The low overpotential regime of acidic water oxidation part I: the importance of O2 detection

The high overpotential required for the oxygen evolution reaction (OER) represents a significant barrier for the production of closed-cycle renewable fuels and chemicals. Ruthenium dioxide is among the most active catalysts for OER in acid, but the activity at low overpotentials can be difficult to measure due to high capacitance. In this work, we use electrochemistry – mass spectrometry to obtain accurate OER activity measurements spanning six orders of magnitude on a model series of ruthenium-based catalysts in acidic electrolyte, quantifying electrocatalytic O2 production at potential as low as 1.30 VRHE. We show that the potential-dependent O2 production rate, i.e., the Tafel slope, exhibits three regimes, revealing a previously unobserved Tafel slope of 25 mV decade−1 below 1.4 VRHE. We fit the expanded activity data to a microkinetic model based on potential-dependent coverage of the surface intermediates from which the rate-determining step takes place. Our results demonstrate how the familiar quantities “onset potential” and “exchange current density” are influenced by the sensitivity of the detection method.


Characterization of samples
, 100 • C (grey) and room temperature (black). The peaks corresponding to rutile RuO2 have been labeled. The spectra were taken with a grazing-incidence (alpha-2θ) geometry with an incidence angle of 0.5 • .  Table 1: Root mean square roughness values for RuOx films deposited at temperatures from 400 • C to room temperature. The films are nominally smooth with a root mean square roughness ranging from 1-3 nm.
2 OER in O2-saturated electrolyte 2.1 O 2 partial pressure at the electrode surface The EC-MS activity measurements presented in the main text were performed with the electrolyte saturated with helium, chosen as an inert gas without interfering mass spectrometry signals. The measurements were thus not done under the standard condition of saturation with 1 bar O 2 , the condition for which the equilibrium potential is 1.23 V RHE . This is why we refer to 1.23 V as the standard equilibrium potential and the difference between an applied potential and 1.23 V RHE as the nominal overpotential. The lack of O 2 saturation influences the OER equilibrium potential according to the Nernst equation: where U eq is the equilibrium potential, U • is the standard equilibrium potential, R is the gas constant, T is the temperature, F is Faraday's constant, and a O 2 is the O 2 activity. The O 2 activity is defined as the ratio of the actual O 2 concentration to that of a solution saturated with O 2 : Where c O 2 el is the O 2 concentration at the electrode and we used the Henry's Law constant of O 2 in water, K O 2 H , to calculate the saturation concentration, c O 2 sat . For a light gas like O 2 , the transport of oxygen away from the electrode surface is limited by diffusion through the working volume [1], and so the concentration at the electrode surface, can be estimated using Fick's first law of diffusion: whereṅ O 2 A el is the flux density of oxygen produced at the electrode, L is the working distance between the electrode and the chip membrane, and D O 2 is the diffusion constant of O 2 in water. The largest deviation from standard conditions occurs at the smallest concentration of O 2 , and thus at the smallest O 2 production rates, which in these experiments means a flux density at our detection limit of around 1 pmol/s/cm 2 .
Thus the equilibrium is more cathodic by about 110 mV in the most extreme case given the actual concentration of O 2 on the surface. However, as we discuss in more detail in Section 6.5 of this SI, the OER is kinetically driven, so it remains for now an open question of whether the shift in equilibrium potential influenes the rate of OER. At high overpotentials, this can be tested simply, by measuring the OER current with and without O 2 in the electrolyte, as shown in this SI in Figure 5.
It is more challenging to determine whether the presence of O 2 effects the OER in the low overpotential regime where detection of O 2 is necessary for reliable OER activity measurement. To overcome this challenge, we designed an experiment in which we use isotope labeling and the gas-switching capability of chip EC-MS.  The current density (black) and the partial current density for 18 O 2 (green) at the end of each constant-potential step. (c) The Faridaic eciencies for 18O2 (green) and 16 O 18 O (red) as a function of potential. The error bar represents the uncertainty due to the standard deviation of the baseline m/z=34 MS signal. Figure 2b shows the results af the activity measurement: Total current density and 18 O 2 partial current density, calculated as j O 2 =ṅ O 2 /(4F), are plotted vs the hold potential. This is done for both the measurement in He-saturated electrolyte (solid lines, circles) and in O 2 -saturated electrolyte (dotted lines, squares). There is no discernable difference, i.e. the activity and 18 O 2 partial current density are identical for OER in the two sets of conditions. The 18 O 2 partial current density falls separates a bit from the total current density at the lowest overpotentials, where capacitive charging current is a significant fraction of the total, as described in the main text. Figure 2c shows

