High catalytic activity for CO oxidation on single Fe atom stabilized in graphene vacancies

Abstract

Inspired by the recently discovered dynamics of single Fe atoms in graphene vacancies, we systemically examined the stable configurations, electronic structures, and catalytic activities of Fe-atom-embedded graphene substrates (including monovacancy graphene (MG) and divacancy graphene (DG)) by using first-principles calculations. We found that the doped Fe on the MG sheet (Fe/MG) is more stable than that on the DG sheet (Fe/DG). Doping with Fe atoms provides more transferred electrons to fill the vacancy defects of graphene and allows it to exhibit a more positive charge, which effectively regulates O₂ and CO adsorption. Also, the degree of interactions between the reactants and substrates are connected to the reaction pathways and energy barriers. For the Fe/MG sheet, the low coadsorption energy of gas molecules can promote the catalytic reaction through the Langmuir–Hinshelwood (LH) mechanism. In comparison, the initial step for CO oxidation on the Fe/DG sheet is through the Eley–Rideal (ER) mechanism, which is an energetically more favorable process. Moreover, the more stable Fe/MG sheet is a much more efficient catalyst for CO oxidation at low temperature, because the sequential reaction processes (LH and ER) have low enough energy barriers. These results provide valuable guidance on selecting the metal dopant in graphene materials to design effective atomic-scale catalysts.

---

1. Introduction

In recent decades, the low temperature catalytic CO oxidation has attracted great interest due to its fundamental and important applications in the area of environmental protection and in avoiding electronic poisoning in fuel cells.^1–3 Generally, CO oxidation has been considered as a vital prototype reaction for exploring the reactivity of metals in heterogeneous catalysis.^4–6 Many strategies have been chosen by using supported noble metals or metal oxides^7–9 as catalysts, such as Pt,^2,10,11 Rh,¹² Au,^4,13–15 and Pd,³ which exhibit high activity for CO oxidation. Furthermore, some reports state that small metal nanoparticles or clusters (e.g., of Au,^15,16 Pt,¹⁷ Pd,¹⁸ and Ag¹⁹) can exhibit exceptional catalytic activity for CO oxidation. However, noble metal catalysts are very costly and usually require high reaction temperatures; also the catalytic activities of metal nanoparticles can be strongly size- and shape-dependent, which limits their general use on a large scale. As a result, catalysts with higher activity and lower cost are urgently required in many practical applications.

To solve these scientific issues, the catalytic activity of noble metals can be dramatically improved by reducing the size of the catalysts to nanoparticles^20–23 and even to single atoms.²⁴ Single-atom catalysts supported on various substrates have attracted attention due to their intrinsic high activity, stability, and low cost.^25–28 Recently, Qiao et al. found that single-atom Pt loading on FeO_x exhibited excellent catalytic activity toward CO oxidation.²⁹ These results illustrated that the kind of single-metal atom and the choice of support substrates can affect the reactivity and stability of catalysts, especially two dimensional (2D) substrates, and consequently 2D materials have been the focus of much research due to their excellent physical and chemical properties.³⁰ Compared to carbon-based nanomaterials, including carbon black and carbon nanotubes (CNTs), graphene is a 2D atomic crystal structure consisting of a single layer of sp²-hybridized carbon atoms³¹ and is now recognized as a promising substrate to support metal atoms due to its outstanding reaction mechanisms,³² and electronic³³ and thermal³⁴ properties for developing new catalysts.³⁵ Moreover, graphene as a support has a large surface-to-volume ratio, which is a benefit for heterogeneous catalysts.³⁶ Recently, small metal clusters supported on graphene substrates exhibited unusually high catalytic activity as electrodes in fuel cells.^37–43 However, the supported nanoclusters usually incorporate several structural isomers and the easy occurrence of structural interconversion between the isomers can affect their stability and catalytic efficiency.⁴⁴ Uniformly dispersed single-metal atoms on a graphene substrate are considered to be highly promising for application in heterogeneous catalysis.

Chemical doping has been confirmed to be an effective approach to tailor the properties of graphene.^45–47 Earlier investigations showed that the substitutional dopants in graphene can control the size and degree of catalyst dispersion,⁴⁸ as well as the stability of the catalysts to exhibit a high reactivity performance.^49–52 Compared to nonmetal dopants in graphene substrates, the much stronger binding between carbon vacancies and metal atoms can effectively improve the structural stability,^53–55 electronic structure, and magnetic properties.^56–59 However, experimental studies in the literature have demonstrated that metallic impurities can originate from the growth process of graphite on metal substrates.⁶⁰ Moreover, carbon vacancies can be deliberately introduced in graphene sheets by high energy atom/ion bombardment⁶¹ and then the carbon vacancies can be filled with the desired metal atom.^62,63 These efficient atomic doping techniques provide a way to analyze the interaction between the introduced atoms and graphene sheets. Theoretically, single-atom Au–,⁶⁴ Fe–,⁶⁵ Cu–,⁶⁶ Pt–,⁶⁷ Pd–,⁶⁸ and Al–embedded graphene⁶⁹ systems have been predicted to be highly active catalysts for CO oxidation. These observations confirmed that the metallic impurities in graphene sheets could be a better candidate for improving the stability and the lifetime of supported catalysts, and that a single-atom catalyst with a low cost and high activity would have great potential application in catalysis.

In general, the degree of interaction between the active sites of catalysts and adsorption species is proportional to the binding energy and the reaction energy barriers.⁷⁰ Among the noble metal-atoms–embedded graphene, Au–embedded graphene shows the best performance for CO oxidation.⁶⁴ However, the adsorption energy of CO is larger than that of the O₂ molecule, indicating that CO prefers to adsorb at the Au atom, which could prevent the continuous oxidation reaction. With reducing the consumption of noble metal atoms, it is necessary to exploit efficient non-noble metal (NNM) atoms supported on a graphene complex for CO oxidation. Previous studies have shown that some NNM-atoms-embedded graphene substrates exhibit high catalytic activity for CO oxidation,^48,65,71 but there is a lack of comparative analysis of the activation barriers of different reaction mechanisms, such as for the Langmuir–Hinshelwood (LH) and Eley–Rideal (ER) reactions. Compared to the noble metal atoms (e.g., Pt or Pd),^68,72,73 we chose Fe as the dispersed single atom, because Fe is inexpensive, environmentally benign, readily available, and is richly abundant in the earth, and so it meets the requirements for a cheap, green, and efficient catalyst. Like in any other real material, structural defects do exist in graphene,^74–76 and these can be useful for achieving new functionalities.^77–80 Recently, Robertson et al. observed that mobile Fe atoms resident on the mono- and divacancies in graphene surfaces are stable in comparison to that on the graphene edge.⁸¹ Here, it is significant to evaluate the catalytic activity of single Fe atoms on defective graphene sheets (including the monovacancy and divacancy).

