Methanol oxidation on Ru(0001) for direct methanol fuel cells: analysis of the competitive reaction mechanism

Abstract

The competitive oxidation reaction mechanism of methanol on the Ru(0001) surface has been investigated by periodic density functional theory (DFT). Stable adsorption configurations, elementary reaction energies and barriers, the potential energy surface (PES), and the electrochemical potential analysis were elucidated. The results showed that O–H bond activation was more competitive than C–H and C–O bond activation during the initial methanol oxidation. Competitive pathways occurred for CH₃OH oxidation to CH₂O via CH₃OH → CH₃O → CH₂O versus CH₃OH → CH₂OH → CH₂O, further to COOH via the CO pathway CH₂O → CHO → CO → COOH versus the non-CO pathway CH₂O → CH₂OOH → CHOOH → COOH, and finally oxidation to CO₂. Taking PES and the electrochemical potential analysis into account, CH₃OH → CH₂OH → CH₂O → CH₂OOH → CHOOH → COOH → CO₂ appeared to be the preferred oxidation pathway. The OH group could inhibit CO formation by directly reacting with CH₂O to yield CH₂OOH but could not efficiently remove the CO that had already been produced by the reactions.

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1. Introduction

Direct methanol fuel cells (DMFCs) have attracted widespread attention as clean, portable, and high-efficiency energy conversion devices that utilize methanol (CH₃OH) oxidation reactions on catalysts. A large number of investigations have been performed to explore the catalysis mechanisms of CH₃OH on various pure metals, such as Ni,^1,2 Cu,^3,4 Ag,⁵ Pd,^6–10 Pt,^11–13 Rh,^14,15 and Ru.^16–19 Among these metals, Ru is generally applied as one of the main components of commercial catalysts in DMFC anodes, which can alleviate the problem of poor anode durability due to CO poisoning.^20–24 To achieve rational modification on the anode catalysts, many efforts have been devoted to understanding the CH₃OH oxidation mechanism on Ru catalysts experimentally. Unfortunately, although these studies were performed by using the same infrared absorption spectroscopy, conflicting evidence on adsorption and the reaction mechanism of CH₃OH oxidation have been observed on clean^16,17 and O-precovered^25,26 Ru(0001) surfaces. For the adsorption of reaction intermediates, Barros et al.¹⁷ found upright and tilted methoxy (CH₃O) and formaldehyde (CH₂O); while Gazdzicki et al.¹⁹ proposed an upright configuration of CH₃O. For CH₃OH oxidation, Gazdzicki et al.^18,19 found that CH₃OH was adsorbed as an intact molecule on clean and O-precovered Ru(0001) at temperatures below 80 K, while CH₃O was detected when annealing to 200–220 K; however, Barros et al.²⁷ observed spontaneous O–H bond breakage to form CH₃O for CH₃OH at 80 K. Although these contradictions exist, researchers generally agreed that CH₃OH could easily dehydrogenate on clean Ru(0001), leaving CO on its surface.^16,17

From the theoretical point of view, CH₃OH oxidation on several clean metal surfaces has been investigated.^{2,8,10–12,28–33} On Ni(111),² the favorable pathway of CH₃OH decomposition involved initial O–H bond scission, followed by sequential hydrogen abstractions to achieve the final products CO and H via CH₂O and CHO. On Pt(111),^11,12 the C–H bond scission of CH₃OH was the primary reaction process relative to the O–H bond scission, and the route CH₃OH → CH₂OH → CHOH → CO was suggested as the competitive pathway. On Pd(111), Schennach et al.⁸ and Jiang et al.¹⁰ found that initial C–H bond scission is preferable to that on Pt(111); by contrast, Zhang et al.⁶ compared initial O–H and C–O bond scissions processes and found that O–H bond scission was energetically favorable. Despite difference in the bond scission mechanisms involved, production CO on clean metal surfaces appeared to be unavoidable. When considering the electrochemical environment induced by introduction of the OH group, theoretical calculations showed that CO poisoning could be alleviated by further oxidizing to CO₂ via CO + OH → COOH → CO₂ + H, which is regarded as “the CO pathway”,^28–30 and/or by “the non-CO pathway” along CHO + OH → CHOOH → CO₂ + 2H.^31–33 Although Ru has been widely used in commercial DMFC anodes, the CH₃OH oxidation mechanism on Ru surfaces remains unclear because of contradictions observed in previous experiments and the lack of theoretical studies. Therefore, more details, including the most stable adsorption configuration, competitive reaction activation process, reaction thermodynamics and kinetics, and selectivity of production, are required to achieve a better understanding of CH₃OH oxidation on Ru catalyst.

