarization energy are shown in Table 2. However, we also found that spin polarization in the cases of gN- and pNH-doped configurations vanished (in contrast to the ether + CH and ether + hydroxyl cases) by just increasing the supercell size to 12 × 12 (see Table 2). This is because of the decrease of the introduced carriers by doped N. In the case of pN + ether configuration, the induced magnetic moment and the corresponding spinpolarization energy decrease as the supercell size increases. The N and O atoms in pN + ether configuration protrude out of graphene sheet in the opposite direction and such protrusion induces the spin polarization associated with the localized σ states. The magnitude of their protrusions and the corresponding energy costs tend to decrease as the supercell size increases (see Table S1 in the Supporting Information). In the case of pN + ether configuration without protrusion, that is, N and O atoms in the same plane of graphene sheet, the spin polarization vanishes. Therefore, the spin polarization appearing in these cases is clearly an artifact of the use of small supercells and will not be discussed further. In our previous study,15 we pointed out that pN at clean MV acts as a hole dopant (see Figures 7a and S7(c) in the Supporting Information). After oxidation, pN is stable in the pN + ether (see Figure 5c) and pN + ether + water (see Figure 5h) configurations, both of which contain an ether group. From their band structures shown in Figure 7b,c, it can be seen that pN does not induce any carriers. As substitution of N for C produces nearly the same effect as hydrogenation of C on the electronic structure, Figure 7b and c look similar to Figure 4b. As found in our previous study,16 pNH at clean MV does not induce any carriers (see Figure 7d). Band structures of graphene with pNH-doped oxidized MVs are presented in Figure 7e−g. We can see that the doping behavior of pNH at MV depends on the hydrogen concentration, rather than the

E int = Etot(AB) + E0 − Etot(A) − Etot(B) = ΔEf (AB) − ΔEf (A) − ΔEf (B)

(6)

where Etot(AB), Etot(A), and Etot(B) are the total energies of graphene, with a complex entity AB, an individual entity A, an individual entity B, respectively. E0 is the total energy of perfect graphene. ΔEf stands for the formation energy. The negative value of Eint indicates that an additional entity A and a single substitutional N attract each other, which means that substitutional N dopants would increase the probability of entity A in/on graphene and vice versa. This is found in the cases of a single substitutional N with a boron dopant,52 native point defects,15 and an amine (NH2) adsorbate.53 Figure 8 summarizes Eint for a single substitutional N with various structural defects (including MV, divacancies, Stone−Wales defect, extended line defect, grain boundary, and edges) in graphene. We can see that among different types of structural defects in graphene the attractive interaction is the strongest for MV. The positive value of Eint indicates that an additional 19801



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Figure 8. Local atomic structures of N-doped structural defects in graphene: (a) MV, (b) monohydrogenated MV, (c) divacancy (DV) consisting of two pentagons and one octagon (5−8−5), (d) reconstructed DV consisting of three pentagons and three heptagons (555−777), (e) reconstructed DV consisting of four pentagons and four heptagons, as well as one hexagon (5555−6−7777), (f) Stone− Wales defect (SW), (g) extended line defect (ELD) consisting of pentagons and octagon, (h) (2,1)(2,1) grain boundary (GB), (i) armchair (ac) edge, (j) N doped at the edge site of zigzag (zz) edge, (k) N doped at the edge-1 site of zz edge, (l) reconstructed zigzag edge (zz57) consisting of pentagon and heptagon, and (m) interaction energy Eint between a single substitutional N and dierent structural defects in graphene. Gray, blue, and white balls stand for C, N, and H atoms, respectively.

Figure 7. Band structures obtained by using a 9 × 9 supercell for graphene with N-doped MVs before and after oxidation: (a) a pyridinic N at clean MV, (b) pN + ether, (c) pN + ether + water, (d) pNH, (e) pNH + ether, (f) pNH + CH + ketone, (g) pNH + 2 ketones, (h) gN + ether + ketone, and (i) gN + 3 ketones. Corresponding atomic structures are shown in Figure 5. Pyridinic N, pyridinium-like N, and graphitic N are denoted as pN, pNH, and gN, respectively. Green solid points indicate fat bands derived from N 2pz state. Note that the original Dirac points (i.e., K and K′ points) in irreducible Brillouin zone (IBZ) of primitive unit cell of graphene are folded into the Brillouin zone center (i.e., Γ point) of IBZ of 9 × 9 supercell. The zero of energy is set at Fermi energy.

repulsive interaction.15 The attractive (repulsive) interaction between an N substitution and an additional entity is closely correlated to the increase (decrease) of aromaticity of graphene. We first examine the cases of a H atom, an O atom, and a hydroxyl group adsorbed on the surface of perfect graphene without and with a single substitutional N. The interaction energies are presented in Figure 9a. The results of interaction energy indicate that the substitutional N and these adsorbates (H atom, O atom, and OH) would attract each other (see the insets in Figure 9a). It suggests that surface modification of graphene by these adsorbates would enhance N doping because of the decrease in the formation energy of N substitution. On the other hand, it also suggests that N substitution will enhance adsorption of oxygen-containing chemical groups on graphene, resulting in removal of oxygen-containing chemical groups on graphene to be thermally more unfavorable. This may be one of the reasons why oxygen-containing chemical groups in N-