Inspired by earlier investigations, we selected monovacancy and divacancy graphene (MG and DG) as the supporting material and single Fe atoms as the catalysts to study the CO oxidation reaction. Based on our calculations, the MG and DG substrates act as support materials for the uniformly dispersed single-atom Fe catalyst (Fe–graphene includes Fe/MG and Fe/DG). In this study, the stable configurations, electronic structures, and magnetic properties of Fe/MG (or Fe/DG) toward reactive gases (CO and O₂) were investigated by first-principles based on density functional theory (DFT). It was found that the CO oxidation reactions on the Fe/MG substrate have lower energy barriers (first through the LH reaction, followed by the ER reaction) as compared with those on the Fe/DG surface. In addition, we further investigated the ER reaction without an intermediate state (i.e., CO + O₂ = CO₂ + O_ads) and then with the dissociation of O₂ molecules as the initial step and the generated O atoms reacting with two CO molecules. To the best of our knowledge, few reports provide much systemic information about the catalytic activities behind CO oxidation on metal-embedded graphene systems (including MG and DG), and hence this report provides a valuable reference for designing graphene-based catalysis systems.

2. Computational model and methods

Spin-polarized DFT calculations were carried out by the Vienna ab initio simulation package (VASP)^82,83 with the projector augmented wave (PAW) pseudo-potentials.⁸⁴ The exchange-correlation functions were described with the generalized gradient approximation (GGA) in the form of the Perdew, Burke, and Ernzernhof (PBE) functional.⁸⁵ The kinetic energy cutoff for the plane-wave basis set was chosen as 450 eV. The C 2s2p, Fe 3d4s, and O 2s2p states were treated as valence electrons. A modified hexagonal graphene ribbon with a 5 × 7 supercell was adopted, and the vacuum layer was set to 15 Å to avoid the interaction among mirror images. The calculated lattice constant for the graphene sheet was 2.47 Å, which nearly approximates to the experimental value of 2.46 Å.⁸⁶ In order to improve the convergence of the states near the Fermi level, the Brillouin zone (BZ) integration was sampled using a 3 × 3 × 1 Γ-centered Monkhorst–Pack (MP) grid, while a Γ-centered MP grid of 15 × 15 × 1 was used for the final density of states (DOS) calculations.

Bader charge analysis⁸⁷ was used to evaluate the atomic charges and electron transfer in the reactions. Adsorption energies and site preferences for each type of gas molecules were tested on the Fe–graphene surfaces. The climbing image nudged elastic band method (CI-NEB)^88–90 was employed to investigate the saddle points and minimum energy path (MEP) for the diffusion and dissociation of adatoms or for the reaction gases on the graphene substrates. The geometric optimization and the search for the transition states (TS) were tested by means of frequency calculations, while those with one imaginary frequency corresponded to the metastable states, which could be viewed as the MS. A number of intermediate images were constructed along the reaction pathways between the initial state (IS) or TS and the final state (FS), and the spring force between adjacent images was set as 5.0 eV Å⁻¹. The images were optimized until the combined force on each atom was less than 0.02 eV Å⁻¹. The energy barrier (E_bar) of each chemical reaction was calculated by the energy difference between the IS and TS in each chemical reaction.

The adsorption energy (E_ads) was calculated using the formula E_ads = E_A + E_B − E_AB, where E_A, E_B, and E_AB are the total energies of the optimized adsorbates in the gas molecules (A: O₂, O, CO, and CO₂), the clean Fe-embedded graphene substrates (B: Fe/MG and Fe/DG), and the adsorbate-substrate systems, respectively. With this definition, a higher E_ads value means a stronger adsorption.

3. Results and discussion

3.1. Geometry stabilities and electronic properties

First, the stable geometries of Fe anchored on MG and DG substrates were investigated, and the corresponding adsorption energies, bond lengths, and transferred electrons are shown in Table 1. As shown in Fig. 1(a), single-atom Fe is embedded into the MG sheet, where one C atom is substituted by one Fe atom. The calculated E_ads of the Fe dopant in graphene is 7.28 eV, and the Fe atom is moved out of the plane to obtain more space (1.20 Å) due to its atomic radius (1.30 Å) being larger than that of the carbon atom. The bond distance between the Fe atom and the neighboring carbon atoms is 1.76 Å, which is in agreement with the reported results.^53,65 Based on the Bader charge analysis,⁸⁷ the transferring electrons (1.07 e) move from the Fe atom to the MG sheet and form strong covalent bonds between the Fe atom and C atoms. As shown in Fig. 1(b), the stable configuration of Fe/DG was investigated after geometry optimization. Compared with the case of the Fe/MG system, the doped Fe atom provides more transferred electrons (1.33 e) to the DG system, the corresponding bond length of Fe–C is longer at 1.90 Å, and the Fe atom nearly retains the planar from of the pristine graphene. It was found that the doped Fe atom in the DG sheet exhibits less stability (6.47 eV) than that on the MG sheet (7.28 eV), yet they are much more stable than the same atom on pristine graphene (pri-graphene, 1.19 eV). In addition, the calculated small diffusion barrier (E_bar, 0.52 eV) indicates that the Fe adatom can easily diffuse on to pri-graphene. For the MG and DG sheets, the Fe adatom on graphene diffuses from the neighboring H site to its neighboring vacancy site with a small difference in E_bar (0.40 eV vs. 0.50 eV), while the inverse pathway needs to overcome a larger energy barrier (6.23 eV vs. 5.51 eV). These results indicate that the Fe adatoms can diffuse easily on the pri-graphene surface and prefer to be trapped at the vacancy site and appear as Fe dopants, since a surface reaction at ambient temperature may occur only when the energy barrier is smaller than the critical barrier of 0.91 eV.⁶⁹ This observation confirms that Fe–graphene systems would be stable enough to be utilized in catalytic reactions. Therefore, it can be seen that the Fe dopants can uniformly disperse on graphene and are quite stable without a clustering formation.

Table 1 The adsorption energy (E_ads, in eV), bond length of Fe–C or O₂/CO (d₁, in Å), adsorption height (d₂, in Å), and the number of electrons transferred from the adsorbate to substrate (Δq, the “+”or “−” denotes gaining or losing electrons), for the Fe dopant or gas molecule (O₂ and CO) adsorbed on graphene or (Fe/MG and Fe/DG) systems

Systems		Eads (eV)	d1 (Å)	Δq (e)	d2 (Å)
Fe/MG	Fe	7.28	1.76	−1.07	1.20
	O2	1.88	1.40	+0.81	1.86
	CO	1.13	1.15	+0.31	1.88
Fe/DG	Fe	6.47	1.90	−1.33	0.00
	O2	1.80	1.34	+0.53	1.96
	CO	1.77	1.16	+0.30	1.78

---

Fig. 1 Top and side views of the geometric structure for (a) Fe/MG and (b) Fe/DG sheets. Black and green balls represent the C and Fe atoms, respectively. (c) Spin-resolved total DOS (TDOS), partial DOS (PDOS), and local PDOS (LDOS) for Fe/MG (thick lines) and Fe/DG sheet (thin lines) systems. The vertical dotted line denotes the Fermi level.