Mechanistic implications
The OER can be divided into four electron transfer steps, conventionally written as: B. D.
As we will discuss in Section 6.2 of these SI, one of these steps can be considered the rate-determining step (RDS), and fitting of the results implies that there are two pre-catalytic states in equilibrium with the active state of the surface, from which the RDS takes place. If we assume that the pre-catalytic states are OER intermediates appearing in the above mechanistic scheme ( * , * OH, * O, and * OOH), then we can write the possible pre-catalytic equilibria as follows: A as RDS.
B as RDS.
C as RDS.
D as RDS.
If A or B were the RDS, we would expect an euilibrium to exist involving O 2 , and thus for the partial pressure of O 2 to effect the pre-catalytic equilibrium giving rise to the active state. This is discussed further in Section 6. If we instead assume that all steps except for the RDS are in equilibrium, then B as RDS would also put O 2 dissociation on the surface in a state of equilibrium, allowing us likewise to rule it out as RDS.
3 Pushing the limit with Ru foam       , 300 • C (in blue) and 400 • C (in red). Two distinct changes in Tafel slope are observed. At 1.4 VRHE, the Tafel slope changes from 30 mV/decade to 60 mV/decade. The potential for the change in Tafel slope from 60 mV/decade is dependent on the sputtering temperature and increases from 1.47 VRHE on the room temperature sputtered film to 1.52 VRHE on the 400 • C sputtered film. Filled circles represent the data obtained using mass spectrometry, filled squares represent the data obtained by potentiostatic measurements and the curve represents the capacitancecorrected cyclic voltammograms. Lines showing the three different Tafel slopes are drawn as a guide to the eye. Horizontal dotted lines are drawn to indicate the transition from one Tafel region to another.

Kinetic model
In this section of the SI, we outline the kinetic models used in main-text Figure 5b. First, below, we introduce the assumptions behind the most general form of the model's a rate equation, introduce all terms in the equation, and motivate the assumptions. Then we describe specific cases: (i) two sites with only one state each (Static coverage model, subsection 6.1), which cannot fit the our observations; and (ii) one site with multiple states (Potentialdependent coverage, subsection 6.2), which can. In subsection 6.4, we describe how the potential-dependent coverage enables an estimation of the energy of the surface states in the catalytic cycle, and describe our fitting procedure to do so.
If we can make the following assumptions about a multi-electron electrochemical reaction: 1. The back reaction is negligible 2. Mass transport is infinitely fast compared to the reaction kinetics 3. The coverage of different sites on the surface, defined as a unit of the surface that can catalyze the reaction by an unchanging mechanism, is constant, though the coverage of the states of each site may change with potential.
4. For each type of site, there is a single electron transfer step in the catalytic cycle, the rate-determining step (RDS), which is the bottleneck. All other steps are essentially at equilibrium.
Then the reaction rate as a function of potential can be described in general as [3] where: • j is the surface-normalized current density • R is the gas constant • T is the temperature (298.15 K) • F is Faraday's constant • U is the potential (E in the main text) • U • is a reference potential (E • in the main text). We will use the standard equilibrium potential for the OER, • M is the number of different sites • θ m,RDS is the coverage of the state of m from which the RDS takes place.
• α m,RDS is the symmetry factor of the RDS of site m. This is defined as the portion of FdU by which the activation barrier for the step is lowered if the potential is increased by dU .
• j • m,RDS is the exchange current density of the state of site m from which its rate determining step takes place. This defined as the surface-normalized current density at U = U • if the surface were fully covered by of the state of site m before its rate-determine step takes place, i.e θ m,RDS = 1. This will in general be not only difficult to measure because it is a small current density, but impossible to measure directly because θ m,RDS < 1 at U = U • . It is thus in general a purely theoretical quantity. Now, we motivate the validity of the assumptions above for our oxygen evolution experiments on RuO 2 at low overpotential.
1. The back reaction (ORR) is negligible, as the current density and O 2 production rate are identical in O 2saturated electrolyte and He-saturated electrolyte (see Figures 2 and 5).
2. The mass transport processes in OER are protons away from the surface (4 per cycle), water to the surface (2 per cycle), and O 2 from the surface (1 per cycle). Of these, the transport of O 2 is by far the slowest, but because no difference in reaction rate was observed in O 2 -saturated electrolyte (see again Figure 2), we conclude that mass transport does not influence the rate at the low current densities explored in this work.
3. The third assumption, that the abundance and mechanism of each type of site is unchanging, is a common assumption in microkinetic modeling [4,5,6,7,8,9]. A motivation of this comes from the stability and repeatability of our activity measurements. The O 2 production rate at constant potential was constant over 15 hours, and the activity measured on the way up was identical to that measured on the way down during a potential staircase experiment (main-text Figure 2). We also argue under the static coverage model that a mechanism that changes with potential cannot by itself explain the data.

