Oxygen reduction reaction on Platinum using DFT

Introduction

The overall performance of a low temperature proton exchange membrane fuel cell (PEMFC) is limited by the slow kinetics of oxygen reduction reaction (ORR) on platinum (Pt) electrocatalyst at its cathode side [1-3]. Hence, fundamental understanding of the ORR on Pt is important for developing novel catalyst for PEMFC. In PEMFC, Pt is usually supported by graphitic carbon. Nafion® is also introduced into the cathode layer for better proton conduction from the catalyst to the membrane. Hydrogen ion and gaseous oxygen are the reactants. Water is the product and is also supplied directly to the fuel cell to humidify the Nafion® membrane. Hence more than one phase is present in the cathode side which makes any type of modeling a challenge. Moreover, ORR is influenced by the presence of adsorbed anions, the degree of salvation, electric field, the flow rate of reactants etc. Therefore complete modeling of ORR reaction is a huge challenge. Generally, kinetic information is obtained by ex-situ experiment in an electrochemical cell as shown in Figure 1 where the reaction of interest takes place at the working electrode, reference for the measurement of voltage is given by the reference electrode, and the circuit is completed by the counter electrode by providing current.

Figure 1. An electrochemical cell.

General schematic of ORR mechanism is shown in Figure 1 [4]. Figure 1 shows that ORR occurs through two pathways; the direct pathway (O2 + 4H+ +4e-= 2H2O) and an indirect pathway involving via H2O2 (O2 + 2H+ +2e-= H2O2 + 2H+ + 2e- = 2H2O). Oxygen molecule dissociatively adsorbs on Pt at 150 K [5].

Figure 2. General scheme of ORR by Wroblowa [4].

Adsorption of O2 is one of the major steps in ORR. Two types of models are popular for O2 adsorption: End-on adsorption and Bridge model (Figure 4) [5]. The end on adsorption leads to series pathway through H2O2 and bridge adsorption results in direct four electron pathway. Experimental results show that O2 molecule dissociatively adsorbs on Pt (111) at 150-300 K and two types of chemisorbed O2 species are present on Pt (111): superoxo species (O2-) with 2-fold coordination and peroxo species (O22-) [5]. Theoretical studies performed using Vienna ab initio simulation program (VASP) on a four-layer slab seprated by 14 Å vacuum have shown that superoxo species favors flat top-bridge-top (t-b-t) geometry and peroxo species favors slightly canted top-hollow(fcc/hcp)-bridge conformation (t-h-b) [6]. It is theorized that t-b-t conformation favors direct four electron pathway while t-h-b conformation favors series pathway depending upon the surface coverage [5].

Figure 3. Models of O2 adsorption on electrode surfaces (M = metal atom, O = oxygen atom) [5].

Figure 4. Surface adsorption of O2 on Pt (111).

In both direct and indirect pathways, the rate determining step (RDS) is postulated to be (Equation 1);

(1)
\begin{align} M + O _{\rm 2} +H^+(aq) + e^-= M-OOH \end{align}

In this paper, density functional theory (DFT) studies of ORR on cluster model of Pt is discussed. In addition, Car-Parrinello molecular dynamic investigation is also presented. Main focus of these discussions will be the mechanism of RDS on the Pt surface.

2. Effect of Pt cluster on O2 interaction

In literature, there is no agreement on an optimum Pt cluster size to study ORR. From these studies it seems that the activity of Pt cluster depends on its size and the type of reaction taking place. Li et al. has studied O2 interaction with Ptn clusters with n = 2-6 [7]. They employed DFT in Gaussian94 program with B3PW91 functional to describe exchange and correlation. Based on binding energy calculated from Equation 2, different stable structures for Ptn clusters were identified as tabulated in Table 1.