To gain more insight into the origin of the high stability of the Fe/MG and Fe/DG systems, we investigated the DOS plots, as shown in Fig. 1(c). We found that the electron states of the MG and DG substrates are strongly altered when an Fe atom is doped in these systems. The broadened partial DOS (PDOS) of the Fe 3d states overlap with the total DOS (TDOS) of the systems and the local PDOS (LDOS) of the C atoms around the Fermi level (E_F), suggesting a strong interaction between the Fe atom and adjacent C atoms. Besides, the spin-up and spin-down channels of the Fe/MG (or Fe/DG) become asymmetric, indicating that these systems exhibit a magnetic character. As shown in Fig. 2, we also investigated the spin charge redistribution between Fe atoms and the MG (or DG) sheet. As shown in Fig. 2(a), more electrons dominantly accumulate in the vicinity of Fe–C interfaces, while fewer electrons are located on the graphene substrate. It is clearly shown that the uneven distribution of the spin charge induces the magnetic property of the system. Compared to the Fe/MG system, the much more pronounced charge density redistribution at the Fe–DG interface induces a large magnetic property, as shown in Fig. 2(b). Although the Fe atom provides more electrons to the DG substrate, the relatively weaker interaction of Fe with DG compared with MG is likely due to the bare DG being more stable than the bare MG. Because the optimized bare DG structure forms two pentagons and one octagon at the divacancy site, this quenches the dangling bonds and renders it a stable structure. Compared to the bare MG and DG sheets (12.0 and 10.0 μ_B), the doped Fe atom induces a change in the magnetic properties of the systems (e.g., the Fe/MG and Fe/DG system display magnetic property values of 10.0 and 13.4 μ_B), which is accordance with the reported results.⁵³ For the metal-decorated graphene system, the hybridization of the metal atom d states and π states of graphene lead to their enhanced interaction. The metal dopant tends to provide more transferred electrons to graphene and induces spin charge redistribution at their interface, which can effectively regulate the electronic structure and magnetic property of graphene-based materials.

Fig. 2 Spin charge density maps for (a) Fe/MG and (b) Fe/DG sheets; the contour value is 0.001 e Å⁻³ intervals.

3.2. Adsorption of CO and O₂ molecules

Based on the highly stable structure of the Fe–graphene substrates, as shown in Fig. 1(a) and (b), we examined the possible adsorption sites in order to find out the most energetically favorable configurations for the reactant gases on Fe/MG or Fe/DG substrates. The corresponding adsorption energies and structural parameters for the optimized structures are listed in Table 1. It was found that the adsorption energies of individual O₂ on the Fe–graphene systems are larger than those for the CO molecule. The adsorptive O₂ has roughly similar configurations on the different graphene substrates, where it prefers to form two bonds with the Fe atom and where the O–O bond is parallel to the Fe–graphene surface, as shown in Fig. 3(a) and (c). Compared to the adsorbed O₂ on the Fe/DG (1.80 eV), the single O₂ has a relatively larger adsorption energy (1.88 eV) on Fe/MG, which is 0.33 eV more favorable than it would be at the end-on configuration. There are also more electrons (0.81 e) transferred from the Fe/MG to the adsorbed O₂, which subsequently leads to elongating the O–O bond (1.40 Å). In comparison, the adsorbed O₂ gains fewer electrons (0.53 e) on the Fe/DG substrate and the O–O bond length is thus shorter at 1.34 Å.

Fig. 3 Top and side views of the geometric structures for (a)–(c) O₂ and (b)–(d) CO adsorbed on the Fe/MG and Fe/DG sheets, respectively. The green, black, and red balls represent Fe, C, and O atoms, respectively.

As shown in Fig. 3(b)–(d), the most stable configurations of the CO molecule adsorbs on the Fe/MG and Fe/DG substrates. It was found that the end-on adsorbed CO is nearly vertical on the Fe/MG surface, with the distance between Fe and CO equal to 1.88 Å, and it has a smaller E_ads (1.13 eV) than that on the Fe/DG substrate (1.77 eV). In comparison, the adsorbed CO is somewhat tilted on the Fe/DG surface, with an Fe–CO distance of 1.78 Å. Herein, we report that we found that the adsorption of O₂ on the Fe–graphene systems were more stable than those of the CO molecule, since there were more transferred electrons from the bound Fe atom to the O₂ molecule. Furthermore, the elongation of the O–O bond was connected to the number of transferred electrons from the Fe–graphene substrates.

The electronic structure, which fundamentally determines the physical and chemical properties of a system, is directly related to the interaction between the adsorbate and the substrate. For the adsorbed O₂ and CO on Fe/MG systems, the corresponding DOS plots were investigated and are shown in Fig. 4. As shown in Fig. 4(a), the broadened PDOS of the Fe 3d states strongly hybridizes with the O₂ 2π*, 5σ and 1π orbitals around the E_F, indicating that there are about 0.81 e transferred from Fe/MG to the adsorbed O₂, which occupy the 2π* orbital of O₂, resulting in elongation of the O–O bond to 1.40 Å. Besides, the hybridization between the Fe and O states induces the magnetic moment of the whole system (12 μ_B) due to the increase in the number of unpaired electrons, thus the spin-up and spin-down channels of the system become asymmetric.

Fig. 4 Spin-resolved TDOS, local DOS (LDOS), PDOS (spin-up labeled with ↑ and spin-down labeled with ↓) for (a) O₂ and (b) CO on the Fe/MG sheet. The solid (dashed) curves represent the TDOS of Fe/MG without (with) O₂ or CO adsorption. The dotted curves represent the PDOS of Fe 3d states with O₂ or CO adsorption, and the dash dotted curves represent the LDOS of adsorbed O₂ (or CO). The vertical dotted line denotes the Fermi level.

The DOS plot for the CO on Fe/MG is shown in Fig. 4(b), where it can be observed that the hybridization between the PDOS of the Fe-3d states and the CO-2π* and 5σ states are near the E_F. Compared to the adsorbed O₂, fewer electrons are transferred from the Fe atom to the CO molecule (0.31 e), indicating a weak interaction between the CO and the Fe/MG. Besides, the CO on the Fe/MG system exhibits a magnetic property (10 μ_B) according to the asymmetry of the spin channels. Therefore, the magnetic properties of graphene systems can be tuned by choosing the kind of gas molecules adsorbed, which may have a bearing on some important applications in electronic and spintronic devices.

