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Modeling the oxygen reduction reaction at platinum-based catalysts: A brief review of recent developments
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Review Article
Modeling the oxygen reduction reaction at platinum-based catalysts: A brief review of recent developments Jun Huang1 and Michael Eikerling2 Abstract
This brief review recapitulates the main kinetic models of the oxygen reduction reaction at platinum-based catalysts. Two major flavors of models are being discussed: the first corresponds to a single Tafel equation with phenomenological treatment of various effects of chemisorbed oxygen intermediates and the second encompasses mechanistic models on the basis of the microkinetic treatment of reaction steps and using fundamental parameters from first principles calculations. The importance of a consistent description of the electrical double layer is highlighted, and a perspective on future developments needed in theory and computation is provided. Addresses 1 Hunan Provincial Key Laboratory of Chemical Power Sources, College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China 2 Department of Chemistry, Simon Fraser University, Burnaby, BC V5A 1S6, Canada Corresponding authors: Huang, Jun ([email protected]); Eikerling, Michael ([email protected])
Current Opinion in Electrochemistry 2019, 13:157–165 This review comes from a themed issue on Fundamental and Theoretical Electrochemistry Edited by Martin Z. Bazant For a complete overview see the Issue and the Editorial Available online 21 January 2019 https://doi.org/10.1016/j.coelec.2019.01.004 2451-9103/© 2019 Elsevier B.V. All rights reserved.
Keywords Oxygen reduction reaction, Microkinetic modeling, First-principles calculations, Double-layer effects, Fuel cell electrocatalysis.
Introduction The oxygen reduction reaction (ORR) is a prototypical multielectron reaction in electrochemistry, as well as the cathodic reaction of polymer electrolyte fuel cells. The ORR contributes the largest solo polarization loss in polymer electrolyte fuel cells and mandates using precious metal catalysts, predominantly on the basis of Pt. As a result, a plethora of efforts have been devoted to understand the origin of the large overpotential of the www.sciencedirect.com
ORR, conceiving highly active and affordable electrocatalysts for Pt replacement, and engineering electrode structures that optimize the effectiveness factors of Pt [1e5]. In activities to date, theory and modeling have played an essential role [6,7]. This observation is exemplified by the use of a modified Tafel equation to rationalize dual Tafel slopes and dual reaction orders of protons in a pioneering study of Damjanovic and Brusic [8], by the efficacy of descriptor-driven approaches based on density functional theory (DFT) in predicting more active ORR catalysts [4], or by the utility of continuum modeling to optimize the catalyst layer structure and composition, demonstrated by Springer et al. [9] and later by Eikerling and Kornyshev [10]. This minireview briefly chronicles the development of ORR models in the past 50 years, as shown in Figure 1, and it puts a major emphasis on the progress in the past few years. Pertinent models can be broadly classified into two subgroups: empirical models based on the Tafel equation [8,11e13] and first-principlesebased microkinetic models [14e20]. After portraying the current state of the art of this field, we present an outlook on necessary future developments by referring to recent experimental and computational advances.
Tafel equation–based empirical models Starting with early contributions in the 1960s, Damjanovic et al. observed that for the ORR on Pt electrodes, the Tafel slope b ¼ vE=vlog j transitions from 60 mV dec1 in the low current density regime to 120 mV dec1 in the high current density regime, while the reaction order with respect to protons assumes values equal to 3/2 and 1, correspondingly [8,11,21]. Understanding the origin of these transitions in macroscopic electrode parameters stimulated further ORR research. Assuming the first electron step, O2 þ Hþ þ e þ /OOH , as the rate-determining step (RDS), Damjanovic and Brusic proposed a modified Tafel equation to describe the ORR, [8] þ DGq bFh (1) exp j ¼ k H ½O2 exp RT RT
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Figure 1
Development of ORR models in the past fifty years. The Damjanovic–Brusic model is based on a single RDS, O2 + H+ + e + /OOH , and modifies the Tafel equation by considering the negative energetic effect of chemisorbed oxygen intermediates [8]. Later on, the Uribe–Wilson–Gottesfeld model emphasizes the site-blocking effect of chemisorbed oxygen intermediates [12]. In 2004, Nørskov et al. used DFT to identify the elementary step with the most positive reaction free energy along the reaction pathway as the potential-determining step (PDS) and assumed that the PDS is the RDS in kinetic analysis [13]. The next category of models is termed first-principles–supported microkinetic models, including the Wang–Zhang–Adzic model [15], the Jinnouchi–Kodama–Hatanaka–Morimoto model [16], the Hansen–Viswanathan–Nørskov model [17], and the Huang–Zhang–Eikerling model [19]. These models use DFT-based first-principles methods to determine the reaction pathway of the ORR, calculate the free energy of all reaction intermediates and activation barriers of each elementary step, and then, conduct full microkinetic analysis without assuming a single RDS. RDS, ratedetermining step; DFT, density functional theory.
with ½H þ and ½O2 being the concentrations of protons and oxygen, respectively, DGq the coverage-dependent activation energy, b the symmetry factor taken as 0.5, h the overpotential, and k the prefactor.
Assuming Temkin adsorption conditions, DGq is given by DGq ¼ DG0 þ xq, with DG0 being the activation energy at zero coverage, x the lateral interaction coefficient, and q the coverage of chemisorbed oxygen intermediate, which was assumed to vary approximately linearly with electrode potential E and solution pH, q ¼ pH pH E q0 þ c E q E þ c q pH; where c q and c q are constant coefficients [8,11]. Substituting these relations into Eq. (1) leads to Current Opinion in Electrochemistry 2019, 13:157–165
1þapH DG0 þ xq0 j ¼ k Hþ ½O2 exp exp RT ! b þ aE Fh RT
(2)
E ¼ xc E RT =F. The Tafel with apH ¼ xc pH q q =2:3 and a slope and reaction order in the low current density regime were then explained by invoking apH ¼ aE ¼ 0:5, pH ¼ 2:3c E namely x ¼ F=2c E q RT and c q q RT =F, while the high current density regime would demand apH ¼ aE ¼ 0 and thus x ¼ 0 corresponding to Langmuir adsorption conditions.
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To summarize, the DamjanoviceBrusic model relied on the following assumptions: (1) the first electron transfer step is the RDS; (2) q varies linearly with respect to E and pH; and (3) Temkin (Frumkin) and Langmuir isotherm apply for the low and high current density regimes, respectively. Specifically, the chemisorbed oxygen intermediates, unidentified yet, exert a negative energetic effect by increasing DGq in the low current density regime. The assumption of a single RDS is problematic when studying reaction kinetics over a wide potential range. The linear relation of q with respect to E is inconsistent with the Temkin (Frumkin) or Langmuir isotherm. Moreover, the transition from Temkin (Frumkin) to Langmuir adsorption conditions with increasing current density is a spurious assumption, invoked to explain experiments but lacking a proper theoretical basis.