(2)
\begin{align} B. E (Pt _{\rm n}) = [ E (Pt _{\rm n} - n(E _{\rm Pt})]/n, n = 2-6 \end{align}

Table 1: Properties of the most stable Ptn clusters as caculated by Li et al. [7]

 cluster Most stable geometry Binding energy/atom (eV/atom) Electron Affinity (eV) Vertical ionization potential (eV) Pt cell-content cell-content 1.50 (2.12) 8.69 (8.98) Pt2 cell-content -1.15(-1.44/-1.86,1.57) 2.41 (1.89) 8.51(8.68) Pt3 Equilateral triangle -1.87 2.05(1.87) 7.96 Pt4 Tetrahedron -2.17 1.89 6.77 Pt5 Square based pyramid -2.28 2.35 6.97

aExperimental values are in parentheses.

From the Table 2, it can be observed that the Pt-Pt bond strengths increase with the cluster size. The O2 molecule adsorbs at the bridge site where electron transfer takes place from the cluster to the molecule as given by the negative Mulliken charge on the molecule. Both superoxo and peroxo species are identified as the precursor for the O2 dissociation. Superoxo species is formed first when O2 approaches Pt, and then peroxo species forms due to more electron transfer from Pt to the adsorbed superoxo species. The dissociation of O2 depends on the Ptn cluster. Table 2 gives the adsorption energy (Eads), site dissociation energy (DE, site), and activation energy (Ea) for O2 dissociation on Ptn. The adsorption energy is calculated using Equation 3, site dissociation energy is calculated using Equation 4, and activation energy is calculated using Equation 5.

Table 2: Adsorption energy, site dissociation energy, and activation energy for O2 dissociation on Ptn clusters.

 Cluster Eads (eV) DE, site (eV) Ea (eV) Pt2superoxo 0.71 -1.25 0.28 Pt4 rhombus 0.72 -1.24 0.29 Pt5 trigonal bipyramid 0.53 -1.44 0.19 Pt5 square pyramid 0.83 -1.14 0.34
(3)
\begin{align} E _{\rm ads} = -(E _{\rm Pt _{\rm n}, O}-E _{\rm Pt _{\rm n}}-E _{\rm O}) \end{align}
(4)
\begin{align} D _{\rm E, site}=D _{\rm E,gas phase} + 2 E _{\rm ads} (O)-E _{\rm ads} (O _{\rm 2}) \end{align}
(5)
\begin{align} E _{\rm a}= {1\over 2}\left[ {E _{\rm ads}(O)\over 2}+D _{\rm E,site}\right] \end{align}

Where, $E _{\rm Pt _{\rm n}, O}$ is the total energy of the adsorbed substrate and host
$E _{\rm Pt _{\rm n}$is the energy of the bare Ptn cluster
$D _{\rm E,gas phase}$ is the gas-phase dissociation energy
$E _{\rm ads} (O)$is the average of experimental adsorption energy of atomic O on Pt
$E _{\rm ads} (O _{\rm 2})$ is the adsorption energy of O2 on Pt

3. Catlaytic effect of Pt

Like many electrochemical reactions, ORR reactions are potential dependent. In a model by Anderson et al., this dependence is modeled by assuming that the electron transfer takes place by radiationless tunneling when electron chemical potential (μ(Pt)) of donor (Pt) matches to the electron affinity (EA) of the reduction center R (Equation 6) [8].

(6)
\begin{align} U = \mu(D) -4.6 6 \end{align}

Where U is the electrode potential, μ is the electron chemical potential of the electron donor (D) and 4.6 is the thermodynamic work function for the standard hydrogen electrode. The electron affinity is determined the difference in energy of R and R- with same structure and depends on the structure of R. Hence, minimum structure of R is found for where EA (R’) = μ(D) where R’ is the activated structure of R. Now activation energy is given by energy of R’ minus energy of R. The computations were performed using second order Møller-Plesset perturbation theory (MP2). They performed a study on solvated hydrogen ion (H+ OH2 (OH2)2) and O2 bonded to single Pt atom where different bond lengths were varied to represent the transition structures. Four reactions were studied;