In this work, the competitive oxidation reaction mechanism of methanol on Ru(0001) surface was investigated by using periodic density functional theory (DFT). The Ru(0001) surface is selected because it is thermodynamically stable and commonly used as a model system.^17,18 All possible adsorption structures and energies, elementary reaction steps, potential energy surface, and electrochemical potential analysis were elucidated along the competitive pathways from CH₃OH to CH₂OH, COOH, and CO₂. The findings of this study are expected to provide deeper insights into the catalytic performance of Ru, adsorption selectivity, sequence of bond scission, competition of elementary reaction processes, thermodynamic and kinetic properties, and thus highlight the intrinsic characteristics of methanol oxidation on Ru(0001) in DMFCs.

2. Computational methods

All calculations were performed in the DFT framework with DMol³ in Materials Studio (Accelrys Inc.).³⁴ The exchange-correlation energy was calculated within the generalized gradient approximation (GGA) using Perdew and Wang (PW91) functional.^35,36 To take the relativity effect into account, the density functional semicore pseudopotential (DSPP)^37,38 method was employed for Ru atoms, and C, H and O atoms were treated with the all-electron basis set. The valence electron functions were expanded into a set of numerical atomic orbitals by a double-numerical basis with polarization functions (DNP). Fermi smearing of 0.005 Hartree and a real-space cutoff of 4.7 Å were used to improve the computational performance.^39,40 Transition state (TS) searches were performed at the same theoretical level by using the complete LST/QST method.⁴¹ The convergence criterion for the TS searches was set to 0.272 eV Å⁻¹ for the root-mean-square of atomic forces. Vibrational frequencies were calculated for all the initial states (ISs) and final states (FSs), as well as the TSs from the Hessian matrix with harmonic approximation. Zero-point energy (ZPE) was calculated from the resulting frequencies.⁴²

Ru(0001) surface was modeled with a three-layer slab with nine Ru atoms per layer representing a (3 × 3) surface unit cell; a vacuum region of 12 Å thickness was used to separate the surface from its periodic image in the direction along the surface normal. The reciprocal space was sampled with a (4 × 4 × 2) k-point grid using the Monkhorst–Pack method.⁴³ A single adsorbate was allowed to adsorb on one side of the unit cell, corresponding to a surface coverage of 1/9 ML. Full-geometry optimization was performed for relevant adsorbates and the uppermost two layers without symmetry constraints, while the bottom layer Ru atoms were fixed to their bulk-truncated positions with the experimentally determined lattice parameters of a = b = 2.71 Å and c = 4.28 Å. Nonperiodical structures were fully optimized at the same theoretical level for the isolated atoms, radicals and molecules involved.

The adsorption energies reported herein are calculated using the equation:

E_ads = E_adsorbate + E_M − E_adsorbate/M (1)

where E_ads is the adsorption energy of the adsorbate on the metal surface; E_adsorbate, E_M and E_adsorbate/M are the energies of the free adsorbate, the clean Ru(0001) slab, and the adsorbate/M adsorption system, respectively. By this definition, the stable adsorption will have a positive adsorption energy.

3. Results and discussion

For clarity, this section is organized as follows: first, adsorption structures and energies for most of the intermediates are presented. Then, the possible elementary reactions along with the relevant reaction network are elucidated. Next, the overall PES for competitive pathways is discussed. Finally, the CH₃OH electrooxidation process on Ru(0001) is analyzed. All energies reported herein are with ZPE corrections.

3.1 Adsorption

Table 1 tabulates the adsorption information for the most stable adsorption modes of intermediates involved, and the corresponding configurations are shown in Fig. 1. Structural parameters and geometries of other intermediates are presented in Table S1 and Fig. S1 (ESI†).

Table 1 Adsorption sites, adsorption energies (in eV), and structural parameters (in angstroms and degrees) for intermediates involved in CH₃OH oxidation on Ru(0001)