Molecular details of elementary steps of the ORR were revealed at the beginning of the new millennium. In 2004, Nørskov et al. [13] proposed a method to calculate the free energy of intermediates of the ORR, on the basis of which it became possible to construct freeenergy pathways of the ORR at various electrode potentials. According to a widely accepted reaction pathway, the ORR in acidic solution proceeds as
The single RDS assumption was inherited by the Los Alamos team, see Ref. [22] in Ref. [12]. The difference was that they emphasized the site-blocking effect of chemisorbed oxygen intermediates and proposed the following formula to model the ORR, [12]
OHad þ Hþ þ e #H2 O Step ð4Þ
bFh j ¼ kð1 qÞexp RT
(3)
At electrode potentials relevant to fuel cell working conditions, OH was considered the dominant siteblocking intermediate. The kinetics of OH formation/reduction from/to water, H2 O þ 4OH þ Hþ þ e , is so fast that this reaction is under equilibrium during the ORR. Under Langmuir adsorption conditions, qOH would be given by qOH ¼ Z=ð1 þ ZÞ with Z ¼ expðFðE E0OH Þ=RT Þ, where E0OH is the equilibrium potential of the OH formation/desorption reaction, which is around 0.7 V (RHE). It is readily seen that qOH 0:99 when E E0OH þ 0:12 and qOH 0:999 when E E0OH þ 0:18 . The siteblocking effect of OH was then used to explain the large onset overpotential, >200 mV, seen on even the best ORR catalysts. This site-blocking viewpoint inspired Stamenkovic et al. [22] to seek more efficient ORR catalysts by increasing the site accessibility. Today, the site-blocking hypothesis remains deeply ingrained in many researchers in this field [12,23]. The aforementioned two models are based on a single RDS and focus on different effects of chemisorbed oxygen intermediates on the reaction kinetics. A combined consideration of the site-blocking effect and the negative energetic effect gives rise to a refined ORR model, [23,24] xq bFh exp j ¼ kð1 qÞexp RT RT
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(4)
O2 þ Hþ þ e #OOHad Step ð1Þ OOHad #Oad þ OHad Step ð2Þ Oad þ Hþ þ e #OHad Step ð3Þ
The Gibbs free energy change for the steps mentioned previously can be expressed as DG1 ¼ DGðOOH Þ DGðO2 Þ DG Hþ þ FE
(5)
DG2 ¼ DGðO Þ þ DGðOH Þ DGðOOH Þ
(6)
DG3 ¼ DGðOH Þ DGðO Þ DG Hþ þ FE
(7)
DG4 ¼ DGðH2 OÞ DGðOH Þ DG Hþ þ FE
(8)
where DGðOXÞ represents the Gibbs free energy for the formation of an intermediate OX. These energies follow scaling relations, [25,26] DGðOOH Þ ¼ 0:5DGðO Þ þ KOOH
(9)
DGðOH Þ ¼ 0:5DGðO Þ þ KOH
(10)
where KOOH and KOH are constants. As a result, all DGi ði ¼ 1; 2; 3; 4Þ can be expressed as functions of DGðO Þ and E. By assuming that the activation barrier for the RDS is equal to the maximum among DGi ði ¼ 1; 2; 3; 4Þ, namely DGa ¼ maxðDGi ði ¼ 1; 2; 3; 4ÞÞ, in the spirit of the Sabatier principle, the ORR current density was written as, [13,27] DGa j ¼ k exp RT
(11)
It was determined that either DG1 or DG4 defines DGa for different catalysts. In other words, this viewpoint implies that the ORR on a specific catalyst is still controlled by an RDS at each potential, while this RDS Current Opinion in Electrochemistry 2019, 13:157–165
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may change at different potentials. The Sabatiervolcano principle has been successfully used in explaining the trends in ORR activity over a wide range of DGðO Þ among different catalysts [4]. However, this basic model neglects important factors, such as the siteblocking and double-layer effects [28]. As a result, the model requires modifications to render it suitable for analyzing the ORR current in a wide potential range for a single catalyst. As to be discussed in the following section, Hansen et al. [17] amended their computational scheme by expanded thermodynamic and kinetic analyses in 2014.
Microkinetic models based on firstprinciples Aforementioned models assume a single RDS and are formulated using a Tafel equation modified according to specific factors. A more sophisticated treatment shall use DFT-based first-principles methods to determine the reaction pathway of the ORR, calculate Gibbs energies of intermediates and activation barriers of elementary steps, and then, conduct a full microkinetic analysis. Models following this route are termed firstprinciplesesupported microkinetic models [14e20]. The complete set of rate equations for the elementary reaction steps from (1) to (4) mentioned previously is, [19] v1 ¼ k1 ½O2 Hþ ðqmax qO qOH qOOH Þ k1 qOOH ; (12) v2 ¼ k2 qOOH ðqmax qO qOH qOOH Þ k2 qO qOH ; (13) v3 ¼ k3 Hþ qO k3 qOH ;
(14)
v4 ¼ k4 Hþ qOH k4 ðqmax qO qOH qOOH Þ; (15)
Here, qi is the coverage of intermediate i, and qmax is the maximum coverage, which is usually taken to be unity. ki are rate constants, DGa;i ; exp RT
ki ¼
k0i
(16)
where k0i ¼ kB T =h is a prefactor with kB being Boltzmann constant and h Planck constant. DGa;i is the activation barrier in either forward ( þ ) or reverse ( ) direction. According to the BronstedeEvansePolanyi relation, DGa;i is linearly related to the corresponding reaction Gibbs energy of the elementary step, DGi , with the proportionality factor being the symmetry factor bi for the forward Current Opinion in Electrochemistry 2019, 13:157–165
reaction and ð1 bi Þ for the reverse reaction. Under steady state, the reaction rates of elementary steps are interrelated. As long as the reaction pathway in step (1)e(4) is considered, the reaction rates must fulfill the following balance, vORR ¼ v1 ¼ v2 ¼ v3 ¼ v4 =2 [19]. Using this relation, solutions for qi and vORR can be obtained. This unifying approach connects elementary mechanistic parameters, such as DGðO Þ, with the ORR activity.