4.
A single rate-determining step is likewise a common assumption in microkinetic modeling [4,5,6,7,8,9], but worth discussing. The second part of this assumption, that the rate-determining step involves an electron transfer, is non-obvious, and is a topic of debate [10]. Both are discussed in more detail below. Briefly, the rate equation can still be approximated by Equation 13 if these assumptions do not hold: with multiple rate-determining step, the rate of each rate-determining step for a single site must be identical, and either could be used, with the caveat that θ m,RDS is not in equilibrium with all other θ's. If the RDS of a specific site is a purely chemical step, then α m,RDS = 0 for that site, such that all of the potential dependence is in θ m,RDS , but the form of Equation 13 still holds.
The goal of the model is to explain our data, wherein a range of RuOx catalysts show a common activity vs potential behavior, with a potential dependence that starts strong, at 25 mV/decade below 1.4 V vs RHE, and gradually weakens with increasing potential, to 120 mV/decade above 1.5 V vs RHE (main-text Figure 4, Figure  S7).

Static coverage models
In a static coverage model, we assume that the rate-determining step takes place from a surface state which does not change in abundance as a function of potential. In other words the active states are static, and have constant coverage, i.e. θ m,RDS = θ m = constant.

One site:
If there is a constant coverage of the active surface species in its active state, then Equation 13 simplifies to: The potential dependence is most conveniently described after taking the logarithm, using base 10 by convention, of the current density normalized to the exchange current density: Note that the Nernst constant, F/(RT ln (10)), which is 60 mV at standard temperature, appears in the equation. The Tafel slope is defined as the reciprocal of the derivative of the base-10 logarithm with respect to potential, i.e. the potential change needed to achieve a factor-10 increase (a decade) in current density: The symmetry factor for simple electron transfer steps is typically 0.5 [3], so, this results in a Tafel slope of 120 mV per decade, much higher than that observed. Symmetry factors are by their definition between 0 and 1, so the smallest Tafel slope possible with a single active state of constant coverage is 60 mV per decade. So even if the mechanism changes, a single-site static coverage model cannot explain a Tafel slope lower than 60 mV per decade.