To further understand the origin of the differences in the electronic structure and magnetic properties according to the type of adsorbates, we investigated the valence charge density (or spin electron redistribution) of the adsorption of reaction gases on Fe–graphene substrates, as shown in Fig. 5. It was found that the adsorbed O₂ and CO on Fe/MG induce spin charge redistribution at their interfaces. The more electrons that dominantly accumulate in the vicinity of the O₂–Fe or CO–Fe interfaces, the fewer electrons are located on the graphene substrates. Compared to the CO molecule (10.0 μ_B), the adsorbed O₂ on the Fe/MG sheet induces a more pronounced spin charge distribution and it thus exhibits a larger magnetic property (12.0 μ_B). Bader charge analysis showed that the Fe atoms lose about 1.44 and 1.23 e in these systems, in which some are partly transferred to the O₂ and CO (0.81 and 0.31 e) and the rest are transferred to the graphene sheets, illustrating that the electrons deplete from the vicinity of the Fe dopants and that the transferred electrons can facilitate the interaction between the gas molecules and graphene substrates.

Fig. 5 The charge distribution and spin charge density plots for (a) and (b) O₂ and (c) and (d) CO adsorbed on the Fe/MG sheet. Contour lines in plots are drawn at about 0.01 (or 0.001) e Å⁻³ intervals.

Compared with the bare Fe–graphene systems, the charge redistribution plots due to the adsorption of O₂ and CO on the Fe–graphene substrates. The more pronounced charge density redistribution and the bond elongation of O₂ on the Fe/MG sheet (0.81 e, 1.40 Å) compared to those on the Fe/DG sheet (0.53 e, 1.34 Å) indicate a stronger interaction of O₂ on Fe/MG (1.88 eV) than that on Fe/DG (1.80 eV). Hence, the elongation of the O–O bond is correlated with the amount of electronic charge transferred to O₂, i.e., the more charge is transferred to O₂ from the Fe–graphene systems, the more elongated the O–O bonds become. In contrast, CO gains fewer electrons on the Fe–graphene substrates compared with the adsorbed O₂ molecules, as shown in Table 1. The larger charge density accumulation between the adsorbed O₂ and Fe–graphene illustrate that their interaction is stronger than that for the adsorption of CO. For the adsorbed CO on Fe–graphene, it was found that the small difference in electron gain induces a larger energy difference, indicating that CO is a more sensitive gas molecule and can be easily influenced by various conditions; or example, the Fe dopant in the Fe/MG system largely weakens the CO adsorption (1.13 eV) compared with that on the Fe/DG (1.77 eV). Hence, the interaction of Fe atoms with different graphene systems would modify the electronic structure and catalytic activity of the Fe catalyst. The losing electrons from the Fe dopants exhibit a positive charge, which can alleviate the CO adsorption and enhance the adsorptive stability of the O₂ molecule, and thus the Fe–graphene sheet is more likely to be useful as a catalytic anode material for facilitating the catalytic reaction of CO oxidation.

Generally, the degree of interaction or the strength of the bonding can determine the reaction energy barriers.⁷⁰ Consequently, it is desired that the interactions between the active sites of catalysts and reactive gases should be adequate. Our calculated results show that the transferred electrons from the Fe dopants can promote the interaction between reactive gases and graphene substrates. Compared to the CO molecule, O₂ is viewed as an electron-acceptor molecule.⁶⁷ As they gain more electrons, O₂ molecules have larger adsorption energies on the Fe–graphene substrates compared to CO. The anchored Fe atom on graphene prefers to be covered by adsorbed O₂ if a mixture of CO and O₂ is injected as the reaction gas. Since O₂ has a larger adsorption energy than that of the CO molecule, the adsorption of O₂ on Fe–graphene substrates takes a higher priority and thus the ER mechanism seems to be more favorable. Besides, the coadsorption of CO and O₂ molecules involve larger E_ads on the Au–graphene (1.82 eV),⁶⁴ Al–graphene (1.95 eV),⁶⁹ Cu–graphene (3.29 eV),⁶⁶ Fe/MG (2.10 eV) and Fe/DG (2.60 eV) sheets than that for the individual CO or O₂ molecules, as shown in Table S1.† Although the adsorption energy difference between CO and O₂ on the Fe/MG is relatively large, the lower coadsorption energy of the O₂ and CO molecules indicates that there is a certain probability of having O₂ and CO coadsorbed on the Fe atom. Therefore, it is worth exploring the catalytic activity of Fe–graphene sheets through comparing different reaction mechanisms for CO oxidation.

3.3. Interaction mechanism between the adsorbed O₂ and CO

3.3.1 CO oxidation reactions on the Fe/MG surface. In general, two main reaction mechanisms for CO oxidation have been established, namely, the LH and ER mechanisms.^20,30,45 The LH mechanism states that the coadsorption of CO and O₂ molecules on a catalyst occurs, leading to formation of a peroxo-type OOCO intermediate state (MS). Finally, the formation and desorption of a CO₂ molecule occurs, leaving an adsorbed O atom (O_ads) at the Fe atom. In the ER mechanism, the CO molecule directly reacts with the preadsorbed O₂ molecule at Fe–graphene surfaces, producing a carbonate-like state of CO₃, which can be viewed as MS. In our study, both mechanisms were comparably investigated. In addition, the dissociative adsorption of O₂ molecules on Fe–graphene were also analyzed, including to assess whether it could provide enough oxygen atoms and promote the catalytic cycle for CO oxidation.

First, several coadsorption configurations of CO and O₂ molecules on Fe/MG through the LH mechanism were tested. The most stable coadsorption configuration was viewed as an IS, where the CO and O₂ are tilted and parallel to the Fe/MG surface, respectively. The FS consists of a physisorbed CO₂ molecule and a chemisorbed O_ads. For CO oxidation, the local configurations between the reactants on the Fe/MG surface at each state along the MEP are displayed in Fig. 6(a), and the corresponding structural parameters for IS, TS, MS, and FS are shown in Table 2(a).

Fig. 6 The minimum energy profiles and configurations of different states for the CO oxidation reaction on the Fe/MG sheet, including (a) CO + O₂ reaction by the LH mechanism, (b) CO + O₂ = CO₂ + O_ads and (c) CO + O_ads reactions by the ER mechanism. The red, green, and black balls represent O, Fe, and C atoms, respectively.