In 2007, Wang et al. [14,15] developed a microkinetic model for the ORR with OH* and O* as reaction intermediates and considering four elementary steps in two reaction pathways. One pathway starts with dissociative adsorption of O2 forming O*, 1=2O2 þ 4O , followed by step (3) and (4) as listed previously. The other starts with reductive adsorption, 1=2O2 þ Hþ þ e 4OH , followed by step (4). Under steady state, model solution gives qOH and qO as functions of E, as well as an intrinsic kinetic equation for the ORR current density. The model was parameterized with experimental data. Using the model, the dual Tafel slope was explained by correlating it with qOH ; the turning point in Tafel slope was identified with the reversible potential of reaction step (3). However, reaction free energies of elementary steps deviate from subsequent firstprinciples results [29,30], and a marked discrepancy in qOH between theory and experiment was found. The WangeZhangeAdzic model has been adopted with some modification in the literature. Moore et al. [31] integrated this model into a multiscale fuel cell computational model and modified it by considering the backward reaction that is neglected in the original model. Through careful model fitting, Moore et al. achieved improved agreement with experiments. Markiewicz et al. [32] amended the model by incorporating reaction step (1) with OOH* as intermediate. Albeit achieving better agreement with polarization curves, the modified model identified OOH* as the dominant reaction intermediate at high overpotentials, which is at odds with most studies [17,33]. As a step further, in 2011, Jinnouchi et al. [16] fed the microkinetic model with parameters from DFT calculations combined with a modified PoissoneBoltzmann model for the electrolyte region. The JKHM (shorthand for Jinnouchi, Kodama, Hatanaka, and Morimoto) model considered the associative pathway via step (1)e(4) as the most probable pathway for the ORR on Pt(111) in acid. The JKHM model also predicted dual Tafel slopes (117 mV dec1 in the low potential region and 35 mV dec1 in the high potential region). Moreover, it determined that the reaction order with respect to O2, gO2 , was bound to decrease from 1 to 0.3 when E decreased from 1.0 V to 0.8 V. The latter theoretical finding is, however, inconsistent with experimental results of the study by Markiewicz et al. [32] which saw gO2 remaining close to unity in the E range between www.sciencedirect.com
ORR modeling Huang and Eikerling
1.0 V and 0.6 V. Of great importance is that the JKHM model attempted to predict macroscopic electrode parameters from first-principles atomic scale simulations. In 2017, this methodology was used for stepped Pt electrodes [18]. Also in 2017, de Morais et al. [34] developed a similar ORR model, which was further integrated into a fuel cell computational model. However, de Morais et al. did not compare the model with experiments. In 2014, Hansen et al. [17] also proposed a microkinetic model for ORR at metal electrodes on the basis of first-principles and evaluating 2e and 4e reduction pathways. A major disadvantage of aforementioned models is the lack of a self-consistent framework treating the formation of chemisorbed oxygen intermediates, surface charging, field-dependent orientational ordering of interfacial water molecules, distribution of ion density and potential in the electrolyte, and electron transfer dynamics. The control variable to steer this complex interplay is the metal phase potential. However, it remains extremely difficult for DFT-based first-principles methods to properly handle the electrode potential, as discussed in several recent reviews [6,35,36]. Recently, Huang [19,37] followed a less ambitious route to tackle this challenge, as detailed in the following section.
Self-consistent ORR model with doublelayer effects
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2RT lD FsM ; ¼ $arsinh F 2εS RT
¼
c bHþ $exp
! Ffsurf S ; RT
(17)
(18)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where lD is the Debye length, lD ¼ εS RT =2F 2 ctot with ctot being the total ion concentration in solution, εS the permittivity of the electrolyte solution, and c bHþ the bulk proton concentration.
The surface charging relation derived from this refined double-layer model is given by, [37,38] 2RT FlD sM dOHP dIHP arsinh þ sM þ F 2RT εS εOHP εIHP m Ntot mw ¼ fM DfM PtO þ tanhðXÞ; εPtO εIHP
(19)
where DfM is the constant potential drop at the metal surface due to the electron spillover, εPtO the permittivity of the Pt oxide layer, εIHP and dIHP the permittivity and thickness of the inner Helmholtz plane, εOHP and dOHP the permittivity and thickness of the outer Helmholtz plane (OHP), respectively, Ntot the Pt atom density, and mw the water dipole moment. The variable X is the dimensionless total field-dependent adsorption energy of water molecules. The interfacial oxide dipole moment mPtO is written as, mPtO ¼ Ntot $ðqO $2O e þ qOH $2OH eÞ$dPtO ;
The HuangeZhangeEikerling model, illustrated in Figure 2(a), features a mean field-type theory of the electrified interface, describing surface modification by chemisorbed oxygen species [37,38]. Chemisorptioninduced surface dipoles and the ordering of interfacial water molecules trigger changes in the free surface charge density, sM , with E that affect the interfacial surf potential, fsurf S , and proton concentration, c Hþ , fsurf S
c surf Hþ
161
(20)
with average charge numbers of chemisorbed oxygen intermediates, 2O and 2OH . It is assumed that OH and O coexist in the surface oxide layer with thickness dPtO . In addition, OOH* is considered unstable with coverage qOOH z0. The negative energetic effect of chemisorbed oxygen intermediates is incorporated in the Huange ZhangeEikerling model by considering coverage dependence of DGðOXÞ in Eqs. (5)e(8).
In steady state, solutions for qO, qOH , and vORR were obtained [19].
1 1 K k þ k4 2 qOH ¼ 1 1 14 1 1 1 1 ; qmax þ k3 þ k4 2 þ K 4 k1 þ K 3 k4 2 þ K 3 K 4 k1 k1
(21)
1 1 1 k þ K k 2 þ K 3 K 4 k1 qO ¼ 1 1 3 1 3 4 1 1 1 ; qmax k1 þ k3 þ k4 2 þ K 4 k1 þ K 3 k4 2 þ K 3 K 4 k1
(22)
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Figure 2
Overall coupling scheme and key results of the Huang–Zhang–Eikerling model. (a) The model presents a self-consistent treatment of the formation of chemisorbed oxygen intermediates, surface charging, field-dependent orientational ordering of interfacial water molecules, distribution of ion density and potential in the electrolyte, and electron transfer dynamics [19]. (b) Model parameterization is conducted according to the polarization curves at three pHs measured using the RDE technique (2500 rpm) on a Pt(111) electrode in NaF/HClO4 electrolyte saturated with O2 of 1 bar at room temperature [40]. The ORR current density is normalized to the value at 0.95 V (RHE). (c) The model gives out the variation of sM and surface reaction conditions, c surf and fsurf S , as functions of fM at pH = 1.2. remaining plots show the (d) rate-determining term in the ORR rate expression, (e) exchange current H+ density, and (f) apparent differential Tafel-slope as a function of the electrode potential. For comparison, results are shown also for the case without surface charge effect, sM ¼ 0, in dashed lines. The experimental Tafel slope data correspond to a Pt(111) electrode in NaF/HClO4 electrolyte saturated with O2 of 1 bar at room temperature. RDE, rotating disk electrode.
