On the role of microkinetic network structure in the interplay between oxygen evolution reaction and catalyst dissolution

Understanding the pathways of oxygen evolution reaction (OER) and the mechanisms of catalyst degradation is of essential importance for developing efficient and stable OER catalysts. Experimentally, a close coupling between OER and catalyst dissolution on metal oxides is reported. In this work, it is analysed how the microkinetic network structure of a generic electrocatalytic cycle, in which a common intermediate causes catalyst dissolution, governs the interplay between electrocatalytic activity and stability. Model discrimination is possible based on the analysis of incorporated microkinetic network structures and the comparison to experimental data. The derived concept is used to analyse the coupling of OER and catalyst dissolution on rutile and reactively sputtered Iridium oxides. For rutile Iridium oxide, the characteristic activity and stability behaviour can be well described by a mono-nuclear, adsorbate evolution mechanism and the chemical type of both competing dissolution and rate-determining OER-step. For the reactively sputtered Iridium oxide surface, experimentally observed characteristics can be captured by the assumption of an additional path via a low oxidation state intermediate, which explains the observed characteristic increase in OER over dissolution selectivity with potential by the competition between electrochemical re-oxidation and chemical dissolution.


Derivation of the OER over dissolution selectivity
A schematic representation of the discussed generic reaction network structure is given in Figure 1. ϑ shall be defined as the ratio of redeposition r diss,b to dissolution rate r diss,f : The concentration of dissolved species in the electrolyte c sol can then be calculated depending on ϑ: r diss,b = r diss,f ⋅ ϑ c sol k diss,b exp(−z diss (1 − β) f E) = Θ n c k diss,f exp(z diss β f E) ϑ c sol = ϑ Θ n c k diss,f k diss,b exp(z diss f E) Θ n c denotes the coverage corresponding to the common intermediate of OER and dissolution and f = F/(R T). z diss = 1 and z diss = 0 is considered for the dissolution step of electrochemical and chemical type, respectively. Note that the standard reversible potential is lumped into the rate constants 1-3 .

Case 1: Defining ̅ for the case of dissolution step in QE (̇ , = ):
While for batch experiments under equilibrium conditions the net dissolution rate is zero, for flow cell experiments a net dissolution rate is observed despite of QE-conditions since fresh electrolyte is introduced into the system. The dissolution rate can then be described by: With the definition for k ̅ diss : Case 2: Defining ̅ for the case of dissolution >> redeposition (̇ , = ): For ϑ = 0 the apparent rate constant shall be defined as k diss app : = k ̅ diss ≠ fun(V̇): With the definition for k ̅ diss : Merging the two cases ( = 1 and = 0) in a compact expression An apparent kinetic rate constant k diss app is then given with: Applying the QE-assumption: With symmetry factor β = 0.5: . Analogously: Inserting Θ 1 : For Θ i it can be stated: Using the definition of the stability-number Similar to the dissolution step, for the rds the effective kinetic rate constant can be expressed in a compact way considering z rds =1 for an electrochemical step and z rds = 0 for a chemical step: k ̅ rds = k rds exp(z rds βfE) The selectivity can be defined as the stability number S num which is the ratio of OER rate over dissolution rate 4 : Here, is the reaction order of the rate-determining step and is determined by the number of (adjacent) reactant species that need to be formed such that the rds can occur.
Derivation of selectivity for a mono-nuclear rds (ν = 1) This case results in a more simple derivation since the coverage Θ n c that represents the coverage of the n EC = n rds − n c here represents the number of electrochemical type steps between the common intermediate and the rds. The nominator of equation SI (7) represents OER activity and is analogous to classic theory for Tafel-slope analysis. The derivation of selectivity in the mononuclear case can be considered as the simpler case since the influence of the coverage simply, mathematically cancels out. As a next step, the type of the dissolution step shall be further defined using equation SI (3): j=n c z rds and z diss are one if the step is electrochemical and zero if the step is of chemical type. Finally gives for the case of mononuclear rds (ν = 1): And the derivative with respect to potential: Derivation of selectivity for a bi-nuclear rds ( = 2) Plugging in equation SI (4) for Θ n rds and Θ n c gives: The closing condition can be expressed as: Insertion of equation SI (4) gives: SI (12) Plugging equation SI (12) into equation SI (10) one then obtains for the selectivity: Furthermore, by using the definitions n EC = n rds − n c and for the dissolution step equation SI (3): And finally:

Non-decreasing selectivity for a mononuclear mechanism with a chemical dissolution step without QEassumption
In this section the non-decreasing selectivity in case of a chemical type dissolution step shall be demonstrated without using the QE-assumption. The selectivity is expressed as: Since a net oxidation reaction is considered it holds 1 < < ∞. The two extremal cases are firstly described by M→1 which represents the QE-case (R n c ,f ≈ R n c ,b ) and secondly the opposite case M→∞ of non-equilibrium (R n c ,f ≫ R n c ,b ). For the selectivity it then holds: Considering the forward reaction as an oxidation reaction without loss of generality the selectivity can be expressed as:

Derivation selectivity for direct competition of rds with catalyst dissolution without QE-assumption
In case of direct competition between rds and dissolution (cases 1-4 in Table 2) the selectivity describtion can be derived without the QE-assumption: S num = Θ n rds k ̅ rds Θ n c k diss app = Θ n c k ̅ rds Θ n c k diss app = k ̅ rds k diss app = k rds exp(z rds βfE) k ̅ diss exp(z diss β(1 + )fE) It follows: Which is the same expression as equation SI (8), when n c = n rds , however here derived without using the QE-assumption.

Model equations
TO-model and high oxidation state path of the RS-model (HOSP): i tot = i LOSP + i HOSP

Simulation parameter values
Supplementary For discussing OER-activity, R is the oxygen evolution reaction rate and for discussing stability R is the dissolution rate. x and y represent different pH values as given in the legend of Supplementary Figure 1 Figure 2, the reaction order of the LOSP is -2 and similar is the dependence of the formation rate of Ir(III), which is considered prone to dissolution. On the other hand, the dissolution step demands the supply of 3 protons following the reaction equation5 for the Ir(III) dissolution: HIrO 2 + 3H + → Ir 3+ + 2 H 2 O. Therefore, this dissolution reaction step incorporates a reaction order of +3. Since the backward reaction rate of the oxidation reaction from adsorbed OH to Ir(III) is suggested by the model fit to be negligibly small, this reaction step does not contribute to an additional effect. The observed maximum proton dependence is related to the maximum of Ir(III) coverage and dissolution via Ir(III), which is shown in Fig 6a. The HOSP contributes with a reaction order of -1, which is especially seen in the evaluation of higher pH. Similar to the reaction order for OER activity, the dissolution proton reaction order approaches zero towards limiting current conditions.