Species	Site	Mode	Eads	dC/H–Ru	dO–Ru	Angles^a
a Values are angles between the surface normal and the C–O axis in the corresponding species.
CH3OH*	Top	η^1(O)	0.56		2.31	53
CH2OH*	Bridge	η^1(C)–η^1(O)	1.98	2.14	2.28	90
CH3O*	fcc	η^3(O)	2.52		2.20, 2.20, 2.20	0
	hcp	η^3(O)	2.54		2.19, 2.19, 2.19	0
CH2O*	Top	η^1(O)	0.45		2.20	49
	fcc	η^1(C)–η^2(O)	0.90	2.15	2.20, 2.20	79
	hcp	η^1(C)–η^2(O)	0.96	2.15	2.18, 2.18	79
CHO*	Bridge	η^1(C)–η^1(O)	2.44	1.99	2.19	81
	fcc	η^2(C)–η^1(O)	2.26	2.12	2.15, 2.19	76
	hcp	η^2(C)–η^1(O)	2.36	2.11	2.13, 2.17	76
CO*	Top	η^1(C)	1.93	1.89		0
	Bridge	η^2(C)	1.66	2.08, 2.08		0
	fcc	η^3(C)	1.70	2.15, 2.16, 2.17		0
	hcp	η^3(C)	1.71	2.14, 2.14, 2.15		0
CH2OOH*	fcc	η^1(O)–η^2(O)	2.73		2.24, 2.22, 2.22	42, 67
	hcp	η^1(O)–η^2(O)	2.77		2.32, 2.19, 2.21	43, 72
CHOOH*	fcc	η^1(C)–η^2(O)	0.62	2.19	2.10, 2.28	87, 90
	hcp	η^1(C)–η^2(O)	0.66	2.18	2.09, 2.27	88, 90
trans-COOH*	Bridge	η^1(C)–η^1(O)	2.69	2.05	2.20	33, 83
cis-COOH*	Bridge	η^1(C)–η^1(O)	2.68	2.05	2.21	31, 85
CO2*	Bridge	η^1(C)–η^1(O)	0.05	2.10	2.22	59, 79
OH*	Top	η^1(O)	2.84		1.99
	Bridge	η^2(O)	3.14		2.16, 2.16
	fcc	η^3(O)	3.19		2.21, 2.21, 2.21
	hcp	η^3(O)	3.19		2.20, 2.20, 2.20
H*	Bridge	η^2(H)	2.80	1.82, 1.82
	fcc	η^3(H)	2.91	1.90, 1.91, 1.92
	hcp	η^3(H)	2.87	1.90, 1.91, 1.92

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Fig. 1 The most stable adsorption configurations of intermediates involved in CH₃OH oxidation on Ru(0001). The C, O, H, and Ru atoms are shown in gray, red, white, and light-blue colors, respectively.

Methanol (CH₃OH). For gas-phase CH₃OH, the bond lengths are calculated to be 1.10 Å for the C–H bonds, 1.43 Å for the C–O bond, and 0.97 Å for the O–H bond, in good agreement with the experimental values of 1.09, 1.43, and 0.95 Å, respectively.⁴⁴ CH₃OH can be stabilized on Ru(0001) without spontaneous decomposition, thus confirming the experimental observation.^18,19 CH₃OH prefers the adsorption at top site of Ru(0001) through oxygen via donation of the lone pair to metallic surfaces^45,46 with the O–Ru distance of 2.31 Å, as shown in Fig. 1 and Table 1. The C–O axis tilts by 53° relative to the surface normal, thereby facilitating binding of CH₃OH to the surface via the oxygen lone pair orbital.⁴⁷ The adsorption energy is calculated to be 0.56 eV; this relatively weak adsorption is consistent with the large O–Ru distance as well as the small structural deformation of CH₃OH upon adsorption. Similar adsorption configurations of CH₃OH can be found on Ni(111),² Pt(111),¹² and Pd(111).¹⁰

Hydroxymethyl (CH₂OH). CH₂OH is obtained from CH₃OH dehydrogenation via C–H bond scission, and tends to adsorb at bridge site through the η¹(C)–η¹(O) mode. The C–O axis is almost parallel to the surface, and the C–Ru and O–Ru distances are 2.14 and 2.28 Å, respectively. The adsorption energy is calculated to be 1.98 eV. Different from that on Ru(0001), CH₂OH on Ni(111),² Pt(111),¹² and Pd(111)¹⁰ prefers to adsorb at top site of the metal atom through the C atom.

Methoxy (CH₃O). The initial O–H bond breaking of CH₃OH produces CH₃O. CH₃O prefers to bind at hollow (hcp) site in an upright configuration, as shown in Fig. 1. This finding agrees well with the IR spectral observation that CH₃O is adsorbed in a C_3v symmetry with the C–O axis parallel to the surface normal.¹⁷ The O–Ru bond length is calculated to be 2.19 Å, in good agreement with Gazdzicki's experimental result of 2.19 Å.¹⁹ The binding energy is 2.54 eV, as shown in Table 1. These results agree well with the previous DFT study of CH₃O adsorption on Ru cluster,⁴⁸ wherein CH₃O was observed to locate at hollow site in an upright configuration with a binding energy of 2.39 eV.