1 1 1 1 qmax ¼ k1 þ k3 þ k4 2 þ K 4 k1 vORR 1 1 þ K 3 k4 2 þ K 3 K 4 k1 ;
(23)
where k1 ¼ k1 ½O2 ½H þ ; k3 ¼ k3 ½H þ ; k4 ¼ k4 ½H þ are rate constants that are dependent on the reactant concentrations and K 3 ¼ k3 =k3 ; K 4 ¼ k4 =k4 are corresponding equilibrium constants. Current Opinion in Electrochemistry 2019, 13:157–165
The potential-dependent qOH and qO were validated against the results of XPS measurements on a Pt(111) electrode in 0.1 M N2-saturated HF solution [33,39]. The ORR rate expression was parameterized according to the polarization curves at three pHs measured using the rotating disk electrode (RDE) technique (2500 rpm) on a Pt(111) electrode in NaF/HClO4 electrolyte saturated with O2 of 1 bar at room temperature, as shown in Figure 2(b) [40]. Nonmonotonic www.sciencedirect.com
ORR modeling Huang and Eikerling
behavior is seen in the sM relation, Figure 2(c), with sM inverting toward negative values above 0.78 V due to chemisorption-induced surface dipoles. The nonmonotonic surface charging relation on Pt(111) was corrobo´ et al. [41] Accordingly, rated by Martı´nez-Hincapie and csurf are strongly interfacial reaction conditions fsurf S Hþ potential-dependent. The separate resistive terms of the ORR rate expression in Eq. (23) are shown in Figure 2(d). The ratedetermining resistance term varies among R1 ¼ ðK 3 K 4 k1 Þ1 for E > 0:86 V, R2 ¼ ðK 4 k1 Þ1 for 0:84 V < E < 0:86 V , and R3 ¼ ðk1 Þ1 for E < 0:84 V. These consecutive transitions provide conclusive explanation of the potential-dependent Tafel slope. As the rate-determining resistance terms share the form, ðK 3 n K 4 m ki Þ1 , with the exponents n; m ¼ 0 or 1, the intrinsic differential Tafel slope reads, [19] b ¼
2:3RT 1 : F n þ m þ 0:5
(24)
It is readily seen that, (1) n ¼ m ¼ 1, by24 mV dec1 when E > 0:86 V ; (2) n ¼ 0; m ¼ 1, by40 mV dec1 when 0:84 V < E < 0:86 V ; (3) n ¼ m ¼ 0, by120 mV dec1 when E < 0:84 V . The model is able to give out continuous functions for macroscopic electrode parameters as a function of E. Figure 2(e) shows that the exchange current density of the ORR, j 0 , increases with decreasing E, explaining the wide variability of values found in experimental studies. Figure 2(f) shows that the apparent Tafel slope increases with decreasing E, which has been observed as well in numerous experimental studies. Moreover, a large impact of surface charging on macroscopic electrode parameters and ORR activity was seen. Double-layer effects are important to understand electrocatalytic reactions, for example, the puzzling pH effect of hydrogen/oxygen reactions [40,42] and the inhibition of peroxodisulfate reduction on Pt(111) in the low potential region [41].
Outlook
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addition, the structural dependence and pH effects, as reviewed in Ref. [3], will be important topics for future modeling activities. Kinetic models of the ORR are usually validated with polarization curves measured in the RDE configuration. In conventional RDE tests, intrinsic kinetics of the ORR are usually inaccessible at potentials below 0.8 V due to massive mass transport effects. Markiewicz et al. [32] developed a new RDE configuration that is able to extend the potential region for mechanistic examination of the ORR kinetics to 0.3 V. Markiewicz et al. [32] found that the WangeZhangeAdzic model overestimates the ORR current density in the low potential region by several orders of magnitude. This apparatus allows ORR models to be validated over a wider potential region. On the side of first-principles calculations, Chen et al. [45] simulated ORR in a network of OH and H2 O and proposed a dissociative mechanism involving the first step, protoneelectron transfer coupled oxygen adsorption, as the rate limiting step. It will be important to compare ORR models corresponding to different reaction pathways. In addition, ORR models usually neglect the 2e reduction pathway to H2 O2 , with few exceptions [17,46]. Future efforts should consider concurrent 2e and 4e pathways, so as to explore how catalyst selectivity to these processes is related to fundamental materials properties and controlled reaction conditions. Last but not least, first-principlesesupported full microkinetic models for other catalyst materials are rare and thus much needed.
Conflict of interest statement Nothing declared.
Acknowledgements J. H. appreciates financial support from National Natural Science Foundation of China (No. 21802170) and the starting fund for new faculty members at Central South University (No. 502045001). M. E. acknowledges financial support from the Catalysis Research for Polymer Electrolyte Fuel Cells (CaRPE-FC) Network administered from Simon Fraser University and supported by Automotive Partnership Canada (APC) grant APCPJ-417858-11 through the National Sciences and Engineering Research Council of Canada (NSERC).
References
We conclude this opinion article with a brief summary of the most relevant progress in experimentation and firstprinciples calculations.
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This model improves over previous ORR models by adopting a selfconsistent treatment of the formation of chemisorbed oxygen intermediates, surface charging, field-dependent orientational ordering of interfacial water molecules, distribution of ion density and potential in the electrolyte, and electron transfer dynamics. 20. Ikeshoji T, Otani M: Toward full simulation of the electrochemical oxygen reduction reaction on Pt using firstprinciples and kinetic calculations. Phys Chem Chem Phys 2017, 19:4447–4453. 21. Sepa DB, Vojnovic MV, Vracar LM, Damjanovic A: Different views regarding the kinetics and mechanisms of oxygen reduction at Pt and Pd electrodes. Electrochim Acta 1987, 32: 129–134. 22. Stamenkovic VR, Fowler B, Mun BS, Wang G, Ross PN, Lucas CA, Markovi c NM: Improved oxygen reduction activity on Pt3Ni(111) via increased surface site availability. Science 2007, 315:493–497. 23. Markovi c NM, Schmidt TJ, Stamenkovi c V, Ross PN: Oxygen reduction reaction on Pt and Pt bimetallic surfaces: a selective review. Fuel Cells 2001, 1:105–116. NM, Gasteiger HA, Grgur BN, Ross PN: Oxygen 24. Markovic reduction reaction on Pt(111): effects of bromide. J Electroanal Chem 1999, 467:157–163. 25. Abild-Pedersen F, Greeley J, Studt F, Rossmeisl J, Munter TR, Moses PG, Skúlason E, Bligaard T, Nørskov JK: Scaling properties of adsorption energies for hydrogen-containing molecules on transition-metal surfaces. Phys Rev Lett 2007, 99. 016105. 26. Koper MTM: Thermodynamic theory of multi-electron transfer reactions: implications for electrocatalysis. J Electroanal Chem 2011, 660:254–260. 27. Rossmeisl J, Karlberg GS, Jaramillo T, Nørskov JK: Steady state oxygen reduction and cyclic voltammetry. Faraday Discuss 2009, 140:337–346. 28. Zeradjanin AR: Is a major breakthrough in the oxygen electrocatalysis possible? Curr Opin Electrochem 2018. V, Skúlason E, Siahrostami S, Nørskov JK, 29. Tripkovic Rossmeisl J: The oxygen reduction reaction mechanism on Pt(111) from density functional theory calculations. Electrochim Acta 2010, 55:7975–7981. 30. Jinnouchi R, Kodama K, Morimoto Y: DFT calculations on H, OH and O adsorbate formations on Pt(111) and Pt(332) electrodes. J Electroanal Chem 2014, 716:31–44. 31. Moore M, Putz A, Secanell M: Investigation of the ORR using the double-trap intrinsic kinetic model. J Electrochem Soc 2013, 160:F670–F681. 32. Markiewicz M, Zalitis C, Kucernak A: Performance measure ments and modelling of the ORR on fuel cell electrocatalysts – the modified double trap model. Electrochim Acta 2015, 179: 126–136. This study develops a new RDE configuration that is able to extend the potential region for mechanistic examination of the ORR kinetics to 0.3 V, thus allowing ORR models to be validated over a wider potential region. 33. Wakisaka M, Udagawa Y, Suzuki H, Uchida H, Watanabe M: Structural effects on the surface oxidation processes at Pt single-crystal electrodes studied by X-ray photoelectron spectroscopy. Energy Environ Sci 2011, 4:1662–1666.
17. Hansen HA, Viswanathan V, Nørskov JK: Unifying kinetic and thermodynamic analysis of 2 e– and 4 e– reduction of oxygen on metal surfaces. J Phys Chem C 2014, 118: 6706–6718. This study extends the DFT-based descriptor-driven approaches by incorporating a microkinetic model.
