Microkinetic Barriers of the Oxygen Evolution on the Oxides of Iridium, Ruthenium and their Binary Mixtures

The performance of electrocatalytic water splitting in polymer electrolyte membrane electrolysis is substantially determined by the microkinetic processes of the oxygen evolution reaction (OER). Even highly active catalysts such as the nanoparticulated transition metal oxides IrO 2 , RuO 2 and their mixtures, Ir x Ru 1 (cid:0) x O 2, exhibit overpotentials up to several hundreds of millivolts. The surface of the oxide mixtures Ir x Ru 1 (cid:0) x O 2 is found to consist of actives sites of both Ir and Ru on which the OER mechanism is processed independently and at different overpotentials. By applying microkinetic modelling and parameterization via cyclic voltammograms we show that there is a correlation between performance and the relative Ir content, that can be explained by two different deprotonation steps. These are in particular the formation of the adsorbate species *OOH on rutile RuO 2 and *OO on IrO 2 . The respective free reaction energies are quantified to 1.44 eV and 1.58 eV, which are the highest values of the process and thus determining the overpotential. The additional finding of adsorbed oxygen *O covering > 40% of the active sites during the OER suggests that subsequent water adsorption is the major performance limiting step. Finally, a synergetic effect between both active sites on the binary transition metal oxides is identified: the respective other metal lowers the potential determining reaction energy on the Ru or Ir active site. This insight into the surface processes on Ir and Ru binary oxides forms the basis for deeper understanding of the active sites for further OER catalyst development.


Introduction
Electrocatalytic water splitting is a highly efficient reaction to convert sustainably generated excess electricity into chemical bonds as in molecular hydrogen. [1]In polymer electrolyte membrane electrolyzers, water is decomposed into oxygen and protons by the anodic oxygen evolution reaction (OER).The protons are reduced to hydrogen at the cathode in the socalled hydrogen evolution reaction.The latter is efficiently catalyzed with Pt-based materials, [2] whereas the OER requires a high overpotential even when using benchmark Ir-based catalyst.It is, therefore, the bottleneck reaction. [3]To increase the electrocatalytic activity of the OER and reduce the amount of the very scarce and, thus, expensive iridium, oxide mixtures containing various transition metals were investigated. [4]So far, the most promising catalyst results from the combination of Ir and Ru oxide, as it benefits from both, the high OER activity found for RuO 2 and the high stability of IrO 2 . [5]6b] The high electrocatalytic activity of single transition metal oxides is explained by complex catalytic processes: the overall OER 2H 2 O ! 4H + + 4e À + O 2 is proceeding in multiple consecutive steps in which the catalyst surface provides active sites to form adsorbed but reactive intermediate species.
According to density functional theory (DFT) studies on the OER on IrO 2 [8] and RuO 2 , [8a,9] several species such as *O, *OH and *OOH are thermodynamically favorable.They are produced by the adsorption of water and subsequent deprotonation.
To understand the overall performance of the electrocatalytic OER, it is crucial to quantify the kinetics of all reaction steps individually.This allows for analysis of the major process limitations in order to provide suggestions to further optimize the catalysts.
8b,11] In our previous microkinetic modeling study, we further identified for the OER on rutile IrO 2 kinetic limitations by slow water adsorption on the *O species and the oxygen detachment, [11] which confirms DFT based findings. [12]Such kinetic limitations have not yet been explicitly quantified for the RuO 2 material.