Formaldehyde (CH₂O). CH₂O is an important intermediate in CH₃OH decomposition and synthesis.⁴⁹ Our calculations show that CH₂O tends to anchor on the Ru(0001) surface at hollow site via the η¹(C)–η²(O) mode, as shown in Fig. 1. The C–Ru bond length is 2.15 Å, and the two O–Ru bond lengths are both 2.18 Å; the C–O axis is titled by 79° relative to the normal of the substrate (Table 1). The adsorption energy is calculated to be 0.96 eV. On Rh(111), the η¹(C)–η²(O) mode of CH₂O is also the most stable structure with a binding energy of 0.98 eV.¹⁵ On group VIII metal surfaces, CH₂O generally adsorbs via the η¹(C)–η¹(O) mode,⁴⁵ stabilizing the system by 0.45–0.63 eV on Pd(111),^8–10 0.50 eV on Pt(111),^11,12 and 1.03 eV on Ni(111).²

Formyl (CHO). The most stable configuration of CHO favors the η¹(C)–η¹(O) adsorption mode at bridge site. As shown in Fig. 1, CHO binds to the metal surface through C and O atoms anchored at two adjacent top sites; the C–Ru and O–Ru bond lengths are 1.99 and 2.19 Å, respectively. The adsorption energy is calculated to be 2.44 eV. On Pt(111)¹¹ and Pd(111),¹⁰ CHO prefers to bind at hollow site with an η²(C)–η¹(O) mode, where the C atom sits over a bridge site and the O atom on top of an adjacent Pd atom.

CH₂OOH, formic acid (CHOOH) and carboxyl (COOH). CH₂OOH is generated by the association of CH₂O with OH, which prefers to adsorb at hcp site via two O atoms. One O atom binds at top site while the other at bridge site, and the CH₂ group is repelled away from the surface. The distances between O atoms and the surface Ru atoms are 2.32, 2.19 and 2.21 Å, respectively. The O–C–O angle is calculated to be 113°, and the adsorption energy is 2.77 eV. CHOOH binds at hcp site with the η¹(C)–η²(O) mode. The C–H bond is located away from the surface whereas the O–H bond is parallel to the surface. The adsorption energy of CHOOH is calculated to be 0.66 eV. COOH is stabilized over bridge site via the η¹(C)–η¹(O) mode. Two opposite orientations of O–H bond lead to two stable isomers of COOH: trans-COOH (Fig. 1) and cis-COOH (Fig. S1†) with the binding energies of 2.69 and 2.68 eV, respectively. The adsorption configuration of trans-COOH characterizes bond lengths of 2.20 and 2.05 Å for the O–Ru and C–Ru bonds, respectively.

Carbon monoxide (CO) and carbon dioxide (CO₂). CO prefers to vertically occupy top site on the Ru(0001) surface via the C atom. The C–Ru bond length is 1.89 Å and the adsorption energy is 1.93 eV. CO tends to bind at hollow site on Pd(111)¹⁰ and Pt(111)¹³ with adsorption energies of about 1.80 and 1.74 eV, respectively. CO₂ locates at bridge site on Ru(0001) with an adsorption energy as low as 0.05 eV; such an energy indicates easy desorption of CO₂ from the surface. The C–Ru and O–Ru bond lengths are 2.10 and 2.22 Å, respectively.

Hydroxyl (OH) and hydrogen (H). OH can stably locate at hollow site through the O atom with an upright configuration. OH has the same adsorption energy of 3.19 eV for both hcp and fcc sites. Koper et al.¹³ studied OH binding on Ru(0001) using the DFT slab model and obtained adsorption energies of 3.52 and 3.49 eV for stable adsorption at fcc and hcp sites, respectively. Atomic H is energetically favored to adsorb at hollow site on the Ru(0001) surface, consistent with the results of a previous electron energy loss spectroscopy study.⁵⁰ The adsorption energy of atomic H is 2.91 eV, agreeing well with previous DFT study of H adsorption on a Ru surface (E_ads = 2.90 eV).⁵¹

3.2 Initial oxidation of CH₃OH to CH₂O

The reaction network of CH₃OH oxidation on Ru(0001) is shown in Fig. 2. Structures of IS, TS, and FS along elementary reaction steps are presented in Fig. 3–6. As a whole, CH₃OH dehydrogenates to CH₂O via the competitive routes of CH₃OH → CH₃O → CH₂O and/or CH₃OH → CH₂OH → CH₂O (Fig. 3), then further oxidizes to trans-COOH via the CO pathway CH₂O → CHO → CO → COOH (Fig. 4) and/or the non-CO pathway CH₂O → CH₂OOH → CHOOH → COOH (Fig. 5), and achieve CO₂ eventually (Fig. 6). For brevity, other elementary reaction steps with relatively high energy barriers are described in Fig. S2,† including the C–O bond scissions of CH₃OH, CH₃O, CH₂OH, CH₂O, and CHO, the combination of CHO and OH to CHOOH, the reaction of CO with OH to cis-COOH, the dehydrogenation of CH₂OOH to CH₂OO, and further dehydrogenation to CHOO.