34. de Morais RF, Sautet P, Loffreda D, Franco AA: A multiscale theoretical methodology for the calculation of electrochemical observables from ab initio data: application to the oxygen reduction reaction in a Pt(111)-based polymer electrolyte membrane fuel cell. Electrochim Acta 2011, 56: 10842–10856.
18. Jinnouchi R, Kodama K, Nagoya A, Morimoto Y: Simulated volcano plot of oxygen reduction reaction on stepped Pt surfaces. Electrochim Acta 2017, 230:470–478.
35. Calle-Vallejo F, Koper MTM: First-principles computational electrochemistry: achievements and challenges. Electrochim Acta 2012, 84:3–11.
19. Huang J, Zhang J, Eikerling M: Unifying theoretical framework for deciphering the oxygen reduction reaction on platinum. Phys Chem Chem Phys 2018, 20:11776–11786.
36. Eslamibidgoli MJ, Eikerling MH: Approaching the selfconsistency challenge of electrocatalysis with theory and computation. Curr Opin Electrochem 2018, 9:189–197.
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37. Huang J, Malek A, Zhang J, Eikerling MH: Non-monotonic surface charging behavior of platinum: a paradigm change. J Phys Chem C 2016, 120:13587–13595. 38. Huang J, Zhou T, Zhang J, Eikerling M: Double layer of platinum electrodes: non-monotonic surface charging phenomena and negative double layer capacitance. J Chem Phys 2018, 148. 044704. 39. Wakisaka M, Suzuki H, Mitsui S, Uchida H, Watanabe M: Identification and quantification of oxygen species adsorbed on Pt(111) single-crystal and polycrystalline Pt electrodes by photoelectron spectroscopy. Langmuir 2009, 25: 1897–1900. 40. Briega-Martos V, Herrero E, Feliu JM: Effect of pH and water structure on the oxygen reduction reaction on platinum electrodes. Electrochim Acta 2017, 241:497–509. 41. Martínez-Hincapié R, Climent V, Feliu JM: Peroxodisulfate reduction as a probe to interfacial charge. Electrochem Commun 2018, 88:43–46.
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42. Ledezma-Yanez I, Wallace WDZ, Sebastián-Pascual P, Climent V, Feliu JM, Koper MTM: Interfacial water reorganization as a pH-dependent descriptor of the hydrogen evolution rate on platinum electrodes. Nat Energy 2017, 2:17031. 43. Gómez-Marín AM, Feliu JM: Oxygen reduction at platinum electrodes: the interplay between surface and surroundings properties. Curr Opin Electrochem 2018, 9:166–172. 44. Gómez–Marín AM, Ticianelli EA: A reviewed vision of the oxygen reduction reaction mechanism on Pt-based catalysts. Curr Opin Electrochem 2018, 9:129–136. 45. Chen J, Fang L, Luo S, Liu Y, Chen S: Electrocatalytic O2 reduction on Pt: multiple roles of oxygenated adsorbates, nature of active sites, and origin of overpotential. J Phys Chem C 2017, 121:6209–6217. 46. Ruvinskiy PS, Bonnefont A, Pham-Huu C, Savinova ER: Using ordered carbon nanomaterials for shedding light on the mechanism of the cathodic oxygen reduction reaction. Langmuir 2011, 27:9018–9027.
Current Opinion in Electrochemistry 2019, 13:157–165
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Review Article
Modeling the oxygen reduction reaction at platinum-based catalysts: A brief review of recent developments Jun Huang1 and Michael Eikerling2 Abstract
This brief review recapitulates the main kinetic models of the oxygen reduction reaction at platinum-based catalysts. Two major flavors of models are being discussed: the first corresponds to a single Tafel equation with phenomenological treatment of various effects of chemisorbed oxygen intermediates and the second encompasses mechanistic models on the basis of the microkinetic treatment of reaction steps and using fundamental parameters from first principles calculations. The importance of a consistent description of the electrical double layer is highlighted, and a perspective on future developments needed in theory and computation is provided. Addresses 1 Hunan Provincial Key Laboratory of Chemical Power Sources, College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China 2 Department of Chemistry, Simon Fraser University, Burnaby, BC V5A 1S6, Canada Corresponding authors: Huang, Jun ([email protected]); Eikerling, Michael ([email protected])
Current Opinion in Electrochemistry 2019, 13:157–165 This review comes from a themed issue on Fundamental and Theoretical Electrochemistry Edited by Martin Z. Bazant For a complete overview see the Issue and the Editorial Available online 21 January 2019 https://doi.org/10.1016/j.coelec.2019.01.004 2451-9103/© 2019 Elsevier B.V. All rights reserved.
Keywords Oxygen reduction reaction, Microkinetic modeling, First-principles calculations, Double-layer effects, Fuel cell electrocatalysis.
Introduction The oxygen reduction reaction (ORR) is a prototypical multielectron reaction in electrochemistry, as well as the cathodic reaction of polymer electrolyte fuel cells. The ORR contributes the largest solo polarization loss in polymer electrolyte fuel cells and mandates using precious metal catalysts, predominantly on the basis of Pt. As a result, a plethora of efforts have been devoted to understand the origin of the large overpotential of the www.sciencedirect.com
ORR, conceiving highly active and affordable electrocatalysts for Pt replacement, and engineering electrode structures that optimize the effectiveness factors of Pt [1e5]. In activities to date, theory and modeling have played an essential role [6,7]. This observation is exemplified by the use of a modified Tafel equation to rationalize dual Tafel slopes and dual reaction orders of protons in a pioneering study of Damjanovic and Brusic [8], by the efficacy of descriptor-driven approaches based on density functional theory (DFT) in predicting more active ORR catalysts [4], or by the utility of continuum modeling to optimize the catalyst layer structure and composition, demonstrated by Springer et al. [9] and later by Eikerling and Kornyshev [10]. This minireview briefly chronicles the development of ORR models in the past 50 years, as shown in Figure 1, and it puts a major emphasis on the progress in the past few years. Pertinent models can be broadly classified into two subgroups: empirical models based on the Tafel equation [8,11e13] and first-principlesebased microkinetic models [14e20]. After portraying the current state of the art of this field, we present an outlook on necessary future developments by referring to recent experimental and computational advances.