(7)
\begin{align} Pt-O _{\rm 2} + H^+ (aq) + e^- = Pt-OOH \end{align}
(8)
$$Pt-OOH + H^+ (aq) + e^-=Pt-OHOH$$
(9)
\begin{align} Pt-OHOH + H^+ (aq) + e^-= Pt-OH + H _{\rm 2}O \end{align}
(10)
\begin{align} Pt-OH + H^+ (aq) + e^-= Pt-OH _{\rm 2} \end{align}

Figure 5 gives the effect of Pt on the reactions (7-9) shown in heavy lines which is compared to the same reactions occurring uncatalyzed in outer-Helmholtz-plane. It shows the overall lowering of the activation energy (Ea) due to Pt. They also provide indirect evidence for the production of H2O2 due to end on adsorption of O2 as the caculated activation energy of Pt-OHOH is high (0.91 eV) while Pt-O bond strength is weak (0.52 eV), so that H2O2 is likely to form rather than reduce.

Figure 5: Catalytic effect of Pt on ORR (Equation 7-9). The heavy lines represent the Pt catalyzed reactions and the dotted lines represent uncatalyzed reactions [8].

4. The rate determining step (RDS)

As already mentioned, the rate determining step is recognized to be first electron reduction step (Equation 1). According to Sidik et al., there is no activation barrier between end on adsorbed O2 molecule and bridge adsorbed O2 on Pt [9]. This study was done using two Pt atom cluster in Gaussian 94 program using B3LYP hybrid DFT. The dependence on electrode potential was modeled similar to Anderson et al. They found that O2 dissociation is not involved in the RDS as the activation barrier for OOH formation is lower than the O2 dissociation barrier, and OOOH easily dissociates. Confirming the experimental results, the first electron reduction is indeed the rate determining step. Proton transfer is involved in the RDS as its electric field increases the EA of the reactant complex (PtOO—H+OH2(OH2)2) which facilitates the reduction. Their activation energy for RDS (0.60 eV) was close to the experimental value of 0.44 eV on Pt (111) in H2SO4 at 1.23 V.

Figure 6. Activation energy for different reactions on Pt2 as computed by Sidik et al. [9].

The role of hydrogen in facilitating electron transfer is further validated by a similar study on Pt5 cluster bonded to O2 molecule by Li et al. [10]. The significance of distance between the adsorbed O2 and the hydrated proton (H3O+) was especially emphasized in this study. Pt was found to stabilize both the adsorbed O2 and H3O+. Formation of PtOOH was characterized by increase of proton-water and decrease of proton-O2Pt5 bond. The charge transfer was evidenced by increase in positive charge on Pt5 cluster and negative charge on adsorbed O2. However, their study suggests that proton transfer might not take part in RDS depending upon the distance between Oads- H+ -Owater; if this distance is below a certain threshold which depends on the degree of solvation, the activation barrier for proton transfer to the adsorbate is too high.

Car-Parrinello molecular dynamics (CPMD) simulation study by Wang et al. [11, 12] shed new light on the RDS mechanism. In CPMD, the motion of nucleus and calculation of electronic ground state through DFT are treated simultaneously through extended Lagragian [13]. The time step for these studies was 0.121 fs and the target temperature was 350 K close to the normal operating temperature of PEMFC (353 K). At the start of the simulation O-O was placed parallel to Pt (111) surface at bridge site configuration. Their results confirm the participation of H+ in RDS, but the proton transfer might precede or follow the electron transfer depending upon the distance between the solvated proton (H3O+(H2O)2) and the unadsorbed O2. IF the distance is less than 3 Å , H+ transfer precede electron transfer and if the distance is 3 Å or more, H+ transfer follow electron transfer. Another interesting finding was the O2 chemisorbs end-on forming H-O-O*, the asterisk symbolizing the site-adsorbed O. Despite popular belief, they have shown that the end-on adsorption does not necessarily favor series pathway.