Fig. 2 The reaction network for CH₃OH oxidation on Ru(0001). “A–B” represents the “A–B” bond scission and “+OH” means the combination with OH group. The energy barrier and reaction energy (in parentheses) are in eV. For simplicity, the H atom is omitted.

Fig. 3 Dehydrogenation of CH₃OH to CH₂O through CH₃OH → CH₃O → CH₂O (a and c) and CH₃OH → CH₂OH → CH₂O (b and d). [A + B]* denotes the coadsorbed A and B species.

Fig. 4 The CO pathway for CH₂O oxidation to trans-COOH.

Fig. 5 The non-CO pathway for CH₂O oxidation to trans-COOH.

Fig. 6 Formation of CO₂ via dehydrogenation of trans-COOH.

Three possible initial bond scissions of CH₃OH are considered, that is, O–H, C–H and C–O bond scissions. C–O bond scission involves a very high energy barrier of 1.68 eV, whereas O–H bond scission involves a relatively low energy barrier of 0.56 eV. The reaction CH₃OH → CH₃O + H leads to elongation of the O–H bond length to 2.10 Å in TS1 (Fig. 3a) relative to 0.98 Å in IS and yields coadsorbed CH₃O and H atom on adjacent hcp sites as FS. As shown in Fig. 3b, C–H bond scission is mirrored by an elongated C–H bond length of 1.58 Å in TS2, together with the CH₂OH group bending towards the surface and the H atom moving to adjacent bridge site. The energy barrier of CH₃OH → CH₂OH + H is 0.83 eV. The reaction process of CH₃OH → CH₃ + OH is presented in Fig. S2.† The activation energies of the C–H and C–O bonds are higher than that of the O–H bond, indicating that initial O–H bond scission of CH₃OH is highly favorable on Ru(0001). During initial oxidation of CH₃OH, O–H bond scission is also preferable on Cu(111)⁵² and Ag(111),⁵ while C–H bond scission is more facile on Pd(111) and Pt(111).^53,54

Subsequently, C–H bond scission of CH₃O starts with its most stable configuration at hcp site and ends with CH₂O at hcp site and H atom at fcc site, as shown in Fig. 3c. In TS3, the C–O axis tilts towards the surface with the O atom above bridge site, thereby facilitating the C–H bond scission. The energy barrier is calculated to be 1.01 eV and the reaction is exothermic by 0.07 eV. For CH₂OH, C–H bond scission involves a high energy barrier of 1.07 eV relative to the 0.76 eV of its O–H bond scission. As shown in Fig. 3d, O–H bond scission of CH₂OH yields CH₂O at fcc site and the H atom at hcp site. The O–H bond length is elongated to 1.48 Å in TS4, and a slight swag vibration facilitates removal of the H atom.

3.3 CH₂O oxidation to COOH via the CO pathway

As shown in Fig. 4a, dehydrogenation of CH₂O to CHO involves rotation of CH₂O along the C–O bond axis, so that one of the H atoms can easily approach a surface Ru atom and form a Ru–H bond. This process is exothermic by 0.48 eV and the energy barrier is 0.53 eV. By comparison, C–O bond scission requires a higher energy barrier of 1.26 eV, as shown in Fig. S2c and Table S1.†

Fig. 4b illustrates that dehydrogenation of CHO starts with CHO binding at bridge site in IS and ends with CO sitting atop a Ru atom in FS. In TS5, CHO is located at off-top site and the C–H bond is elongated by 0.10 Å; C–H bond scission is triggered by a swag vibration of the adsorbed CHO, giving rise to the H atom close to the surface. This process is strongly exothermic by 1.17 eV with a relatively low energy barrier of 0.34 eV. Comparatively, C–O bond scission and combination of CHO with OH to form CHOOH involve energy barriers of up to 1.62 and 1.92 eV, respectively, as shown in Fig. S2c, d and Table S1.†

Oxidation of the adsorbed CO by OH can produce trans-COOH and cis-COOH in FS. The energy barriers for these reaction steps are as high as 1.74 and 2.07 eV, respectively. To achieve the formation of trans-COOH, as shown in Fig. 4c, CO and OH groups approach each other together with the elevation of the OH group in TS6.