Despite the progress in the field, less effort was made to analyze the mechanism and kinetics on binary Iridium-Ruthenium oxide mixtures.It is known that they form well mixed bulk structures [13] as the bulk formation energy gets lowered. [14]The surface processes under OER conditions, however, are rarely studied.In a recent study of Reksten et al., lumped kinetic equations were derived for analyzing various options of limiting steps at combined IrÀ Ru active sites. [15]By parameterizing the equations with experimental steady state polarization curves, the deprotonation of the *OH species was identified as rate limiting step. [15]Yet, further studies showed that good agreement with the experimental polarization data may be insufficient for a reliable kinetic identification.This was pointed out in microkinetic studies, in which different parameter sets and, thus, limiting steps were able to reproduce the same polarization curve of the general OER. [16]Also the assumption of a combined active site contradicts with DFT based findings of distinguishable Ru and Ir active sites.It was predicted that the CUS consists of either Ir or Ru surface atoms and that they show composition dependent binding energies for *O, *OH and *OOH adsorbed species. [14]6b] The finding of the Ircontent dependent binding energies [14] indicates that transferring the insights from the single transition metal oxides to binary mixtures might not be trivial.However, a significant influence on the OER performance can be expected.This impact of the material mixing on the kinetics of all individual steps in the OER mechanism on distinguishable Ir and Ru active surface sites was, to the best of our knowledge, never reported so far.
For a reliable identification of the kinetic surface processes, the use of dynamic analysis is suggested.16b] For dynamic analysis, a dynamic microkinetic modelling approach of the complex OER mechanism has shown to be a powerful tool to reproduce and study the interactions during a catalytic process. [11]In addition, the method allows to validate the model and its parameters with dynamic experimental data such as impedance spectroscopy [17] and CV measurements. [18]ithin this publication we determine and analyze the reaction kinetics and process interactions during the OER on rutile structured IrÀ , RuÀ and Ir x Ru 1À x O 2 mixtures by employing a microkinetic model approach.A widely accepted OER mechanism from literature provides the basis to formulate the model equations.Parameterization is conducted by comparing the dynamic simulation results to experimental CV curves.With this, thermodynamic parameters such as the free reaction energies and free activation energies of individual process steps are quantified.We not only experimentally confirm theoretical findings on the single transition metal oxides IrO 2 and RuO 2 but also quantify and clarify the kinetics of individual process steps during the OER on binary Ir x Ru 1À x O 2 mixtures.In a later section we will give an in-depth understanding of the performance limiting reactions and identification of synergetic effects by material mixing.

Results and Discussion
In the following sections, we first present and discuss the microkinetics and thermodynamic energies for the single transition metal oxides RuO 2 and IrO 2 .The results were gained from the model-based analysis method, which is in detail explained in the methodical section at the end of this paper.In short, the model equations were derived based on an OER mechanism gained from literature and shown in Scheme 1.The reaction rates were considered in forward and backward direction for all chemical and electrochemical processes at the active sites.This allows for dynamic simulations and the identification of the kinetic and thermodynamic properties by comparison to experimental CV curves.After the analysis of the single transition metal oxides, the microkinetics on Ir x Ru 1À x O 2 mixtures will be reported and discussed in detail, as well as the effect of material mixing on the OER performance.

Kinetic Analysis of the OER at RuO 2 and IrO 2
For the following model-based analysis, high model validity is key to provide accurate and trustworthy results.With a threestep parameter estimation algorithm, which contains global and local optimization as well as a check for parameter identifiability, the main process defining parameter values were carefully quantified (see Computational Methods).Excellent agreement between the experimental CV results and the dynamic simulation data is shown for the OER on RuO 2 in Figure 1a and on IrO 2 in Figure 1b.The experimentally observed features for RuO 2 and IrO 2 are reproduced well by the models and both simulations show low root mean square errors (rmse) of 0.024 mA cm À 2 and 0.069 mA cm À 2 , respectively.Even when applying different potential scan rates, good reproducibility is achieved as shown in Figure S1 in the supporting information (SI).The high identifiability of the free reaction energy parameters is visible from rmse profile analysis shown in Figure S2 and in Figure S3 in the SI.In conclusion, a valid model with identified parameters is gained, which shows trustworthy results due to its excellent reproducibility of experimental data.