Two sites:
We consider the activity originating from two sites, named such that site 1 has a larger coverage-weighted exchange current density than site 2, i.e.
The total current density is a superposition of the current density due to the two sites: We now consider the three possible relationships between the symmetry factors below, i.e., α 1 = α 2 , α 1 > α 2 , and α 1 < α 2 .
If the symmetry factors for the two current densities are equal, i.e. α 1 = α 2 , then the terms can be grouped and it reduces to the form for a single site: This would imply a constant Tafel slope and so cannot explain the data.
If the symmetry factors are not equal, then there is a potential at which the two sites in theory contribute equally to the overall current density, which we will call U cross . By setting j 1 = j 2 , we can solve for this potential: If the site with the highest exchange current density also has the highest symmetry factor, i.e. α 1 > α 2 , then U cross < U • and the site with the higher exchange current density will dominate at all potentials higher than U • : Finally, if one site has a higher exchange current density but a second site has a higher symmetry factor, then the dominant site switches at a potential U cross which is greater than U • . Below this potential, the first site dominates: Above U cross , the second site dominates: Since α 1 > α 2 , the potential-dependence of log(j) increases as the potential increases past U cross , i.e. the Tafel slope decreases. This is the opposite of what is observed in our experiments, where the lowest Tafel slope (strongest potential-dependence of log(j)) is observed at low potentials and the Tafel slope increases at higher potentials.
This conclusion holds if there are more then two sites of static coverage on the surface, since any two of them can be labeled 1 and 2 and compared as above. Thus, we can rule out multiple sites of static coverage as an explanation of the changing Tafel slope we observe.

Potential-dependent coverage
Now, we consider the case where state of the active site, and thus the coverage of the active state, changes as a function of potential. We consider only one site for simplicity. Equation 13 reduces to: Taking the logarithm, this becomes and differentiating with respect to potential, the reciprocal Tafel slope is: The potential dependence now has two terms. One, α RDS /(60[mV]), is from the activation of the RDS, while the other, ∂ log(θRDS) ∂U , is due to the increasing coverage of the active state with potential. Using a typical symmetry factor of 0.5 and the experimental Tafel slope, which at the lowest measured potentials is ≈ 24 mV/decade (rounding to the nearest divider of 120 mV/decade), we can solve for the potential dependence of the coverage of the active state: In other words, at these low overpotentials, while it takes 120 mV to increase the rate of O 2 evolution normalized to the coverage of the active state by a factor of 10, it only takes 30 mV to increase the population of that state by a factor 10. Thus, according to this explanation, the coverage term is the most important for the overall potential dependence. We presented this analysis on a smaller data sets in refs [11,9]. To elaborate on this explanation and determine if it can describe the changing Tafel slope in the experimental data, we develop an equation for θ RDS . For this coverage to be changing, the site must be able to occupy one or more states. Specifically, we consider the state from which the rate-determining step takes place, or the active state, denoted S RDS , a state less oxidized than this state by one electron, denoted S RDS−1 , and so on as S RDS−n up to n = N electrons less oxidized than the rate-determining state (in practice we will use at most N = 2, or a total of three states). Each of the additional states can be oxidized to the active state according to the following reaction: Note that: • S RDS−n with n > 0 can be but do not need to be part in the electrocatalytic cycle.
• While we have written Reaction 36 with an equal number of proton and electron transfers, pH-dependence studies would be needed to confirm this.
The equilibrium coverage of the states depends on their relative standard free energies. We define ∆ RDS RDS−n G 0 to be the standard free energy of the state n electrons reduced of the active state (S RDS−n ) relative to the active state (S RDS ). Here "standard", denoted by the subscript 0 , means at idealized unity coverage, and should not be mixed up with the superscript • , used to indicate the reference potential of U • = 1.23 V RHE . The standard free energy of a surface state relative to RDS can be expanded to make its potential dependence explicit: where ∆ f G • 0 is the standard free energy of formation of the indicated state at idealized unity coverage at the reference potential. This is the quantity that can be calculated by density functional theory (DFT) given a guess at the structure of the surface state (on which which the present work does not speculate).
The standard free energy of S RDS−n relative to S RDS at the reference potential, ∆ RDS RDS−n G • 0 , is the quantity which will be used as a fitting parameter in the present work.
From the relative standard free energy, we can calculate an equilibrium constant K RDS RDS−n , which is the ratio of the coverage of S RDS−n to the coverage of S RDS . At the reference potential, this ratio is: At other potentials, this coverage ratio is: In the coming steps, it is more convenient to use its reciprocal, Note that in the special case that n = 0, the state S RDS−n is the same as S RDS and this equilibrium constant K naturally becomes unity.
As such, assuming we have all states represented, we can compactly express the coverage of any state as: The most interesting coverage for the OER is, of course, the coverage of the state from which the rate-determining step takes place. Its expanded expression is: As such, we have all that is needed for modeling the OER kinetics. The fitting parameters are ∆ RDS RDS−n G • 0 and j • RDS . But how many values of n to include?
The analysis above of the lowest overpotentials can help. We determined that the potential dependence of the coverage of the active state should be a decade per 30 mV.
Differentiating Equation 46, let alone its logarithm, with respect to U would be difficult, so for now we make the simplification that one state, S RDS−n , dominates the surface: This is much more wieldly. Taking the logarithm and differentiating by U , we get the potential dependence of the coverage: So the potential dependence of the active state is a decade for every 60 mV divided by the difference in oxidation between it and the state dominating the surface. Since we determined above that the potential dependence of the active state should be about a decade every 30 mV at the low overpotentials where it is steepest, N = 2 will suffice for fitting.