3.4 CH₂O oxidation to COOH via the non-CO pathway

CH₂O can react with OH to form CH₂OOH on Pd,⁵³ Ag,^54,55 and Cu.⁵⁶ In the real electrochemical environment of DMFCs, the OH group usually comes from the reaction between coadsorbed H₂O and O_ad (H₂O + O_ad → 2OH)⁵⁷ or direct decomposition of H₂O (H₂O → H + OH). On Ru(0001), the adsorbed CH₂O at hcp site reacts with OH at fcc site in IS and ends with CH₂OOH at hcp site, as shown in Fig. 5a. The binding energy for coadsorbed CH₂O and OH is 5.68 eV, much higher than the sum of their individual adsorption energies of 0.96 eV for CH₂O and 3.19 eV for OH. This result indicates the strong attraction between CH₂O and OH, which stabilizes the coadsorption system so as to further bind these two species. In TS7, the OH group migrates to bridge site, thus facilitating interactions with the elevated CH₂ group in CH₂O. The energy barrier here is 0.97 eV, and the reaction is exothermic by 0.13 eV.

As shown in Fig. 5b, CH₂OOH dehydrogenation via C–H bond scission results in CHOOH located at top site and the H atom at hcp site. In TS8, the C–H bond is broken and the detached H atom sits at top site. This process is exothermic by 0.63 eV, and the energy barrier is 0.24 eV. CH₂OOH dehydrogenation can also proceed via O–H bond scission (Fig. S2g†), that is, CH₂OOH → CH₂OO + H. The barrier here is 0.92 eV and the reaction energy is 0.18 eV.

Fig. 5c illustrates C–H bond scission of CHOOH, which starts with CHOOH located at hcp site and ends with trans-COOH at bridge site and H atom at fcc site. In TS9, the C–H bond distance is elongated by 0.21 Å with the OH group detached from the surface; slight rotation of the C–O bond facilitates the C–H bond scission. This dehydrogenation step is exothermic by 0.72 eV, and the energy barrier is 0.38 eV. O–H bond scission for CHOOH (CHOOH → CHOO + H, Fig. S2h†) involves an energy barrier of 0.61 eV and a reaction energy of 0.54 eV.

3.5 Formation of CO₂

Fig. 6 reveals that stretch vibrations of the O–H bond can induce the H atom of trans-COOH to approach the surface such that trans-COOH decomposes to COO and atomic H. Obviously, O–H bond scission is more likely to take advantage of the downward-facing mode of trans-COOH than the up-facing mode of cis-COOH. In TS10, the CO₂ fragment remains at bridge site while the O–H bond is broken with an O–H distance of 1.53 Å. This process is almost thermoneutral with a reaction energy of 0.01 eV and an energy barrier of 0.96 eV.

3.6 Potential energy surface (PES)

The overall PES of CH₃OH oxidation on Ru(0001) is illustrated in Fig. 7, including three-stage oxidation products of CH₂O, COOH and CO₂. Competitive pathways appear for the first two steps, that is, CH₃OH → CH₃O → CH₂O versus CH₃OH → CH₂OH → CH₂O for CH₂O; and the CO pathway CH₂O → CHO → CO → trans-COOH versus the non-CO pathway CH₂O → CH₂OOH → CHOOH → trans-COOH for COOH.

Fig. 7 PES of CH₃OH oxidation on Ru(0001). All energies (eV) are relative to the energy gaseous molecules of hydroxy and one gaseous molecule of methanol plus the clean Ru(0001) surface with ZPE corrections. [A + B]* denotes the coadsorbed A and B, and A* + B* represents respective adsorptions of A and B on two separated slabs.

For CH₃OH oxidation to CH₂O, the dehydrogenation sequence plays a crucial role in the reaction kinetics via two competitive pathways. Along the CH₃OH → CH₃O → CH₂O pathway, the activation energies of O–H and C–H bond scission are 0.56 and 1.01 eV, respectively. By comparison, along the CH₃OH → CH₂OH → CH₂O pathway, the energy barriers of C–H and O–H bond scissions are 0.83 and 0.76 eV, respectively. Thus, to achieve oxidation of CH₃OH on Ru(0001), initial O–H bond scission (E_a = 0.56 eV) is more facile than the C–H bond scission (E_a = 0.83 eV). Once CH₃O is formed, subsequent C–H bond scission involves a larger barrier of 1.01 eV. Therefore, CH₃O can accumulate to a certain extent on the Ru surface, which explains why CH₃O is consistently detected in the experiments.^18,19 Considering the relative smooth PES, the CH₃OH → CH₂OH → CH₂O pathway is more competitive for forming CH₂O than the CH₃OH → CH₃O → CH₂O pathway.