Table 2 Structural parameters for the coadsorption of CO and O₂ for the IS, TS, MS, and FS along the MEP for CO oxidation on the Fe/MG system, (a) LH reaction (CO + O₂ → OOCO → CO₂ + O_ads), (b) and (c) ER reaction (CO + O₂ = CO₂ + O_ads and CO + O → CO₂), as displayed in Fig. 6(a)–(c)

(a)
Distance (Å)	IS	TS1	MS	TS2	FS
dC–O	1.15	1.16	1.20	1.17	1.18
dC–Fe	1.96	2.03	2.07	2.65	3.79
dC–O1	2.61	1.95	1.37	1.17	1.17
dO1–Fe	1.99	2.46	2.56	2.90	4.39
dO2–Fe	2.00	1.91	1.88	1.65	1.62
dO1–O2	1.33	1.36	1.48	2.12	2.99

---

(b)
Distance (Å)	IS	TS	FS
dO1–O2	1.39	1.34	2.79
dC–O1	3.19	2.29	1.16
dO1–Fe	1.86	2.67	3.52

---

(c)
dO2–Fe	1.62	1.68	1.84
dO2–C	2.72	1.75	1.16
dC–O	1.14	1.16	1.15

---

Once the coadsorption of CO and O₂ takes place on Fe/MG, the distance between O₂ and CO is about 2.38 Å, while the Fe–CO and Fe–O₂ distances are 1.93 and 2.04 Å, respectively. To proceed, the O₂ molecule turns around so that one of its oxygen atoms now approaches the CO molecule, while another oxygen atom is anchored at the Fe atom. Passing over the TS1, the OOCO complex (MS) is formed, and the corresponding energy barrier (E_bar) along the MEP is estimated to be 0.29 eV. In this reaction process, the bond length of O₂ (d_O1–O2) is gradually elongated from 1.34 to 1.48 Å. The reaction continuously proceeds from MS to FS through TS2 without any energy barrier, where the O1–O2 bond is broken and a CO₂ molecule is formed, leaving an atomic O2 to adsorb at the Fe atom, which is expected to be active and can be used for the CO oxidation reaction. According to the reported result by Chen,⁹¹ we checked the possible reactions for CO oxidation through the ER mechanism without any intermediate state (i.e., CO + O₂ = CO₂ + O_ads), as shown in Fig. 6(b). The first physisorbed CO above O₂ preadsorbed on the Fe/MG sheet was selected as the IS, and the distance between CO and O₂ was 3.19 Å. As shown in Table 2(b), the migration of the CO molecule involves moving toward the preadsorbed O₂ molecule and the distance changes from 3.19 to 1.16 Å, and then CO₂ is generated, where the calculated energy barrier is 0.56 eV in this process. After desorbing of the CO₂ molecule, we further checked the oxidation process of a second CO molecule reacting with the atomic O2 to produce CO₂. As shown in Fig. 6(c), the configuration with a CO molecule more than 2.72 Å away from the preadsorbed O_ads (E_ads, 5.45 eV) on the Fe atom is viewed as the IS. The adsorption configuration of CO₂ on the Fe/MG sheet is considered as the FS. When the carbon atom of CO approaches the atomic O2, a TS with a CO–O_ads distance of 1.75 Å is formed, as shown in Table 2(c). It was found that the CO oxidation through the first ER reaction (CO + O₂ = CO₂ + O_ads) has a relatively larger energy barrier (0.56 eV) than that of the second one (CO + O_ads = CO₂, 0.38 eV), which are both higher than for the first step (TS1, 0.29 eV) through the LH reaction.

As an important reference, the physisorbed CO molecule directly reacts with the preadsorbed O₂ through the ER mechanism through an intermediate state (i.e., CO + O₂ → CO₃), with the corresponding atomic configurations of each state along the MEP displayed in Fig. 7 and Table 3. At first, the configuration of the physisorbed CO above O₂ preadsorbed on the Fe/MG sheet was selected as an IS. When approaching the activated O₂, one CO molecule can be inserted into the O–O bond to form a carbonate-like CO₃ complex (MS) with a small energy barrier of 0.32 eV (TS1). Then, the reaction can proceed with the dissociating of CO₃ into CO₂ and leaving an O_ads atom (FS). The energy barrier (TS2) for this process was estimated to 0.72 eV, which is quite similar to the case of CO oxidation on Mo–graphene⁹² and Pt-anchored graphene oxide.⁹³ However, it was found that the formed CO₃ is more stable than the final products (CO₂ and O_ads), since the reversible reaction (CO₂ + O_ads → CO₃) has a relatively small energy barrier (0.41 eV), as shown in Fig. 7(a), and consequently the more stable CO₃ is an energetically unfavorable reaction for generating CO₂. Furthermore, the possible reaction pathway after the formation of CO₃ is to react with another CO molecule (IS) to produce two CO₂ molecules (FS) through the TS, as shown in Fig. 7(b). In this reaction (CO₃ + CO → 2CO₂), the corresponding energy barrier (0.61 eV) is smaller than the direct dissociation energy of the CO₃ complex (0.72 eV), indicating that the presence of a CO molecule can promote the dissociation of a CO₃ complex on the Fe/MG surface.

Fig. 7 The minimum energy profiles and configurations of different states for the CO oxidation reaction on the Fe/MG sheet, including (a) CO + O₂ and (b) CO₃ + CO reactions by the ER reactions. The red, green, and black balls represent O, Fe, and C atoms, respectively.

Table 3 Structural parameters for the preadsorbed O₂ with CO for the IS, TS, MS, and FS along the MEP for CO oxidation on the Fe/MG system through ER reactions, which includes (a) CO + O₂ → CO₃ → CO₂ + O_ads and (b) CO + CO₃ → 2CO₂; the corresponding reaction pathways are displayed in Fig. 7(a) and (b)

(a)
Distance (Å)	IS	TS1	MS	TS2	FS
dC–O	1.14	1.14	1.21	1.18	1.17
dC–O1	3.00	2.42	1.35	1.19	1.17
dC–O2	3.00	2.42	1.35	2.07	2.56
dO1–Fe	1.87	1.85	1.91	2.70	3.35
dO2–Fe	1.87	1.85	1.91	1.65	1.62
dO1–O2	1.40	1.43	2.18	2.52	2.87

---

(b)
Distance (Å)	IS	TS	FS
dO2–C	1.36	2.21	2.80
dO2–C2	3.01	3.19	1.18
dO2–Fe	1.89	1.63	2.59

---

After the dissociation reaction of an O₂ molecule on Fe/MG, we further checked whether the dissociated atomic O_ads is active for CO oxidation through ER reactions, as shown in Fig. 8. In these reaction processes, the O–O bond is elongated from 1.40 to 3.06 Å and the formed two O atoms are anchored at the top site of the carbon atoms, and the corresponding energy barrier is estimated to be 1.01 eV, as shown in Fig. 8(a). As shown in Fig. 8(b), the CO oxidation reactions on the Fe/MG surface were investigated, and these include a two-step process for the interaction between two O atoms and two CO molecules. First, the configuration with preadsorbed O_ads and a subsequent CO near the Fe is viewed as the IS, where the CO–O distance is 3.11 Å. It was found that the CO reaches and reacts with the O_ads through an ER reaction, with an E_bar of 0.67 eV. Second, the physisorbed CO molecule is close to the binding O atom, where the corresponding distance CO–O is 3.15 Å. When the carbon atom of CO approaches the O atom, it generates a second CO₂ with an E_bar of 0.79 eV. In the sequential reactions, it was found that the dissociative adsorption of an O₂ molecule (1.01 eV) is more difficult than that of the formed CO₂ molecules (0.67 and 0.79 eV), yet these energy barriers are much larger than that on the top site of the Fe atom (CO + O → CO₂, 0.38 eV). This indicates that the dissociative adsorption of O₂ as a starting step is an energetically unfavorable reaction for CO oxidation. Based on the above discussions, the coadsorption of CO and O₂ through the LH reaction (0.29 eV) has a much smaller E_bar than those of the ER reactions. Hence, the LH reaction as a starting step is the more favorable process on the Fe/MG surface.