Table 2. Total Magnetic Moment (Mt, μB per cell) and SpinPolarization Energy (ESP in eV) of N-Doped Oxidized MVs Obtained by n × n Supercells (n = 9, 12, and 15) configuration Figure No. Mt, 9 × 9 ESP, 9 × 9 Mt, 12 × 12 ESP, 12 × 12 Mt, 15 × 15 ESP, 15 × 15

pN + ether 5c 0.96 −0.017 0.82 −0.006 0.74 −0.007

pNH + CH + ketone 5e 0.61 −0.003 0.0 0.0 0.0 0.0

gN + ether + ketone 5f 0.58 −0.005 0.0 0.0 0.0 0.0

object A and a single N tends to repel each other and that they are energetically unfavorable to be aggregated. For example, two N dopants in perfect graphene show a long-ranged 19802



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MV depends on the oxidation degree. Pyridinic N at MV acts as a hole dopant before oxidation, while it does not induce any carrier after oxidation. During the ORR of carbon alloy catalysts in PEMFC, a pyridinic N at MV would be easily protonated to form a pyridinium-like N. Our results also show both pyridinic N and pyridinium-like N at MV would not facilitate the ORR because the carbon atoms next to vacancy site would be thermodynamically oxidized by the oxygen molecule and the resulting oxygen functional groups (e.g., ether and ketone groups) are unlikely to be electrochemically reduced. We also explain why the oxygen-containing chemical groups in Ngraphene cannot be removed completely.

Figure 9. Interaction energy Eint between a single substitutional N and (a) individual H, O, and hydroxyl (OH) adsorbates on defect-free graphene and (b) oxidized MV. The red solid (black dashed) line indicates the interaction energy between a single substitutional N and an unoxidized (monohydrogenated) MV. Inserts show local atomic structures of N-doped congurations. Gray, blue, red, and white balls stand for C, N, O, and H atoms, respectively.

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ASSOCIATED CONTENT

S Supporting Information *

Additional results are presented: (1) the bond length between N and O atoms as well as their protrusion in the pN + ether configuration of N-doped oxidized MV; (2) the thermochemistry data for H2, N2, and O2 molecules in the gas state; (3) the whole region of a 9 × 9 supercell of graphene with and without a MV; (4) the squared wave function |ψ(ε)|2, partial density of states (PDOSs), simulated scanning tunneling microscope (STM) image for the 3-fold oxygen configuration of oxidized MV; (5) the PDOSs and the possible ways of arranging Clar sextets and double bonds for the ether + CH configuration of oxidized MV; (6) the PDOSs and the possible ways of arranging Clar sextets and double bonds for the ether + ketone configuration of oxidized MV; (7) the PDOSs and the possible ways of arranging Clar sextets and double bonds for the ether + ketone + epoxy configuration of oxidized MV; (8) the effective band structures unfolded into the Brillouin zone of the primitive cell of graphene for the configurations of a 3-fold oxygen, ether + ketone, a pyridinic N at clean MV, pNH + 2 ketones, gN + ether + ketone, and gN + 3 ketones. This material is available free of charge via the Internet at http:// pubs.acs.org.

graphene cannot be removed completely.5−7 For example, the formation energy of an expoxy-like oxygen on graphene is calculated to be about 0.98 eV (see the dashed line in Figure 2a) and it will be lowered by −0.66 eV (≃25.8kBTrt, where kB is Boltzmann’s constant and Trt is the room temperature) by N substitution. It is found in experiment that the epoxy group on graphene can be thermally removed when the annealing temperature is above 260 °C.54 Therefore, the oxygen on Ngraphene cannot be thermally removed by increasing the annealing temperature. Figure 9b shows the results for Eint between an oxidized MV and a single substitutional N. For comparison, Eint between a clean MV and a single substitutional N is indicated by the dashed line in Figure 9b. As already discussed in our previous paper,15 a single substitutional N and a clean MV exhibit attractive interaction. The N substitution is energetically favorable at the carbon atom next to vacancy site to form pN. In the case of oxidized MV, interaction energies between a single substitutional N and different oxidized MVs are still negative; however, the absolute values are reduced with respect to that of clean MV. It suggests that oxidation of MV just weakens the attractive interaction between substitutional N and MV.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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4. CONCLUSIONS We have studied the effect of the oxidation of monovacancy (MV) on the N doping of graphene using DFT electronic structure calculations. Our calculations show that the ether group (−O− in plane) is one of basic components in the thermally stable configurations of oxidized MV. Under oxygenrich and hydrogen-rich conditions without N doping, two of the three carbon atoms next to the vacancy site will participate in the formation of an ether group, and the remaining one will be passivated by dihydrogenation (or monohydrogenation plus a hydroxyl group) to form an sp3 hybridization or by oxidation to form a ketone group. The resulting configurations of oxidized MV are aromatic and, thus, they are very stable. Under oxygen-poor and hydrogen-deficient conditions, a configuration of oxidized MV consisting of an ether group and a monohydrogenated C could be stable and it is nonaromatic. The oxidation of MV weakens the attractive interaction between substitutional N and MV. Graphitic N nearby MV is unstable before oxidation, but it can be stabilized after heavy oxidation. The carrier-doping behavior of graphitic N nearby

ACKNOWLEDGMENTS This work was performed under Project 10000829-0 at the New Energy and Industrial Technology Development Organization (NEDO). The computation was performed using the supercomputing facilities in the Center for Information Science in JAIST. Parts of the computations were done on TSUBAME Grid Cluster at the Global Scientific Information and Computing Center of the Tokyo Institute of Technology.

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REFERENCES

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Interplay between Oxidized Monovacancy and Nitrogen Doping in

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