For CH₂O oxidation to COOH, the energy barriers along the CO pathway are 0.53 eV for CH₂O → CHO, 0.34 eV for CHO → CO, and 1.74 eV for CO + OH → COOH. The rate-determining step along the CO pathway appears to be the combination of CO and co-adsorbed OH to form COOH. By comparison, the energy barriers along the non-CO pathway are 0.97 eV for CH₂O + OH → CH₂OOH, 0.24 eV for CH₂OOH → CHOOH + H, and 0.38 eV for CHOOH → COOH + H. The rate-determining step along the non-CO pathway appears to be the combination of CH₂O and co-adsorbed OH to produce CH₂OOH. Note that the rate-determining steps along both pathways appear when reacting with the coadsorbed OH to form the C–O bond. Comparing these two pathways, CO seems to be easier to form along the CO pathway and accumulate on Ru(0001) because of the high energy barrier required for further combination with OH. However, since the OH group pre-exists in the electrolyte and has a much larger adsorption energy than CO (2.84–3.19 eV for OH versus 1.66–1.93 eV for CO, Table 1), most of the adsorption sites would be covered by OH under working conditions. Thus, the coverage of newly-formed CO is low and the formation of CO on Ru(0001) is inhibited. Comparatively, the non-CO pathway is more favorable and followed by COOH dehydrogenization to form CO₂. Participation of the OH group on Ru(0001) avoid the CO formation during CH₃OH oxidation along the non-CO pathway, but cannot remove the CO that had already been produced because of the very high barriers involved in the transformation of CO + OH → COOH (1.74 eV for trans-COOH and 2.07 eV for cis-COOH).

3.7 Electrochemical potential analysis

The standard hydrogen electrode (SHE)⁵⁸ is used to treat the electrochemical potential (U). The overall electrochemical reaction on the anode of a DMFC is: CH₃OH + H₂O → CO₂ + 6H⁺ + 6e⁻. Under standard conditions, the free energy of two protons and two electrons at zero potential is equal to the free energy of a hydrogen molecule. The change in free energy at a given potential U of a reaction involving the formation of a proton electron pair versus that at the SHE is equivalent to ΔG = −eU, where e is the charge on the electron. Additionally, intermediates that are closed-shell molecules (e.g., CH₃OH and CO₂) are treated as gas-phase molecules, as the bond energy to the surface will be unlikely to overcome the entropy loss through surface binding. Based on this approach, the required lowest potential U can be obtained to discuss the competitive reaction pathways of CH₃OH electro-oxidation on Ru(0001), as successfully applied in similar reactions.^54,58–60 The details of this method refer to the previous literature.^54,59

The free energies of all of the intermediates are calculated relative to H₂O(l), CO₂(g) and H₂(g), as presented in Table 2. The free energy of CH₃OH, for example, is calculated as follows,

CO₂(g) + 3H₂(g) → CH₃OH(g) + H₂O(l) (2)

Table 2 Calculated free energies ΔG (in eV) of adsorbed intermediates and closed-shell gas-phase intermediates at standard conditions (298 K, 1 bar) for CH₃OH electrooxidation on Ru(0001)^a

CH3OH	CH3O	CH2OH	CH2O	H2COOH	CHO	CHOOH	CO	COOH	CO2
a CO2(g), H2O(l), and H2(g) are used as reference. Zero-point energy and entropy corrections are included.
0.10	−0.01	0.32	0.63	0.36	0.16	0.28	−0.79	−0.05	0.00

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ΔG_CH3OH = TE_H2O + TE_CH3OH − TE_CO2 − 3TE_H2 + ZPE_H2O + ZPE_CH3OH − ZPE_CO2 − 3ZPE_H2 − T(S_H2O + S_CH3OH − 3S_H2 − S_CO2), where TE is the total energy of the reactant and product species, T is the standard temperature (298 K), ZPE is the zero-point energy, and S is the entropy of the species. For gas- and liquid-phase molecules, the entropy values are taken from the literature.⁶¹ The free energies of surface intermediates are also calculated in a similar manner, for example,

CO₂(g) + 2.5H₂(g) + * → CH₃O* + H₂O(l) (3)