Fig. 8 The minimum energy profiles and configurations of different states for the CO oxidation reaction on the Fe/MG sheet, including (a) the dissociative adsorption of an O₂ molecule and (b) 2CO + 2O_ads reactions by the ER mechanism. The red, green, and black balls represent O, Fe, and C atoms, respectively.

3.3.2 CO oxidation reactions on the Fe/DG surface. In order to understand the specific reaction mechanisms for CO oxidation on different Fe–graphene substrates, for example, the relationship between the adsorption energies and energy barriers existing within the reactants and substrates were investigated. The calculated results show that the individual CO and O₂ molecules on the Fe/DG surface have a large adsorption energy and small energy difference, which may affect the catalytic pathways and energy barriers for CO oxidation. As shown in Fig. S1–S3,† the catalytic reactions of CO oxidation on the Fe/DG sheet through the same reaction processes (including LH and ER reactions) were investigated and compared. For the LH reaction, the coadsorption of CO and O₂ as a starting step has a much larger energy barrier (0.91 eV) than that on the Fe/MG (0.29 eV). For the ER mechanism without any intermediate state (i.e., CO + O₂ = CO₂ + O_ads), these is a relatively smaller energy barrier (0.30 eV) on the Fe/DG than that on the Fe/MG (0.56 eV), yet the second step of CO oxidation on the Fe/DG (CO + O_ads → CO₂) has a relatively large energy barrier (0.68 eV), since the atomic O_ads on the Fe/DG sheet has a larger E_ads (5.78 eV) than that on the Fe/MG sheet (5.45 eV), as shown in Fig. S1(a)–(c).† As shown in Fig. S2(a),† the ER mechanism with an intermediate state (i.e., CO + O₂ = CO₃) on the Fe/DG sheet has a smaller energy barrier (0.47 eV) than that on the Fe/MG sheet. Then, the carbonate-like CO₃ complex directly dissociates to produce a physisorbed CO₂ and an atomic O_ads, and this process experiences a relatively large energy barrier (0.66 eV), which includes the energy cost for breaking the C–O bond and for the desorbing of the CO₂. As shown in Fig. S2(b),† the carbonate-like CO₃ complex reacts with another CO molecule to produce two CO molecules through TS (1.04 eV), which is a larger value than for that on the Fe/MG sheet. As shown in Fig. S3(a) and (b),† the dissociative adsorption of an O₂ molecule generates two atomic O_ads and then two CO molecules approach the activated O_ads to produce two CO₂ molecules. It was found that these reactions have larger energy barriers (1.18, 1.03, and 1.56 eV) than those on the Fe/MG sheet.

For the CO oxidation reactions on the Fe–graphene substrates, the coadsorption of CO and O₂ as the starting step has a much lower energy barrier on the Fe/MG sheet (0.29 eV), while, the second step for CO oxidation through the ER reaction involves a relatively large energy (0.38 eV). Thus, the complete CO oxidation reactions on the Fe/MG substrate include a two-step process: the LH reaction as the starting step (CO + O₂ → OOCO → CO₂ + O_ads), followed by the ER reaction (CO + O_ads → CO₂). Compared with the LH reactions, the formation of a CO₂ molecule through the ER reaction involves a larger energy barrier, and so it can be viewed as the rate limiting step. Furthermore, these energy barriers are low enough (<0.4 eV) for the catalytic reaction to proceed rapidly at low temperature.⁶⁴ For the Fe/DG sheet, it was found that the CO oxidation processes through the ER reactions have smaller energy barriers (<0.7 eV) than those of the LH reaction, illustrating that the ER reaction as a starting state is a favorable mechanism. In the ER reactions, the oxidation process on the Fe/DG (CO + O_ads → CO₂, 0.68 eV) has a larger energy barrier than that of the other processes (0.30 eV, 0.47 eV, and 0.66 eV), and so it can be viewed as the rate limiting step. These results indicate that the reaction efficiency and energy barriers can be controlled by choosing different substrates or reaction mechanisms. For the Fe/MG sheet, the large energy difference and the low coadsorption energy of the reaction gases through LH mechanism may promote the catalytic reaction of CO oxidation. In comparison, the larger coadsorption energy of CO and O₂ on the Fe/DG sheet need to overcome a higher activation energy barrier, thus the LH mechanism as a starting step is energetically unfavorable. So, the CO oxidation reaction on the Fe/DG sheet through the ER mechanism is more possible or proceeds with greater ease. Compared with the ER reaction, the LH reactions on the Fe/MG sheet have smaller energy barriers, which ensure high efficiency in the catalytic reaction of CO oxidation.

In light of the aforementioned discussion, it can be concluded that the sequential reactions of CO oxidation through LH reactions have low enough energy barriers on the Fe/MG sheet (<0.4 eV), while the ER reaction as an IS on the Fe/DG sheet is an energetically more favorable process. These results indicate that the different vacancies in graphene sheets can regulate the stability and catalytic activity of the metal Fe dopant. Compared with the LH reaction on Cu– (0.54 eV),⁶⁶ Pd– (0.54 eV),⁶⁸ Pt– (0.59 eV),⁶⁷ Co– (0.42 eV),⁹⁴ Al– (0.32 eV),⁶⁹ Au–graphene (0.31 eV),⁶⁴ and Fe/DG (0.91 eV), the CO oxidation reaction on the Fe/MG sheet has a smaller energy barrier (0.29 eV). The sequential processes of CO oxidation on the Fe/MG sheet are more likely to proceed rapidly in practical reactions because of the low activation barriers involved. Therefore, single-atom Fe catalyst-embedded graphene substrates have a high activity for the catalytic oxidation CO reaction, which provides a valuable reference to fabricate functionalized graphene-based devices with low cost and high catalytic efficiency.

4. Conclusions

In summary, we carried out a comprehensive study of the structural stability and CO oxidation activity of single-atom Fe catalyst-embedded MG and DG sheets by means of DFT computations. It was found that the Fe dopants in MG and DG sheets introduce electronic doping, which can significantly regulate the electronic structure and magnetic property of the systems, as well as the strength of the interaction between the reactants and Fe–graphene. The individual O₂ molecule can be strongly bonded and activated on the Fe–graphene sheets with larger adsorption energies than that of a CO molecule. In addition, the catalytic reactions of CO oxidation were investigated and compared through comparing the LH and ER mechanisms. As a result, the CO oxidation reactions were found to be more likely to proceed rapidly on the Fe/MG sheet through the LH reaction (CO + O₂ → OOCO → CO₂ + O_ads, 0.29 eV), followed by the ER reaction (CO + O_ads → CO₂, 0.38 eV), because these catalytic processes have low enough energy barriers. In comparison, the ER reaction as the starting step is a favorable mechanism on the Fe/DG sheet. Our results demonstrate that the Fe–graphene sheets are promising anode materials for CO oxidation and can proceed at low temperature, and this report provides a comprehensive understanding of graphene–metal composite materials for the fields of catalysis and gas sensing.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. U1404109, 11504334, 51401078 and U1504108), the Application Foundation and Advanced Technology Research Program of Henan Province (Grant No. 152300410167).