The assumed mechanism in Scheme 1 and the corresponding kinetics are thus a valid choice to reproduce the dynamic electrochemical behavior on both catalysts.To elucidate the kinetic limitations on RuO 2 and compare them to the kinetics on IrO 2 , the seven reaction steps in Equations ( 1) to (7) can now be analyzed individually over a wide potential range.The sets of all estimated parameters for the reaction free energies, the activation free energies, the interaction free energies, the density of active sites and the double-layer capacitance are given in the SI.The values of the reaction free energy are normalized to electrochemical standard conditions, which are defined at room temperature and with the activities of all substances at unity.Note that, unless specified, the values are given at 0 V.At the lowest simulated potential of 0.4 V, water adsorption takes place: The ratio between the free active site * and adsorbed water is defined by the reaction free reaction energy, which was quantified to ΔG 0 r,1 = 0.24 eV on RuO 2 and ΔG 0 r,1 = 0.11 eV on IrO 2 .Water adsorption is, therefore, thermodynamically unfavorable, whereas kinetic simulation yields a water coverage of 10.4 % on the RuO 2 surface and 34.8 % on the IrO 2 surface.The high amount of free active sites on RuO 2 is also known from near ambient pressure X-ray photoelectron spectroscopy on RuO 2 . [19]An increase in potential above 0.4 V starts the electrochemically driven deprotonation of adsorbed water, given in Equation (2).
The reaction free energy values of ΔG 0 r,2 = 0.51 eV on RuO 2 and ΔG 0 r,2 = 0.73 eV on IrO 2 correlate with the potentials of the first redox transitions in Figure 1.Deviations from the noted potential values arise due to the preceding slow water adsorption.The small but notable value of the activation free energy for this process on RuO 2 of ΔG a,2 = 0.1 eV is in good agreement with the shift in the absolute cathodic to anodic peak maxima observed in the experimental CV.On IrO 2 , rather no shift is observed between cathodic and anodic absolute peak maxima of the experimental redox transition; this corresponds to an activation energy of ΔG a,2 = 0 eV.Comparably low activation barriers of deprotonation steps were also reported in a DFT study, in which the authors explain this finding by the short traveling distance of the proton from the surface oxygen to the water molecule in the electrolyte. [20]A further increase in potential initiates the second deprotonation step, the deprotonation of *OH in Equation (3).
Mayor differences are observed in the potential and the reaction free energy parameters of this redox transition between both materials.On RuO 2 , the process starts at a higher potential, which corresponds to a higher reaction free energy of ΔG 0 r,3 = 1.28 eV on RuO 2 than ΔG 0 r,3 = 1.12 eV on IrO 2 .In comparison to DFT-based calculations, [21] our estimation for the reaction free energy on RuO 2 is in good accordance but the value on IrO 2 is slightly lower.
The subsequent step is the second water adsorption: On both catalysts, this chemical reaction requires high reaction energies of ΔG 0 r,4 = 0.39 eV on RuO 2 and ΔG 0 r,4 = 0.54 eV on IrO 2 .This finding is qualitatively in good agreement with reported DFT results for RuO 2 [22] and IrO 2 . [12]This reaction energy does not only influence the lower potential region.It has also significant impact on the OER performance at potentials above 1.5 V. Figure 2a shows the free energies of all reaction steps on RuO 2 and IrO 2 corrected to the standard redox potential of the OER of 1.23 V.It is clearly visible, that the second water adsorption in step 4 possesses the largest free energy of all steps.In consequence, this step limits the overall process chemically and is causing a high accumulation of the reactant species on the surface as shown in the SI in Figure S4 and Figure S5 on the Ru and the Ir active site, respectively.Adsorbed atomic oxygen, *O, is dominant even at the highest simulated potentials of 1.55 V and 1.6 V at which the OER is typically performed.This proves that chemical adsorption of water limits the overall OER rate.The third deprotonation step in Equation ( 5) (5) occurs on RuO 2 directly at the onset of the exponential increase of the OER, which has the overall highest value in reaction free energy of ΔG 0 r,5 = 1.44 eV.Hence, it is describing the potential determining step of the OER.As shown in the energy diagram in Figure 2b, an applied potential of 1.44 V is required to reach equilibrium conditions for this process step.On IrO 2 in contrast, the energy is lower with a value of ΔG 0 r,5 = 1.23 eV and, thus, the reaction takes place at potentials lower than the actual OER onset.