Inserting this into Equation 32
gives which motivates the definition of an effective symmetry factor α eff (called α * in the main text), also called the transfer coefficient: This is a specific case of a more general equation, presented elsewhere [12,9] as where n f is the effective number of electron transfers to produce the active state; ν is the number of occurances of the RDS per catalytic cycle, here 1; n r is the number of electrons transferred per RDS, here 1; and the symmetry factor of the RDS is called β. Finally, we introduce n , which is the effective average difference in oxidation between the active state and the surface: This quantity, which can approximate n in Equation 50, decreases with increasing potential, so a potentialdependent coverage model of the active state is able to explain the decreasing potential dependence (increasing Tafel slope) observed.

Relative importance of coverage and driving force
In this subsection, we analyze the rate equation of the coverage dependent model derived above.
First, we expand Equation 28 by substituting Equation 46 for θ RDS and, based on the observed Tafel slope, limiting the sum to three sites (i ∈ [0, 1, 2]), to get: Then, we substitute Equation 39 for (K RDS−i RDS ) • , regroup, and simplify the notation by introducing This is the rate equation for an electrochemical reaction proceding from an active state in equilibrium with two more reduced states.
In the next section we use this rate equation to fit the experimental data. Here we comment on its characteristics.
At high overpotentials, the exponential terms in the bottom go quickly to zero and the potential dependence comes purely from the term in the top. This gives a Tafel slope of 2 RT F ln(10) = 120 mV per decade. This is the contribution to the potential dependence of the driving force to the RDS, which is constant: Driving the RDS or, equivalently, reducing its barrier, requires 120 meV improvement to increase activity by a factor of 10.
The potential dependence of the denominator, on the other hand, is not constant. It changes directly with the coverage of the three states S RDS , S RDS−1 , and S RDS−2 . At high overpotentials, as described in the last paragraph, the first term dominates and the denominator has no potential dependence. This corresponds to saturation of the surface sites with the active state, S RDS . At low overpotential, the third term dominates, corresponding to coverage of the surface with S RDS−2 . Under these conditions, the rate equation can be rewritten as The potential dependence of the second exponential factor is due to the effect of potential in bringing S RDS−2 up to S RDS . Its contribution to the overall potential dependence corresponds to a Tafel slope of 1 2 RT F ln(10) = 30 mV per decade. Driving the population of the active state, or, equivalently, stabilizing it with respect to other surface states, only requires 30 meV improvement to increase activity by a factor of 10.
This is an important point for electrocatalyst design.
An interesting related note is on the difference between potential-determining step and rate-determining step.
In the traditional metal-peroxide mechanistic model of oxygen evolution electrocatalysis, the scaling of the energies of the four surface states (*, *OH, *O, and *OOH) involved mean that in the best case two electron transfers or, more often, one electron transfer is much more uphill than the others, requiring higher potential to become downhill. A thermodynamic approach considers this last step to be come downhill the potential determining step.
On the other hand, a single rate-determing step means that when the free energies of the states of the electrocatalytic cycle are adjusted for the coverage of the intermediates, the entire excess energy input by the overpotential is released in a single step. This is how we sketched it in the inset to the lower panel of main-text Figure 5.
At the lowest potential that we were able to measure O 2 production, 1.29 V RHE , the excess free energy input is per catalytic cycle. By the above reasoning, this entire excess free energy input goes to the RDS. Interestingly, this corresponds approximately to the expected limiting overpotential. But the coverage of the active state is minuscule. The reason much higher overpotential is required to get a substantial current density is that the vast majority of the extra driving force goes to populating the active state.