Tafel equation–based empirical models Starting with early contributions in the 1960s, Damjanovic et al. observed that for the ORR on Pt electrodes, the Tafel slope b ¼ vE=vlog j transitions from 60 mV dec1 in the low current density regime to 120 mV dec1 in the high current density regime, while the reaction order with respect to protons assumes values equal to 3/2 and 1, correspondingly [8,11,21]. Understanding the origin of these transitions in macroscopic electrode parameters stimulated further ORR research. Assuming the first electron step, O2 þ Hþ þ e þ /OOH , as the rate-determining step (RDS), Damjanovic and Brusic proposed a modified Tafel equation to describe the ORR, [8] þ DGq bFh (1) exp j ¼ k H ½O2 exp RT RT
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Figure 1
Development of ORR models in the past fifty years. The Damjanovic–Brusic model is based on a single RDS, O2 + H+ + e + /OOH , and modifies the Tafel equation by considering the negative energetic effect of chemisorbed oxygen intermediates [8]. Later on, the Uribe–Wilson–Gottesfeld model emphasizes the site-blocking effect of chemisorbed oxygen intermediates [12]. In 2004, Nørskov et al. used DFT to identify the elementary step with the most positive reaction free energy along the reaction pathway as the potential-determining step (PDS) and assumed that the PDS is the RDS in kinetic analysis [13]. The next category of models is termed first-principles–supported microkinetic models, including the Wang–Zhang–Adzic model [15], the Jinnouchi–Kodama–Hatanaka–Morimoto model [16], the Hansen–Viswanathan–Nørskov model [17], and the Huang–Zhang–Eikerling model [19]. These models use DFT-based first-principles methods to determine the reaction pathway of the ORR, calculate the free energy of all reaction intermediates and activation barriers of each elementary step, and then, conduct full microkinetic analysis without assuming a single RDS. RDS, ratedetermining step; DFT, density functional theory.
with ½H þ and ½O2 being the concentrations of protons and oxygen, respectively, DGq the coverage-dependent activation energy, b the symmetry factor taken as 0.5, h the overpotential, and k the prefactor.
Assuming Temkin adsorption conditions, DGq is given by DGq ¼ DG0 þ xq, with DG0 being the activation energy at zero coverage, x the lateral interaction coefficient, and q the coverage of chemisorbed oxygen intermediate, which was assumed to vary approximately linearly with electrode potential E and solution pH, q ¼ pH pH E q0 þ c E q E þ c q pH; where c q and c q are constant coefficients [8,11]. Substituting these relations into Eq. (1) leads to Current Opinion in Electrochemistry 2019, 13:157–165
1þapH DG0 þ xq0 j ¼ k Hþ ½O2 exp exp RT ! b þ aE Fh RT
(2)
E ¼ xc E RT =F. The Tafel with apH ¼ xc pH q q =2:3 and a slope and reaction order in the low current density regime were then explained by invoking apH ¼ aE ¼ 0:5, pH ¼ 2:3c E namely x ¼ F=2c E q RT and c q q RT =F, while the high current density regime would demand apH ¼ aE ¼ 0 and thus x ¼ 0 corresponding to Langmuir adsorption conditions.
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159
To summarize, the DamjanoviceBrusic model relied on the following assumptions: (1) the first electron transfer step is the RDS; (2) q varies linearly with respect to E and pH; and (3) Temkin (Frumkin) and Langmuir isotherm apply for the low and high current density regimes, respectively. Specifically, the chemisorbed oxygen intermediates, unidentified yet, exert a negative energetic effect by increasing DGq in the low current density regime. The assumption of a single RDS is problematic when studying reaction kinetics over a wide potential range. The linear relation of q with respect to E is inconsistent with the Temkin (Frumkin) or Langmuir isotherm. Moreover, the transition from Temkin (Frumkin) to Langmuir adsorption conditions with increasing current density is a spurious assumption, invoked to explain experiments but lacking a proper theoretical basis.
Molecular details of elementary steps of the ORR were revealed at the beginning of the new millennium. In 2004, Nørskov et al. [13] proposed a method to calculate the free energy of intermediates of the ORR, on the basis of which it became possible to construct freeenergy pathways of the ORR at various electrode potentials. According to a widely accepted reaction pathway, the ORR in acidic solution proceeds as
The single RDS assumption was inherited by the Los Alamos team, see Ref. [22] in Ref. [12]. The difference was that they emphasized the site-blocking effect of chemisorbed oxygen intermediates and proposed the following formula to model the ORR, [12]
OHad þ Hþ þ e #H2 O Step ð4Þ
bFh j ¼ kð1 qÞexp RT
(3)
At electrode potentials relevant to fuel cell working conditions, OH was considered the dominant siteblocking intermediate. The kinetics of OH formation/reduction from/to water, H2 O þ 4OH þ Hþ þ e , is so fast that this reaction is under equilibrium during the ORR. Under Langmuir adsorption conditions, qOH would be given by qOH ¼ Z=ð1 þ ZÞ with Z ¼ expðFðE E0OH Þ=RT Þ, where E0OH is the equilibrium potential of the OH formation/desorption reaction, which is around 0.7 V (RHE). It is readily seen that qOH 0:99 when E E0OH þ 0:12 and qOH 0:999 when E E0OH þ 0:18 . The siteblocking effect of OH was then used to explain the large onset overpotential, >200 mV, seen on even the best ORR catalysts. This site-blocking viewpoint inspired Stamenkovic et al. [22] to seek more efficient ORR catalysts by increasing the site accessibility. Today, the site-blocking hypothesis remains deeply ingrained in many researchers in this field [12,23]. The aforementioned two models are based on a single RDS and focus on different effects of chemisorbed oxygen intermediates on the reaction kinetics. A combined consideration of the site-blocking effect and the negative energetic effect gives rise to a refined ORR model, [23,24] xq bFh exp j ¼ kð1 qÞexp RT RT
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(4)
O2 þ Hþ þ e #OOHad Step ð1Þ OOHad #Oad þ OHad Step ð2Þ Oad þ Hþ þ e #OHad Step ð3Þ
The Gibbs free energy change for the steps mentioned previously can be expressed as DG1 ¼ DGðOOH Þ DGðO2 Þ DG Hþ þ FE
(5)
DG2 ¼ DGðO Þ þ DGðOH Þ DGðOOH Þ
(6)
DG3 ¼ DGðOH Þ DGðO Þ DG Hþ þ FE
(7)
DG4 ¼ DGðH2 OÞ DGðOH Þ DG Hþ þ FE
(8)
where DGðOXÞ represents the Gibbs free energy for the formation of an intermediate OX. These energies follow scaling relations, [25,26] DGðOOH Þ ¼ 0:5DGðO Þ þ KOOH
(9)
DGðOH Þ ¼ 0:5DGðO Þ þ KOH
(10)
where KOOH and KOH are constants. As a result, all DGi ði ¼ 1; 2; 3; 4Þ can be expressed as functions of DGðO Þ and E. By assuming that the activation barrier for the RDS is equal to the maximum among DGi ði ¼ 1; 2; 3; 4Þ, namely DGa ¼ maxðDGi ði ¼ 1; 2; 3; 4ÞÞ, in the spirit of the Sabatier principle, the ORR current density was written as, [13,27] DGa j ¼ k exp RT
(11)
It was determined that either DG1 or DG4 defines DGa for different catalysts. In other words, this viewpoint implies that the ORR on a specific catalyst is still controlled by an RDS at each potential, while this RDS Current Opinion in Electrochemistry 2019, 13:157–165
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may change at different potentials. The Sabatiervolcano principle has been successfully used in explaining the trends in ORR activity over a wide range of DGðO Þ among different catalysts [4]. However, this basic model neglects important factors, such as the siteblocking and double-layer effects [28]. As a result, the model requires modifications to render it suitable for analyzing the ORR current in a wide potential range for a single catalyst. As to be discussed in the following section, Hansen et al. [17] amended their computational scheme by expanded thermodynamic and kinetic analyses in 2014.