The reaction free energy of the fourth deprotonation step on RuO 2 ΔG 0 r,6 = 1.37 eV is smaller than the value from the previous step and is, thus, not the potential limiting step.However, on IrO 2 this step is crucial.With a reaction free energy value of ΔG 0 r,6 = 1.58 eV as the overall maximum, it represents the potential determining step.According to the energy diagram in Figure 2c, the thermodynamic equilibrium is reached at an applied potential of 1.58 V.The final step of the OER reaction mechanism marks the oxygen detachment given in Equation (7).
The chemical process is thermodynamically favorable due to negative reaction free energies of ΔG 0 r,7 = À 0.32 eV on RuO 2 and ΔG 0 r,7 = À 0.40 eV on IrO 2 , suggesting a fast reaction.Yet, the step is facing a strong kinetic barrier.In contrast to the previous reaction steps, very high activation free energies of ΔG a,7 = 0.34 eV on RuO 2 and ΔG a,7 = 0.43 eV on IrO 2 are quantified for the oxygen release, which is in qualitative agreement to DFT based findings on IrO 2 of ΔG a = 0.58 eV. [12]his activation barriers not only limit the overall OER process, but also lead to an accumulation of the reactant species *OO on the Ru and the Ir active site, as shown in the SI in Figure S4 and Figure S5, respectively.
In conclusion, the OER performance is constrained by three steps on each catalyst material: a chemical limitation by water adsorption on *O in Equation (4), the potential defining deprotonation of *OH 2 O on RuO 2 in Equation (5) and of *OOH on IrO 2 in Equation (6).Finally, a kinetic limitation of the oxygen detachment in Equation ( 7) is observed and explained by the high activation energy.Although the mechanism is identical on both materials, the catalytic activity is especially defined by the energy values of the respective potential determining steps.As those steps are different, we will analyze in the following, how the processes interact when mixing the materials.

Kinetic Analysis of the OER at Oxide Mixtures of Ir x Ru 1À x O 2
Binary mixtures of transition metal oxides may inherit characteristics from both materials.Ideally, this can lead to improved overall properties.6b] In the following, we will analyze the OER kinetics on Ir x Ru 1À x O 2 mixtures in order to understand the interactions and processes on the active sites and surface species, which lead to the observed increase in OER performance.
6b] In consequence, the OER mechanism including all the adsorption, desorption and deprotonation steps shown in Scheme 1 is assumed to proceed on both active sites independently.In a first step, the energy parameter values quantified for RuO 2 and IrO 2 were used and the relative Ir content x as well as the density of active sites were parameterized in order to minimize the deviation from experimental data.The experimental and simulated CV curves are given in the SI in Figure S6.A clear discrepancy between the experimental and simulated current density is observable between 1.3 V and 1.5 V.This results in deviations that are higher than for the single oxides and indicate, that the kinetics of at least one reaction step is not reproduced correctly by the parameters from the single oxides.Mixing the material causes, thus, interactions, which possibly have a synergetic effect of the activity and will be analyzed in the following.
To evaluate whether a change in energy parameters without modification of the OER mechanism allows to properly describe the experimental observed behavior of the mixtures, the parameters were newly identified by using the parameters from RuO 2 and IrO 2 as initial values for the Ru and Ir active sites, respectively.The assumption of different energy values is in full agreement with DFT calculations, which suggested a change in binding energy of adsorbed species with different relative Ir content. [14]Also the density of active sites, the double-layer capacitance and the relative content of Ir active sites was identified.6b] The parameter sets as well as the rmse profile are given in the SI.The resulting simulated CV curves in Figure 3 show an excellent agreement with the experimental CV curves for all three binary catalyst mixtures.This confirms that the mechanism still holds, but that there exist energetic interactions for the mixtures.