References

1. A. Alavi, P. Hu, T. Deutsch, P. L. Silvestrelli and J. Hutter, Phys. Rev. Lett., 1998, 80, 3650–3653.
2. M. Ackermann, T. Pedersen, B. Hendriksen, O. Robach, S. Bobaru, I. Popa, C. Quiros, H. Kim, B. Hammer, S. Ferrer and J. W. M. Frenken, Phys. Rev. Lett., 2005, 95, 255505.
3. C. Zhang and P. Hu, J. Am. Chem. Soc., 2001, 123, 1166–1172.
4. A. A. Herzing, C. J. Kiely, A. F. Carley, P. Landon and G. J. Hutchings, Science, 2008, 321, 1331–1335.
5. S. H. Oh and G. B. Hoflund, J. Catal., 2007, 245, 35–44.
6. X. Xie, Y. Li, Z. Q. Liu, M. Haruta and W. Shen, Nature, 2009, 458, 746–749.
7. Z. P. Liu, X. Q. Gong, J. Kohanoff, C. Sanchez and P. Hu, Phys. Rev. Lett., 2003, 91, 266102.
8. X. Q. Gong, Z. P. Liu, R. Raval and P. Hu, J. Am. Chem. Soc., 2004, 126, 8–9.
9. L. Molina and B. Hammer, Phys. Rev. Lett., 2003, 90, 206102.
10. I. Nakai, H. Kondoh, K. Amemiya, M. Nagasaka, A. Nambu, T. Shimada and T. Ohta, J. Chem. Phys., 2004, 121, 5035.
11. M. Nagasaka, H. Kondoh, I. Nakai and T. Ohta, J. Chem. Phys., 2007, 126, 044704.
12. M. Chen, Y. Cai, Z. Yan, K. Gath, S. Axnanda and D. W. Goodman, Surf. Sci., 2007, 601, 5326–5331.
13. X. Liu, A. Wang, X. Wang, C. Y. Mou and T. Zhang, Chem. Commun., 2008, 27, 3187–3189.
14. S. N. Rashkeev, A. R. Lupini, S. H. Overbury, S. J. Pennycook and S. T. Pantelides, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 035438.
15. C. Chang, C. Cheng and C. Wei, J. Chem. Phys., 2008, 128, 124710.
16. N. Lopez and J. K. Nørskov, J. Am. Chem. Soc., 2002, 124, 11262–11263.
17. H. Falsig, B. Hvolbak, I. S. Kristensen, T. Jiang, T. Bligaard, C. H. Christensen and J. K. Norskov, Angew. Chem., 2008, 120, 4913–4917.
18. B. Kalita and R. C. Deka, J. Am. Chem. Soc., 2009, 131, 13252–13254.
19. H. Kim, S. Han, J. Ryu and H. Lee, J. Phys. Chem. C, 2010, 114, 3156–3160.
20. S. Dobrin, Phys. Chem. Chem. Phys., 2012, 14, 12122–12129.
21. B. H. Morrow, D. E. Resasco, A. Striolo and M. B. Nardelli, J. Phys. Chem. C, 2011, 115, 5637–5647.
22. W. Liu, Y. Zhao, R. Zhang, Y. Li, E. J. Lavernia and Q. Jiang, ChemPhysChem, 2009, 10, 3295–3302.
23. C. Liu, Y. Tan, S. Lin, H. Li, X. Wu, L. Li, Y. Pei and X. C. Zeng, J. Am. Chem. Soc., 2013, 135, 2583–2595.
24. X.-F. Yang, A. Wang, B. Qiao, J. Li, J. Liu and T. Zhang, Acc. Chem. Res., 2013, 46, 1740–1748.
25. D. Ma, Z. Wang, H. Cui, J. Zeng, C. He and Z. Lu, Sens. Actuators, B, 2016, 224, 372–380.
26. F. Li, Y. Li, X. C. Zeng and Z. Chen, ACS Catal., 2015, 5, 544–552.
27. D. Ma, Q. Wang, T. Li, Z. Tang, G. Yang, C. He and Z. Lu, J. Mater. Chem. C, 2015, 3, 9964–9972.
28. C. Du, H. Lin, B. Lin, Z. Ma, T. Hou, J. Tang and Y. Li, J. Mater. Chem. A, 2015, 3, 23113–23119.
29. B. Qiao, A. Wang, X. Yang, L. F. Allard, Z. Jiang, Y. Cui, J. Liu, J. Li and T. Zhang, Nat. Chem., 2011, 3, 634–641.
30. D. Deng, K. S. Novoselov, Q. Fu, N. Zheng, Z. Tian and X. Bao, Nat. Nanotechnol., 2016, 11, 218–230.
31. A. Geim and K. Novoselov, Nat. Mater., 2007, 6, 183–191.
32. C. Lee, X. Wei, J. W. Kysar and J. Hone, Science, 2008, 321, 385–388.
33. K. Novoselov, A. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grigorieva, S. Dubonos and A. Firsov, Nature, 2005, 438, 197–200.
34. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao and C. N. Lau, Nano Lett., 2008, 8, 902–907.
35. C. Huang, C. Li and G. Shi, Energy Environ. Sci., 2012, 5, 8848–8868.
36. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung and E. Tutuc, Science, 2009, 324, 1312.
37. Y. Tang, Z. Yang and X. Dai, J. Nanopart. Res., 2012, 14, 844.
38. Y. Tang, Z. Lu, W. Chen, W. Li and X. Dai, Phys. Chem. Chem. Phys., 2015, 17, 11598–11608.
39. E. Yoo, T. Okata, T. Akita, M. Kohyama, J. Nakamura and I. Honma, Nano Lett., 2009, 9, 2255–2259.
40. R. Siburian and J. Nakamura, J. Phys. Chem. C, 2012, 116, 22947–22953.
41. E. Yoo, T. Okada, T. Akita, M. Kohyama, I. Honma and J. Nakamura, J. Power Sources, 2011, 196, 110–115.
42. G. Chen, S. J. Li, Y. Su, V. Wang, H. Mizuseki and Y. Kawazoe, J. Phys. Chem. C, 2011, 115, 20168–20174.
43. B. Seger and P. Kamat, J. Phys. Chem. C, 2009, 113, 7990–7995.
44. N. Cuong, A. Sugiyama, A. Fujiwara, T. Mitani and D. Chi, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 235417.
45. Q. Tang, Z. Zhou and Z. Chen, Nanoscale, 2013, 5, 4541–4583.
46. A. Kasry, M. A. Kuroda, G. J. Martyna, G. S. Tulevski and A. A. Bol, ACS Nano, 2010, 4, 3839–3844.
47. M. N. Groves, C. Malardier-Jugroot and M. Jugroot, J. Phys. Chem. C, 2012, 116, 10548–10556.