ΔG_CH3O^* = TE_H2O + TE_CH3O^* − TE_CO2 − 2TE_H2 − TE_clean + ZPE_H2O + ZPE_CH3O^* − ZPE_CO2 − 2.5ZPE_H2 − T(S_H2O + S_CH3O^* − 2.5S_H2 − S_CO2), where TE_clean is the total energy of the clean slab, TE_CH3O^* is the total energy of CH₃O* adsorbed on a clean slab, and ZPE_CH3O^* and S_CH3O^* are the zero-point energy and entropy for the adsorbed CH₃O*, respectively. For molecules bound to the surface, the vibrational entropy is calculated assuming a quantum mechanical harmonic oscillator with the same vibrational frequencies as those applied to the zero-point energy. As shown in Table 2, the free energies for closed-shell gas-phase intermediates are as follows: CH₃OH = 0.10 eV, CH₂O = 0.63 eV, CHOOH = 0.28 eV, and CO₂ = 0.0 eV; these values are comparable with previous DFT results⁵⁴ of 0.11, 0.71 eV, 0.42 eV, and 0.0 eV, respectively. As a reference, the standard table values are: CH₃OH(g) = 0.05 eV, CH₂O(g) = 0.57 eV, CHOOH(g) = 0.44 eV, and CO(g) = 0.0 eV. The negative values of adsorbed CH₃O, CO, and COOH indicate that these surface intermediates are thermodynamically more stable than the reference molecules at standard conditions [i.e., CO₂(g), H₂O(l), and H₂(g) at 298 K and 1 bar pressure]. Of these intermediates, CO has the lowest free energy because of its strong bonding with Ru(0001), as noted previously. Positive values of all other adsorbed intermediates (i.e., CH₂OH, CH₂OOH, and CHO) suggest that the surface species is not as stable as the reference molecules at standard conditions; thus, the reaction to form the reference molecules from the surface species would be exothermic on Ru(0001) at standard conditions.

A comparison of the electrochemical potentials for the competitive reactions on Ru(0001) is shown in Fig. 8. For the initial CH₃OH oxidation processes CH₃OH → CH₃O versus CH₃OH → CH₂OH, a lower potential is required to strip off the hydroxyl proton than that required to strip off the methoxyl proton, in agreement with previous experimental observations.⁶² Similar case takes place for proton stripped from the hydroxyl with a lower potential along the subsequent oxidation to formaldehyde (CH₂OH → CH₂O versus CH₃O → CH₂O). Along the CO pathway CH₂O → CHO → CO → COOH, the highest potential is calculated to be 0.74 V for CO + OH → COOH; by contrast, the non-CO pathway CH₂O → CH₂OOH → CHOOH → COOH requires a much lower potential than 0.74 V. Therefore, at low potentials, CH₃OH electrooxidation on Ru(0001) proceeds primarily via the non-CO pathway to produce CO₂; at high potentials, both the CO and non-CO pathways are thermodynamically available on Ru(0001).

Fig. 8 The electrochemical potentials for CH₃OH oxidation on Ru(0001). The x-axis indicates how many proton/electron pairs have been created from CH₃OH.

4. Conclusions

Our theoretical investigation provides a systematic understanding of the competitive oxidation reaction mechanism of methanol on Ru(0001) surface for DMFCs. The following findings are obtained:

(1) To achieve a stable adsorption configuration, CH₃OH and CO prefer to adsorb at top site, CH₂OH, CHO and COOH prefer to adsorb at bridge site, and CH₃O, CH₂O, CH₂OOH and CHOOH prefer to adsorb at hollow site on the Ru(0001) surface.

(2) O–H bond activation is more competitive than C–H and C–O bonds activations during CH₃OH and CH₂OH oxidation. Competitive oxidation pathways to CH₂O occur via CH₃OH → CH₃O → CH₂O versus CH₃OH → CH₂OH → CH₂O, further to COOH by virtue of OH group via the CO pathway CH₂O → CHO → CO + OH → COOH versus the non-CO pathway CH₂O + OH → CH₂OOH → CHOOH → COOH, and finally oxidation to CO₂. For both the CO and non-CO pathways, the rate-determining step appears to be the C–O bond formation when interacting with the OH group.

(3) PES analysis confirms that CH₃OH → CH₂OH → CH₂O → CH₂OOH → CHOOH → COOH → CO₂ is the preferred pathway, agreeing well with the electrochemical potential analysis for CH₃OH electro-oxidation. The OH group could inhibit CO formation by directly reacting with CH₂O to yield CH₂OOH, but cannot remove the CO that had already been produced.

Acknowledgements

This work was supported by NSFC (21303266), National Basic Research Program of China (2014CB239204), Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (BS2013CL031), and the Fundamental Research Funds for the Central Universities (15CX05050A, 15CX08010A, 14CX02214A).

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Footnote

† Electronic supplementary information (ESI) available: The metastable adsorption configurations, and other elementary reaction steps with relatively high energy barriers in CH₃OH oxidation routes are presented. See DOI: 10.1039/c5ra21793h

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