The analysis of the free energy values and the changes of surface coverages with potential in Figure S4 and Figure S5 in the SI reveals similar process limitations for all mixtures as for the previously discussed single oxides: On both Ir and Ru active sites, the water adsorption step in Equation (4) shows limiting behavior.Also, the oxygen detachment step of Equation ( 7) faces a high, thus kinetically limiting, activation energy.The highest reaction free energy on the Ir active site is obtained for the deprotonation of *OOH in Equation ( 6) for all mixtures.And the highest reaction free energy on the Ru active site is identified for the deprotonation of *OH 2 O, Equation ( 5), for all mixtures with high Ru-content, i. e., Ir 0.2 Ru 0.8 O 2 and Ir 0.5 Ru 0.5 O 2 .In contrast, for Ir 0.8 Ru 0.2 O 2 , deprotonation energy of *OH 2 O gets lower and the deprotonation of *OOH becomes limiting, similar to the Ir-sites.Since the highest reaction free energy on the Ru active site is lower compared to the value on the Ir site, the mentioned steps on the Ru active site are determining the overall potential.
We will now analyze the contribution of Ru and Ir sites to the performance of the CV.At Ir 0.2 Ru 0.8 O 2 , the current density shown in Figure 3a is strongly impacted by deprotonation on both, Ru and Ir active sites.The single processes at Ir and Ru sites occur at similar potentials as on the discussed single oxides; as the potentials differ between RuO 2 and IrO 2 , redox transitions at Ir and Ru sites can be distinguished.The large share of Ir to the current in the CV can be explained as follows: Although the nominal relative bulk Ir content is 0.2, the identified relative active site content at the surface is twice this value, with a share of 0.4.Thus, the Ir signal contributes much more than 20 % to the CV curves at potentials below OER.5a,6b] The experimental values in Figure 4 are in good accordance with the model results.The accumulation of Ir at the surface can also be seen in the experimental and simulation data of Ir 0.5 Ru 0.5 O 2 and less pronounced in the data of Ir 0.8 Ru 0.2 O 2 .Finally, it is interesting to see for Ir 0.2 Ru 0.8 O 2 a notable difference between current shares in the CV between the adsorption region and the OER region.Whereas currents in the adsorption region below 1.5 V are equally strong on both active sites, the turnover frequency of the OER is mainly defined by the processes at the Ru active sites: Ru sites convert more than two third of the electrons at the highest simulated potential of 1.55 V. Thus, Ru sites are more active during the OER.
In Figure 3b, the experimental and simulated cyclic voltammograms of Ir 0.5 Ru 0.5 O 2 are shown.At potentials prior to the , with rmse values of 0.033 mA cm À 2 , 0.017 mA cm À 2 and 0.032 mA cm À 2 , respectively.The simulations allow to distinguish between the processes at the Ru and Ir active sites, which results in the current densities given with the dotted red and green lines, respectively.The data was recorded at 200 mV s À 1 in 0.1 M H 2 SO 4 solution at room temperature.6b] oxygen evolution, the main current contribution arises from the deprotonation processes on the Ir active site.Also, here the identified share of active Ir sites on the catalyst surface is 0.7 and thus higher than the bulk value.6b] As a result, the contribution of the processes on Ir to the overall current in the CV is much higher than at Ir 0.2 Ru 0.8 O 2 .At the OER potential of 1.55 V, the number of electrons, which are transferred at all active Ir and Ru sites are roughly the same.This seemingly contradicts thermodynamic expectations, as the reaction energy of the potential determining step on Ir sites, ΔG 0 r,6 = 1.57eV, is higher than on the Ru site with ΔG 0 r,5 = 1.40 eV.Yet, it can be well explained by the increased Ir site content and the kinetics, as the share of the surface covered by reactant species differs from of θ Ru,OH2O < 0.01 on the Ru site to θ Ir,OOH = 0.17 on the Ir site.Thus, the potential determining step on the Ru site is decelerated due to the low amount of both the reactant species and the active sites.