Microkinetic models based on firstprinciples Aforementioned models assume a single RDS and are formulated using a Tafel equation modified according to specific factors. A more sophisticated treatment shall use DFT-based first-principles methods to determine the reaction pathway of the ORR, calculate Gibbs energies of intermediates and activation barriers of elementary steps, and then, conduct a full microkinetic analysis. Models following this route are termed firstprinciplesesupported microkinetic models [14e20]. The complete set of rate equations for the elementary reaction steps from (1) to (4) mentioned previously is, [19] v1 ¼ k1 ½O2 Hþ ðqmax qO qOH qOOH Þ k1 qOOH ; (12) v2 ¼ k2 qOOH ðqmax qO qOH qOOH Þ k2 qO qOH ; (13) v3 ¼ k3 Hþ qO k3 qOH ;
(14)
v4 ¼ k4 Hþ qOH k4 ðqmax qO qOH qOOH Þ; (15)
Here, qi is the coverage of intermediate i, and qmax is the maximum coverage, which is usually taken to be unity. ki are rate constants, DGa;i ; exp RT
ki ¼
k0i
(16)
where k0i ¼ kB T =h is a prefactor with kB being Boltzmann constant and h Planck constant. DGa;i is the activation barrier in either forward ( þ ) or reverse ( ) direction. According to the BronstedeEvansePolanyi relation, DGa;i is linearly related to the corresponding reaction Gibbs energy of the elementary step, DGi , with the proportionality factor being the symmetry factor bi for the forward Current Opinion in Electrochemistry 2019, 13:157–165
reaction and ð1 bi Þ for the reverse reaction. Under steady state, the reaction rates of elementary steps are interrelated. As long as the reaction pathway in step (1)e(4) is considered, the reaction rates must fulfill the following balance, vORR ¼ v1 ¼ v2 ¼ v3 ¼ v4 =2 [19]. Using this relation, solutions for qi and vORR can be obtained. This unifying approach connects elementary mechanistic parameters, such as DGðO Þ, with the ORR activity.
In 2007, Wang et al. [14,15] developed a microkinetic model for the ORR with OH* and O* as reaction intermediates and considering four elementary steps in two reaction pathways. One pathway starts with dissociative adsorption of O2 forming O*, 1=2O2 þ 4O , followed by step (3) and (4) as listed previously. The other starts with reductive adsorption, 1=2O2 þ Hþ þ e 4OH , followed by step (4). Under steady state, model solution gives qOH and qO as functions of E, as well as an intrinsic kinetic equation for the ORR current density. The model was parameterized with experimental data. Using the model, the dual Tafel slope was explained by correlating it with qOH ; the turning point in Tafel slope was identified with the reversible potential of reaction step (3). However, reaction free energies of elementary steps deviate from subsequent firstprinciples results [29,30], and a marked discrepancy in qOH between theory and experiment was found. The WangeZhangeAdzic model has been adopted with some modification in the literature. Moore et al. [31] integrated this model into a multiscale fuel cell computational model and modified it by considering the backward reaction that is neglected in the original model. Through careful model fitting, Moore et al. achieved improved agreement with experiments. Markiewicz et al. [32] amended the model by incorporating reaction step (1) with OOH* as intermediate. Albeit achieving better agreement with polarization curves, the modified model identified OOH* as the dominant reaction intermediate at high overpotentials, which is at odds with most studies [17,33]. As a step further, in 2011, Jinnouchi et al. [16] fed the microkinetic model with parameters from DFT calculations combined with a modified PoissoneBoltzmann model for the electrolyte region. The JKHM (shorthand for Jinnouchi, Kodama, Hatanaka, and Morimoto) model considered the associative pathway via step (1)e(4) as the most probable pathway for the ORR on Pt(111) in acid. The JKHM model also predicted dual Tafel slopes (117 mV dec1 in the low potential region and 35 mV dec1 in the high potential region). Moreover, it determined that the reaction order with respect to O2, gO2 , was bound to decrease from 1 to 0.3 when E decreased from 1.0 V to 0.8 V. The latter theoretical finding is, however, inconsistent with experimental results of the study by Markiewicz et al. [32] which saw gO2 remaining close to unity in the E range between www.sciencedirect.com
ORR modeling Huang and Eikerling
1.0 V and 0.6 V. Of great importance is that the JKHM model attempted to predict macroscopic electrode parameters from first-principles atomic scale simulations. In 2017, this methodology was used for stepped Pt electrodes [18]. Also in 2017, de Morais et al. [34] developed a similar ORR model, which was further integrated into a fuel cell computational model. However, de Morais et al. did not compare the model with experiments. In 2014, Hansen et al. [17] also proposed a microkinetic model for ORR at metal electrodes on the basis of first-principles and evaluating 2e and 4e reduction pathways. A major disadvantage of aforementioned models is the lack of a self-consistent framework treating the formation of chemisorbed oxygen intermediates, surface charging, field-dependent orientational ordering of interfacial water molecules, distribution of ion density and potential in the electrolyte, and electron transfer dynamics. The control variable to steer this complex interplay is the metal phase potential. However, it remains extremely difficult for DFT-based first-principles methods to properly handle the electrode potential, as discussed in several recent reviews [6,35,36]. Recently, Huang [19,37] followed a less ambitious route to tackle this challenge, as detailed in the following section.
Self-consistent ORR model with doublelayer effects
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2RT lD FsM ; ¼ $arsinh F 2εS RT
¼
c bHþ $exp
! Ffsurf S ; RT
(17)
(18)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where lD is the Debye length, lD ¼ εS RT =2F 2 ctot with ctot being the total ion concentration in solution, εS the permittivity of the electrolyte solution, and c bHþ the bulk proton concentration.
The surface charging relation derived from this refined double-layer model is given by, [37,38] 2RT FlD sM dOHP dIHP arsinh þ sM þ F 2RT εS εOHP εIHP m Ntot mw ¼ fM DfM PtO þ tanhðXÞ; εPtO εIHP
(19)
where DfM is the constant potential drop at the metal surface due to the electron spillover, εPtO the permittivity of the Pt oxide layer, εIHP and dIHP the permittivity and thickness of the inner Helmholtz plane, εOHP and dOHP the permittivity and thickness of the outer Helmholtz plane (OHP), respectively, Ntot the Pt atom density, and mw the water dipole moment. The variable X is the dimensionless total field-dependent adsorption energy of water molecules. The interfacial oxide dipole moment mPtO is written as, mPtO ¼ Ntot $ðqO $2O e þ qOH $2OH eÞ$dPtO ;
The HuangeZhangeEikerling model, illustrated in Figure 2(a), features a mean field-type theory of the electrified interface, describing surface modification by chemisorbed oxygen species [37,38]. Chemisorptioninduced surface dipoles and the ordering of interfacial water molecules trigger changes in the free surface charge density, sM , with E that affect the interfacial surf potential, fsurf S , and proton concentration, c Hþ , fsurf S
c surf Hþ
161
(20)
with average charge numbers of chemisorbed oxygen intermediates, 2O and 2OH . It is assumed that OH and O coexist in the surface oxide layer with thickness dPtO . In addition, OOH* is considered unstable with coverage qOOH z0. The negative energetic effect of chemisorbed oxygen intermediates is incorporated in the Huange ZhangeEikerling model by considering coverage dependence of DGðOXÞ in Eqs. (5)e(8).