Fitting procedure for the coverage dependent model
As input to the fitting, we use experimental capacitance-normalized OER current (in amperes per farad, A/F) vs potential (in V vs RHE) for all sputter-deposited RuO x (deposited at 25, 200, 300, and 400 • C) and Ru foam samples. We use the O 2 signal measured by EC-MS below 1.45 V RHE at all potentials where it was significantly different than the background signal. Higher potentials are excluded because of concerns about the potential distribution in the EC-MS cell at higher current densities. We use results from experiments in both H 18 2 O and H 16 2 O electrolytes. We add to this data set potential-hold activity measurements in the range 1.4 to 1.5 V vs RHE from RDE for RuO x sputter-deposited at each temperature. All data points in this data set are weighted equally for the fit.
The experimental normalized current density are fit with the normalized current density calculated by Equation 28, the rate equation for one site under the assumptions at the start of this section. In its expanded form, it is: Three fitting parameters are used: • j • RDS , the hypothetical capacitance-normalized OER current at the reference potential (U • = 1.23 [V RHE ]) given unit activity (full coverage) of the active state. Note that for this fitting we did not vary α RDS but instead set it to 1/2. In the last subsection, we motivated that additional sites more reduced than S RDS−2 are not needed, based on the Tafel slope observed.
Fitting was done by square error minimization using the minimize function from the optimize module of the scipy python package. Since the behavior at small overpotentials is of as much interest as the behavior at high overpotentials, we minimize the square error log(j) instead of the square error on j. The function to minimize is: Where i indicates an experimental data point (U i , j i,exp. ). The results of the optimization is: where we have used Avogadro's number N A to convert between kilojoules per mol of sites and electron volts per site (note that e · N A = F).
The root-mean-square error (in decades) is Error representing a factor of 10 0.35 ≈ 3 spread in the combined set of activity measurements. While that may sound like a lot, note that at the lowest overpotentials, due to the very low Tafel slope this corresponds only to approximately ±10 mV variation between samples.
With the fitting parameters solved, we can also describe the free energies of the states relative to the active state via Equation