Finally, the CV curves of the Ir 0.8 Ru 0.2 O 2 binary oxide and the corresponding partial current densities are given in Figure 3c.They show dominating processes at the Ir site over the full potential range due to the fact, that the estimated share of Ir active sites given in Figure 4 is 0.88.Nevertheless, as the OER processes at 1.55 V, the Ru site still contributes roughly 20 % of the total current density.Thus, the turn over frequency per active site is still higher on the Ru site, then on the Ir site.
Having discussed the partial currents in the CV curves on the Ir and Ru active sites, we will now elucidate the synergetic effect of material mixing on the potential determining OER steps.An overview of the changes in reaction free energies, which essentially determine the activity of the IrO 2 , RuO 2 and their mixed oxides is shown in Figure 5.As previously explained, for Ir-contents until 50 %, the potential determining step of OER on the Ru active site is the deprotonation step *OH 2 OÐ*OOH + H + + e À given in Equation ( 5).In contrast, on the Ir active site the deprotonation step *OOHÐ*OO + H + + e À in Equation ( 6) was identified as potential determining step of the reaction.For the energy values, there is a clear trend that applies for both sites: as the content of the dominant active site decreases, the reaction free energy of this site is lowered.Thus, the mixed oxides exhibit a synergetic effect that results in higher OER activity at both individual active sites.On the Ru site this effect is strongest for the mixed oxides with a relative Ir content of 0.8.On this material the reaction free energy ΔG 0 r,5 = 1.34 eV of the step in Equation ( 5) is lowered and undercuts the reaction free energy ΔG 0 r,6 = 1.37 eV of the subsequent process in Equation ( 6).This results in *OOH deprotonation becoming the potential determining step on Ru for high Ir contents.Despite the fact of a lowered share of active Ru sites present at the surface, the synergies promoted by the material structure provide overall improved kinetics at both active sites.
This work clearly shows that while the same mechanism holds for the single transition metal oxides and the binary mixtures, the material mixing leads to a decrease in reaction free energies of the potential determining steps and, thus, improved OER performance at both active sites.As the reaction free energies are directly related to the binding energy of adsorbed species, we show that these can be tuned by adding other atoms in such way that higher catalytic activity is achieved.While Ir x Ru 1À x O 2 is also commercially attractive, it serves as a well characterized material to study the origin of this effect and a possible correlation to the electronic band structure, to gain an in-depth understanding of the active catalyst material.Ir mixing with other materials than Ru lowers the cost and might also provide an increased activity of the Ir active sites.This prediction might be especially useful for future studies, which are aiming for further catalyst development.

Conclusion
In the presented work we provided an in-depth kinetic analysis of the reactions and adsorption processes and their limitations on Ir and Ru active sites during the OER via a microkinetic model.The kinetic model and the underlying mechanism allow to reproduce CV curves of IrO 2 , RuO 2 and their binary mixtures Ir x Ru 1À x O 2 .The surface of the binary mixed oxides Ir x Ru 1À x O 2 show an accumulation of Ir active sites, which exceeds that of the bulk stoichiometry and is in accordance with recent experimental studies.Major findings are that two chemical steps, which are the water adsorption (*OÐ*OH 2 O) and the oxygen release (*OO!* + O 2 ) significantly impact the OER on all catalysts.Further, two different deprotonation steps, depending on whether the active site consists of Ru (*OH 2 O Ð*OOH + H + + e À ) or Ir (*OOHÐ*OO + H + + e À ) determine the OER potential at which the OER is conducted.We reveal that the surface processes of the OER are taking place on both, the Ru and the Ir active site, individually, by a quantification of both corresponding current densities.Yet, a positive synergetic impact on the electrocatalytic activity by mixing the materials is revealed: the thermodynamic reaction free energies of the potential determining steps are lowered for the processes on both the Ru and the Ir active sites.In consequence, not only the presence of the highly active Ru sites provides increased performance but also the compositional change leads to better Ir site activity.This effect might have a beneficial impact in further mixed oxide catalyst development.