Figure 7. Snap shots of CPMD simulation of (O2+ H3O+(H2O)2+e-)/Pt(111). Time step=0.121fs. [12]

5. The fate of Pt-OOH

The calculated activation energy for formation of Pt-OOH by many groups (Wang et al. (0.4 V), Sidik et al. (0.4 V)) matches the experimental value 0.4 V at Pt (111) surface in H2SO4.However, the dissociation of Pt-OOH into Pt-OH and Pt-O occurs readily without any activation barrier [11, 12]. The Pt-O*OH is likely to be top-bridge adsorbed species, after dissociation two top sites are formed Pt-O*H and Pt-O* [12]. The OH species moves to bridge site whereas the O remains at top due to formation of hydrogen bond with water and hydroxyl species. Then H+ is transferred to O*H species and forms H2O*. Due to formation of hydrogen bond between H+ from H2O* travels to O* species to give two atop adsorbed O*H species. There is also a possibility of formation of formation of end on adsorbed HOO*H species that can give rise to H2O2 intermediate and provide explanation for series pathway. But the authors found that HOO*H readily dissociates to give one atop adsorbed O*H and another bridge adsorbed O*H species. Also, O*H species formed in later way are relatively unstable than that formed from O* and O*H. Next reduction step occurs on one of the adsorbed O*H species to give H2O*. The last reduction step results in proton and an electron transfer in another O*H species giving two H2O* atop adsorbed species which are bonded to each other by hydrogen bond and are oriented flat to the (111) plane.

Figure 8. Complete ORR according to Wang et al. [12].

6. Future work

As ORR on Pt is such a complicated system as stated earlier, the picture provided by the theoretical computational work is not complete. There exists many conflicting views such as the adsorption of O2. Using CPMD, Wang et al. [12] showed end-on adsorption to occur while many DFT work favor bridge type adsorption to be stable. Also, no one has come up with satisfying explanation of occurrence of H2O2. Since, H2O2 is said to form when end-on adsorption occurs but clearly surface coverage by other anions such as sulfate plays great role. This can be studied using ab initio technique by covering surface with other adatoms such as silver Ag. The surface coverage can be varied by changing the size of the supercell and the amount of O2, H2O,and H+.

Although, the effect of electrode potential has been well studied [8,9], the effect of electric field created by anions or cations is not found in the literature although some work has been can be found in the literature [8-12]. More work needs to be done in this area.

Also, the effect of temperature and pressure is missing in the literature. The effect of temperature and pressure can be easily modeled by finding equilibrium geometry relating to lowest surface energy ($\gamma(T, (p _{\rm i}))$) which can be related to Gibbs free energy$G (T,(p _{\rm i}))$ of the finite crystal and chemical potential of ith species ($\mu _{\rm i}(T,p_{\rm i})$) [14].

(11)
\begin{align} \gamma(T, (p _{\rm i})) = 1/A[G (T,(p _{\rm i})) - \Sigma _{\rm i} N _{\rm i} \mu_{\rm i}(T,p _{\rm 1}) \end{align}

The effect of reactant concentration can be found by dependence of chemical potential of ith species to its partial molar ratio [15].

(12)
\begin{align} \mu _{\rm i}^{eq} = \mu _{\rm i}^0+k _{\rm B}T ln ({y _{\rm i}^{eq}\over y _{\rm i}^0}) \end{align}

Where $\mu _{\rm i}^0$ and $y _{\rm i}^0$ are the standard chemical potential and mole fraction at standard conditions.

Pt is only a model, such kinetic investigation can be further extended to other noble metals such as Pd, Ir and bimetallic and trimetallic alloys. Also, different structure of these alloys such as core shell structure can be studied. One of the neglected parameter is the role of catalyst support such as carbon which has not been studied extensively either experimentally or theoretically. Ab initio studies can provide valuable insight into the role of these supports.

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