48. F. Li, J. Zhao and Z. Chen, J. Phys. Chem. C, 2012, 116, 2507–2514.
49. M. N. Groves, A. S. W. Chan, C. Malardier-Jugroot and M. Jugroot, Chem. Phys. Lett., 2009, 481, 214–219.
50. H. M. Jeong, J. W. Lee, W. H. Shin, Y. J. Choi, H. J. Shin, J. K. Kang and J. W. Choi, Nano Lett., 2011, 11, 2472–2477.
51. X. Zhang, Z. Lu, G. Xu, T. Wang, D. Ma, Z. Yang and L. Yang, Phys. Chem. Chem. Phys., 2015, 17, 20006–20013.
52. Y. Tang, Z. Yang, X. Dai, D. Ma and Z. Fu, J. Phys. Chem. C, 2013, 117, 5258–5268.
53. A. Krasheninnikov, P. Lehtinen, A. Foster, P. Pyykkö and R. Nieminen, Phys. Rev. Lett., 2009, 102, 126807.
54. O. Cretu, A. V. Krasheninnikov, J. A. Rodríguez-Manzo, L. Sun, R. M. Nieminen and F. Banhart, Phys. Rev. Lett., 2010, 105, 196102.
55. J. Rodriguez-Manzo, O. Cretu and F. Banhart, ACS Nano, 2010, 4, 3422–3428.
56. Y. N. Tang, Z. X. Yang and X. Q. Dai, J. Chem. Phys., 2011, 135, 224704.
57. E. J. G. Santos, D. Sanchez-Portal and A. Ayuela, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 81, 125433.
58. E. J. G. Santos, A. Ayuela and D. Sánchez-Portal, New J. Phys., 2010, 12, 053012.
59. Y. Mao and J. Zhong, Nanotechnology, 2008, 19, 205708.
60. A. Ambrosi, S. Y. Chee, B. Khezri, R. D. Webster, Z. Sofer and M. Pumera, Angew. Chem., Int. Ed., 2012, 51, 500–503.
61. J. A. Rodriguez-Manzo and F. Banhart, Nano Lett., 2009, 9, 2285–2289.
62. Y. J. Gan, L. T. Sun and F. Banhart, Small, 2008, 4, 587–591.
63. H. Wang, Q. Wang, Y. Cheng, K. Li, Y. Yao, Q. Zhang, C. Dong, P. Wang, U. Schwingenschlögl, W. Yang and X. X. Zhang, Nano Lett., 2012, 12, 141–144.
64. Y. Lu, M. Zhou, C. Zhang and Y. Feng, J. Phys. Chem. C, 2009, 113, 20156–20160.
65. Y. Li, Z. Zhou, G. Yu, W. Chen and Z. Chen, J. Phys. Chem. C, 2010, 114, 6250–6254.
66. E. H. Song, Z. Wen and Q. Jiang, J. Phys. Chem. C, 2011, 115, 3678–3683.
67. Y. Tang, Z. Yang and X. Dai, Phys. Chem. Chem. Phys., 2012, 14, 16566–16572.
68. T.-T. Jia, C.-H. Lu, Y.-F. Zhang and W.-K. Chen, J. Nanopart. Res., 2014, 16, 1–11.
69. Q. G. Jiang, Z. M. Ao, S. Li and Z. Wen, RSC Adv., 2014, 4, 20290–20296.
70. H. Liu, B. Wang, M. Fan, N. Henson, Y. Zhang, B. F. Towler and H. G. Harris, Fuel, 2013, 113, 712–718.
71. Y. Tang, X. Dai, Z. Yang, Z. Liu, L. Pan, D. Ma and Z. Lu, Carbon, 2014, 71, 139–149.
72. Z. Lu, S. Li, P. Lv, C. He, D. Ma and Z. Yang, Appl. Surf. Sci., 2016, 360, 1–7.
73. L. Xin, S. Yanhui, D. Ting, M. Changong and H. Yu, Phys. Chem. Chem. Phys., 2014, 16, 23584–23593.
74. M. Ugeda, D. Fernández-Torre, I. Brihuega, P. Pou, A. Martínez-Galera, R. Pérez and J. Gómez-Rodríguez, Phys. Rev. Lett., 2011, 107, 116803.
75. F. Banhart, J. Kotakoski and A. V. Krasheninnikov, ACS Nano, 2011, 5, 26–41.
76. M. T. Lusk and L. D. Carr, Phys. Rev. Lett., 2008, 100, 175503.
77. A. Barinov, H. Ustunel, S. Fabris, L. Gregoratti, L. Aballe, P. Dudin, S. Baroni and M. Kiskinova, Phys. Rev. Lett., 2007, 99, 46803.
78. A. Hashimoto, K. Suenaga, A. Gloter, K. Urita and S. Iijima, Nature, 2004, 430, 870–873.
79. D. H. Lim and J. Wilcox, J. Phys. Chem. C, 2011, 115, 22742–22747.
80. S. Kattel, P. Atanassov and B. Kiefer, J. Phys. Chem. C, 2012, 116, 8161–8166.
81. A. W. Robertson, B. Montanari, K. He, J. Kim, C. S. Allen, Y. A. Wu, J. Olivier, J. Neethling, N. Harrison and A. I. Kirkland, Nano Lett., 2013, 13, 1468–1475.
82. G. Kresse and J. Furthmüller, Comput. Mater. Sci., 1996, 6, 15–50.
83. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
84. G. Kresse and D. Joubert, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758–1775.
85. J. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
86. J. Carlsson and M. Scheffler, Phys. Rev. Lett., 2006, 96, 46806.
87. G. Henkelman, A. Arnaldsson and H. Jónsson, Comput. Mater. Sci., 2006, 36, 354–360.
88. G. Henkelman, B. Uberuaga and H. Jónsson, J. Chem. Phys., 2000, 113, 9901–9904.
89. G. Henkelman and H. Jónsson, J. Chem. Phys., 2000, 113, 9978–9985.
90. T. Zhu, J. Li and S. Yip, Phys. Rev. Lett., 2004, 93, 25503.
91. Z. W. Chen, J. M. Yan, W. T. Zheng and Q. Jiang, Sci. Rep., 2015, 5, 11230.
92. Y. Tang, L. Pan, W. Chen, C. Li, Z. Shen and X. Dai, Appl. Phys. A, 2015, 119, 475–485.
93. Y. Tang, X. Dai, Z. Yang, L. Pan, W. Chen, D. Ma and Z. Lu, Phys. Chem. Chem. Phys., 2014, 16, 7887–7895.
94. Y. Tang, D. Ma, W. Chen and X. Dai, Sens. Actuators, B, 2015, 211, 227–234.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra14476d

---