In steady state, solutions for qO, qOH , and vORR were obtained [19].
1 1 K k þ k4 2 qOH ¼ 1 1 14 1 1 1 1 ; qmax þ k3 þ k4 2 þ K 4 k1 þ K 3 k4 2 þ K 3 K 4 k1 k1
(21)
1 1 1 k þ K k 2 þ K 3 K 4 k1 qO ¼ 1 1 3 1 3 4 1 1 1 ; qmax k1 þ k3 þ k4 2 þ K 4 k1 þ K 3 k4 2 þ K 3 K 4 k1
(22)
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Figure 2
Overall coupling scheme and key results of the Huang–Zhang–Eikerling model. (a) The model presents a self-consistent treatment of the formation of chemisorbed oxygen intermediates, surface charging, field-dependent orientational ordering of interfacial water molecules, distribution of ion density and potential in the electrolyte, and electron transfer dynamics [19]. (b) Model parameterization is conducted according to the polarization curves at three pHs measured using the RDE technique (2500 rpm) on a Pt(111) electrode in NaF/HClO4 electrolyte saturated with O2 of 1 bar at room temperature [40]. The ORR current density is normalized to the value at 0.95 V (RHE). (c) The model gives out the variation of sM and surface reaction conditions, c surf and fsurf S , as functions of fM at pH = 1.2. remaining plots show the (d) rate-determining term in the ORR rate expression, (e) exchange current H+ density, and (f) apparent differential Tafel-slope as a function of the electrode potential. For comparison, results are shown also for the case without surface charge effect, sM ¼ 0, in dashed lines. The experimental Tafel slope data correspond to a Pt(111) electrode in NaF/HClO4 electrolyte saturated with O2 of 1 bar at room temperature. RDE, rotating disk electrode.
1 1 1 1 qmax ¼ k1 þ k3 þ k4 2 þ K 4 k1 vORR 1 1 þ K 3 k4 2 þ K 3 K 4 k1 ;
(23)
where k1 ¼ k1 ½O2 ½H þ ; k3 ¼ k3 ½H þ ; k4 ¼ k4 ½H þ are rate constants that are dependent on the reactant concentrations and K 3 ¼ k3 =k3 ; K 4 ¼ k4 =k4 are corresponding equilibrium constants. Current Opinion in Electrochemistry 2019, 13:157–165
The potential-dependent qOH and qO were validated against the results of XPS measurements on a Pt(111) electrode in 0.1 M N2-saturated HF solution [33,39]. The ORR rate expression was parameterized according to the polarization curves at three pHs measured using the rotating disk electrode (RDE) technique (2500 rpm) on a Pt(111) electrode in NaF/HClO4 electrolyte saturated with O2 of 1 bar at room temperature, as shown in Figure 2(b) [40]. Nonmonotonic www.sciencedirect.com
ORR modeling Huang and Eikerling
behavior is seen in the sM relation, Figure 2(c), with sM inverting toward negative values above 0.78 V due to chemisorption-induced surface dipoles. The nonmonotonic surface charging relation on Pt(111) was corrobo´ et al. [41] Accordingly, rated by Martı´nez-Hincapie and csurf are strongly interfacial reaction conditions fsurf S Hþ potential-dependent. The separate resistive terms of the ORR rate expression in Eq. (23) are shown in Figure 2(d). The ratedetermining resistance term varies among R1 ¼ ðK 3 K 4 k1 Þ1 for E > 0:86 V, R2 ¼ ðK 4 k1 Þ1 for 0:84 V < E < 0:86 V , and R3 ¼ ðk1 Þ1 for E < 0:84 V. These consecutive transitions provide conclusive explanation of the potential-dependent Tafel slope. As the rate-determining resistance terms share the form, ðK 3 n K 4 m ki Þ1 , with the exponents n; m ¼ 0 or 1, the intrinsic differential Tafel slope reads, [19] b ¼
2:3RT 1 : F n þ m þ 0:5
(24)
It is readily seen that, (1) n ¼ m ¼ 1, by24 mV dec1 when E > 0:86 V ; (2) n ¼ 0; m ¼ 1, by40 mV dec1 when 0:84 V < E < 0:86 V ; (3) n ¼ m ¼ 0, by120 mV dec1 when E < 0:84 V . The model is able to give out continuous functions for macroscopic electrode parameters as a function of E. Figure 2(e) shows that the exchange current density of the ORR, j 0 , increases with decreasing E, explaining the wide variability of values found in experimental studies. Figure 2(f) shows that the apparent Tafel slope increases with decreasing E, which has been observed as well in numerous experimental studies. Moreover, a large impact of surface charging on macroscopic electrode parameters and ORR activity was seen. Double-layer effects are important to understand electrocatalytic reactions, for example, the puzzling pH effect of hydrogen/oxygen reactions [40,42] and the inhibition of peroxodisulfate reduction on Pt(111) in the low potential region [41].
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addition, the structural dependence and pH effects, as reviewed in Ref. [3], will be important topics for future modeling activities. Kinetic models of the ORR are usually validated with polarization curves measured in the RDE configuration. In conventional RDE tests, intrinsic kinetics of the ORR are usually inaccessible at potentials below 0.8 V due to massive mass transport effects. Markiewicz et al. [32] developed a new RDE configuration that is able to extend the potential region for mechanistic examination of the ORR kinetics to 0.3 V. Markiewicz et al. [32] found that the WangeZhangeAdzic model overestimates the ORR current density in the low potential region by several orders of magnitude. This apparatus allows ORR models to be validated over a wider potential region. On the side of first-principles calculations, Chen et al. [45] simulated ORR in a network of OH and H2 O and proposed a dissociative mechanism involving the first step, protoneelectron transfer coupled oxygen adsorption, as the rate limiting step. It will be important to compare ORR models corresponding to different reaction pathways. In addition, ORR models usually neglect the 2e reduction pathway to H2 O2 , with few exceptions [17,46]. Future efforts should consider concurrent 2e and 4e pathways, so as to explore how catalyst selectivity to these processes is related to fundamental materials properties and controlled reaction conditions. Last but not least, first-principlesesupported full microkinetic models for other catalyst materials are rare and thus much needed.
Conflict of interest statement Nothing declared.
Acknowledgements J. H. appreciates financial support from National Natural Science Foundation of China (No. 21802170) and the starting fund for new faculty members at Central South University (No. 502045001). M. E. acknowledges financial support from the Catalysis Research for Polymer Electrolyte Fuel Cells (CaRPE-FC) Network administered from Simon Fraser University and supported by Automotive Partnership Canada (APC) grant APCPJ-417858-11 through the National Sciences and Engineering Research Council of Canada (NSERC).
References
We conclude this opinion article with a brief summary of the most relevant progress in experimentation and firstprinciples calculations.
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On the experimental side, Gomez-Marin and Feliu have proposed a new reaction mechanism involving a soluble intermediate species, OOHaq, which could be responsible for unexpected production of H2O2 under high mass-transfer conditions and the lack of reductive current at potential higher than the onset potential. More details can be found in two recent opinions articles published in this journal [43,44]. In
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of special interest of outstanding interest
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