Experimental Section
To parameterize the microkinetic model, a proper experimental dataset is required.The experimental current densities from the CV data used for this analysis were already published for the pure oxides and the mixtures by Escalera-López et al. [6b] CV curves of IrO 2 and Ir 0.8 Ru 0.2 O 2 were remeasured with the same method but with a higher applied maximum potential of up to 1.6 V vs RHE to guarantee for a full exploitation of the OER behavior.We here briefly summarize the experimental method: Flame spray pyrolyzed nanoparticles were calcined at 600 °C, which results in rutile structured single crystals.2 mg of the material was mixed with 750 μL of deionized water, 250 μL of isopropanol 8.58 μL of Nafion 5 % dispersion (D-520, VWR) and 1.2 μL of 1 M KOH. 10 μL of the resulting ink was drop casted onto in a glassy carbon working electrode with a geometric area of A = 0.1963 cm 2 .The electrode with the pristine particles was put into the PTFE cell filled with 0.1 M H 2 SO 4 electrolyte solution together with a Pt wire as counter electrode and a HydroFlex reversible hydrogen electrode from Gaskatel GmbH.Using a Gamry Reference 600 + potentiostat, impedance spectroscopy measurements at open circuit potential with frequencies from f = 10 À 1 to f = 10 5 Hz and a perturbation amplitude of E = 10 mV as well as three consecutive CV curves in between potentials of E = 0.05 and 1.6 V were recorded with a potential rate of dE/dt = 200 mV s À 1 .The potential was corrected afterwards by the Ohmic resistance gained from the impedance spectroscopy analysis.16b] Aiming for a better process discrimination, the careful analysis of the potential region prior to the OER allows to gain essential kinetic information about of the reactions proceeding here as well.

Computational Methods
The microkinetic simulations were conducted with a model implemented in the software MATLAB 2020b.The procedure follows that of our prior work. [11]In the following section, we provide the assumptions and main equations of the model as well as the parameterization process.
It is shown in Scheme 1 and consists of water adsorbing on the active site, denoted with *, in steps ( 1) and (4), producing *H 2 O and *OH 2 O, respectively.Via deprotonation in steps ( 2), ( 3), (5), and (6), several respective intermediate species *OH, *O, *OOH and *OO are formed, and adsorbed OO is detached in step (7), resulting in the final product of molecular oxygen.
To simulate the dynamic changes during a CV, a time t dependent potential E is set in Equation ( 8) With a starting potential E 0 and a constant potential rate dE/dt to reproduce the experimentally applied potential.The experimental potential drop in the electrolyte is corrected by subtracting its measure calculated by multiplying the current density j, the geometric electrode area A and the electrolyte resistance R. The reaction rates r i of the single steps i 2 1; 2; 3 ::: 7 f g according to Scheme 1 are calculated in Equation ( 9) and (10) for forward direction r + i and for backward directions r À i , respectively. The and the activities a j of all electrolyte species j2Ω el = {H + ; H 2 O; O 2 } are set constant as given by the experimental conditions.The matrix of the stoichiometric coefficients n of the adsorbed species, the electrolyte species and the transferred electrons are derived from the mechanism in Scheme 1 in forward n þ and backward direction n À .The differences in binding energies of the product and the reactant species of each reaction i are defined as the reaction free energies ΔG r,i .Additional kinetic energy barriers in both directions alongside the reaction coordinate are considered by the activation free energy ΔG a,i .Further, the temperature T, the Boltzmann constant k B , the elementary charge e and the symmetry factor β are implemented.The preexponential frequency factor k 0 is set to a constant value for all reactions to avoid over-parameterization, as the experimental data does not allow to determine the frequency factor and the free activation energy independently. [23]We consider additional effects on the energy level of species through areal spacing of the surface sites and the interaction of adsorbed species ΔG int,j .For this, we implement the van der Waals adsorption isotherm or also called Hill-de-Boer isotherm.As described elsewhere, [18a,24] the isotherm is adapted to the model in the form of a function f i q ð Þ; 8 j 2 W sur ; 8 i for forward and backward direction in Equation ( 11) and ( 12), respectively.