Remarks on equilibrium
We now return to the concept of equilibrium, touched upon in Section 2 of this SI. There, we mentioned that the equilibrium potential depends on the O 2 concentration at the electrode surface according to the Nernst equation (eq. 1), and that the O 2 concentration at the electrode surface in EC-MS experiments is linearly related to the geometric O 2 production rate according to the mass transport of O 2 from the surface, equation 3. We can define the Nernst overpotential as the difference between this equilibrium potential and the applied (ohmic-drop-corrected) potential: This is in contrast to the nominal overpotential referred to occasionally in the text, which ignores the Nernst shift and is simply the applied (ohmic-drop-corrected) potential in excess of U • = 1.23 V vs RHE: In the EC-MS measurements, the only O 2 present is that generated by the electrode and removed through the chip, and the accessible potential range (avoiding bubbles) is that for which this is below saturation coverage, i.e. a O 2 ECMS < 1. Thus, the Nernst overpotential is greater than the nominal overpotential. In the rotating disk electrode (RDE) chronoampermetric measurements included in the activity dataset, the electrolyte is saturated with O 2 , so a O 2 RDE = 1 and the Nernst overpotential is equal to the nominal overpotential. Figure 8a-b show the activity results plotted vs overpotential. The faded symbols show the activity against nominal overpotential, and the solid symbols against Nernst overpotential. When, in Figure 8b, the results have been normalized to capacitance, they converge well against nominal overpotential, but not against Nernst overpotential. This result agrees with that in Figures 2 and 5, which show that the oxygen partial pressure does not affect activity. In other words, the OER in the systems studied here is kinetically controlled and not equilibrium controlled. For this reason, we refer prefer referring to the absolute potential on the RHE scale and not the overpotential. The question remains, why doesn't the Nernst overpotential matter? We'll now attempt to answer. The modelled normalized OER current is green, the hypothetical normalized ORR current under 1 bar O2 in red dashed trace, and the hypothetical total current in black dotted trace. Note E is referred to as U in the SI text (please forgive us).
Equilibrium is defined as a set of conditions in which the forward and the backward reaction run at the same rate. For OER, the backwards reaction is the oxygen reduction reaction (ORR), O 2 + 4 (H + + e ) 2 H 2 O. The OER and ORR can be thought of as each having an independent current-vs-potential profile, and the equilibrium potential is where the currents associated with the two processes are of equal magnitude. Treating the forward and backward reactions as if they were elementary reactions (more on that below), the reason that the equilibrium potential shifts in a cathodic direction when p(O2) is decreased is a result of a change in ORR, not necessarily OER. This is illustrated in Figure 8c-d.
Here we assume an O 2 -saturated electrolyte and assume that materials are equally good ORR catalysts as OER catalysts, i.e. we the magnitude of the ORR current at a given ORR overpotential is equal to the magnitude of the OER current at the same OER overpotential. Mathematically we assume that, where η is the ORR overpotential and j OER is assumed to be that predicted by the model, Equation 59, fit to the experimental data. Note that this is almost definitely a huge overestimate of the ORR current density, since in reality RuO 2 is a much worse ORR catalyst than OER catalyst. However, Equation 67 must hold at U = 1.23 , V RHE , i.e. η = 0, because the second law of thermodynamics demands that there is no net activity at the equilibrium potential: This assumption gives the symmetry around U • in Figure 8, but functions only as a conceptual help because j ORR is only treated hypothetically. Nonetheless it makes clear that, in the potential range of our OER data, U ≥ 1.29 V RHE , the ORR current must be at least as small as the exchange current density, and thus several orders of magnitude smaller than the OER current density. This is in stark contrast to the case of hydrogen evolution on platinum, where there is a sizeable potential range over which both forward and backward reaction play a role. The inset of Figure 8d, hypothetical in our case, will look concretely familiar to an experimentalist who has worked with HER on Pt.
Because the ORR current is expected to be undetectably small at the potentials in which we are able to observe O2 generation (at 1.30 VRHE in O2-saturated electrolyte, we would predict the ORR current to be ten thousand times smaller than the OER current), the presence or absence of ORR, and thus the equilibrium potential, does not affect the measured OER activity. It also explains why the oxygen partial pressure does not effect the OER activity (Figures 2 and 5): Changing the O 2 partial pressure changes the ORR current, but this makes no difference to the total current where we can measure the OER rate.
The attentive SI reader might object at this point that we've just treated the OER as a single reaction, right after having broken it into steps -couldn't the O 2 partial pressure have an effect on the rate if it was involved in one of the elementary steps?
The answer to this must be yes -O 2 partial pressure would effect the rate if O 2 were involved in the equilibrium before the rate determining step. In other words, we sneakily assumed that Reaction 36 did not involve any O 2 . The lack of dependence of rate on O 2 partial pressure would seem to confirm this. Like the lack of isotopic scrambling between dissolved O 2 and the oxygen in the water being oxidized (Section 2 of this SI), the observation is consistent with * OOH O 2 + * + (H + + e -) being the rate determining step. Note that, unlike the O 2 partial pressure, the proton concentration is expected to influence the equilibrium of the steps up to the active state. Low-overpotential regime pH effects are therefore of high interest for future mechanistic investigations, but are out of the scope of the present work.

Database contents
This section shows figures of some of the datasets included in the database accompanying this article, available when this article is published at https://github.com/ixdat/LowOverpotentialRegime