(11) (12)   The balance of all species covering the surface is given in Equation ( 13).
The balance of charge q in Equation ( 14) allows to calculate the current density and, hence, to solve the set of equations dynamically.This equation accounts for the charge accumulated in the double layer of the catalyst with its capacitance C dl and the sum of sinks and sources due to the electrochemical reactions by taking the Faraday constant F and the density of active sites 1 with respect to the geometric electrode area into account.
The resulting current density j of a cyclically applied potential is compared to experimental current j exp during the CV with the aim to estimate the model parameters, which are the free energies, the density of active sites and the double-layer capacitance.For best estimation, the root mean squared error (rmse) in Equation (15)   rmse ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 1 N is minimized by two optimization algorithms: 10 6 sets of randomly defined parameter values are simulated.The 20 sets of parameters resulting in the lowest rmse are further optimized by the MATLAB build-in pattern search algorithm, each with a total of 98,000 objective function iterations.For the reaction free energy parameters of the single transition metal oxides RuO 2 and IrO 2 , a profile rmse analysis with deviations of {(À 0.2); À 0.1; À 0.05; 0; 0.05; 0.1; (0.2)} eV was conducted with 25,000 objective function iterations.This is used in the same way as the profile likelihood method is used to check for parameter identifiability. [25]

Figure 1 .
Figure 1.Experimental and simulated CV curves a) on RuO 2 and b) on IrO 2 nanoparticulated catalysts in a 0.1 M H 2 SO 4 solution at room temperature and a scan rate of 200 mV s À 1 .Numbers in the figures correspond to the reaction steps of the reaction mechanism shown in the inset.The experimental data on RuO 2 was published previously. [6b]

Figure 2 .
Figure 2. Energy diagrams along the reaction coordinate of the OER mechanism given in Scheme 1 on RuO 2 (red) and on IrO 2 (green).The potential dependent reaction free energy values are denoted in full lines and the activation free energy barriers in dotted lines.Values are given at electrochemical standard conditions (room temperature and the activities of all substances at unity) and different potentials of a) 1.23 V, b) 1.44 V and c) 1.58 V.

Figure 3 .
Figure 3. Experimental and simulated cyclic voltammetry curves on the binary oxides a) Ir 0.2 Ru 0.8 O 2 , b) Ir 0.5 Ru 0.5 O 2 and c) Ir 0.8 Ru 0.2 O 2, with rmse values of 0.033 mA cm À 2 , 0.017 mA cm À 2 and 0.032 mA cm À 2 , respectively.The simulations allow to distinguish between the processes at the Ru and Ir active sites, which results in the current densities given with the dotted red and green lines, respectively.The data was recorded at 200 mV s À 1 in 0.1 M H 2 SO 4 solution at room temperature.The experimental data on Ir 0.2 Ru 0.8 O 2 and Ir 0.5 Ru 0.5 O 2 was published previously.[6b]

Figure 4 .
Figure 4. Model-based estimation and XPS-measured values of the relative content of Ir active sites on the surface in comparison to the nominal bulk content.The experimental data was published previously. [6b]

Figure 5 .
Figure 5. Reaction free energy values identified for the potential determining deprotonation steps of the OER on the Ru active site (circle, square) and the Ir active site (x) of RuO 2 , IrO 2 and the Ir x Ru 1À x O 2 mixtures with respect to the nominal relative content of bulk Ir.