How To Get Mechanistic Information from Partial Pressure-Dependent Current–Voltage Measurements of Oxygen Exchange on Mixed Conducting Electrodes

The oxygen incorporation and evolution reaction on mixed conducting electrodes of solid oxide fuel or electrolysis cells involves gas molecules as well as ionic and electronic point defects in the electrode. The defect concentrations depend on the gas phase and can be modified by the overpotential. These interrelationships make a mechanistic analysis of partial pressure-dependent current–voltage experiments challenging. In this contribution it is described how to exploit this complex situation to unravel the kinetic roles of surface adsorbates and electrode point defects. Essential is a counterbalancing of oxygen partial pressure and dc electrode polarization such that the point defect concentrations in the electrode remain constant despite varying the oxygen partial pressure. It is exemplarily shown for La0.6Sr0.4FeO3−δ (LSF) thin film electrodes on yttria-stabilized zirconia how mechanistically relevant reaction orders can be obtained from current–voltage curves, measured in a three-electrode setup. This analysis strongly suggests electron holes as the limiting defect species for the oxygen evolution on LSF and reveals the dependence of the oxygen incorporation rate on the oxygen vacancy concentration. A virtual independence of the reaction rate from the oxygen partial pressure was empirically found for moderate oxygen pressures. This effect, however, arises from a counterbalancing of defect and adsorbate concentration changes.


Samples
: Cross section SEM image of a LSF film (100 nm) on top of a YSZ single crystal (100) substrate. Figure S2: Sketch of the three-electrode setup used in this study.

S-2
Impedance spectroscopy Impedance spectra were measured at oxygen partial pressures from 2.5 × 10 −4 bar to 1 bar to determine the electrolyte resistance R offset . Figure S3 displays the impedance spectra and the corresponding fits to the equivalent circuit shown in the inset. A CPE element with impedance Z CPE = −i(ωT ) −P was used to model an imperfect capacitance. The fit results are listed in table S1 and the polarization resistance is also plotted in figure S4 versus the oxygen partial pressure. At low p O 2 the data can be fit to a power law with an exponent of -0.73. Above 20 mbar the polarization resistance increases with p O 2 . This is consistent with the bend found for both anodic and cathodic current voltage curves in the same pressure region.  Figure S3: Impedance spectra (1 MHz to 100 mHz, 5 points per decade) measured between an LSF thin film electrode and the reference electrode at 600 • C in various oxygen partial pressures. Symbols are measured data, lines are fits to the equivalent circuit shown in the inset. Only the low frequency semicircles/arcs were included in the fits.

Deduction of a rate equation
Charge transfer at aqueous electrolyte|electrode interfaces is frequently studied and detailed models have been established, describing the corresponding current-voltage characteristics according to Butler-Volmer's equation S1,S2 Here, j denotes the net current density, j 0 is the exchange current density and includes the reactant concentrations, η is the overpotential, α represents the symmetry factor -for electronic transfer it is often close to 0.5 -and z is the charge number of the transferred species.
Electrochemical reactions at mixed conducting oxide electrode|gas interfaces, however, differ from aqueous reactions in several respects, making the analysis in terms of equation (1) unsuitable. First, the applied overpotential changes the oxygen chemical potential in the electrode bulk and thus modifies the concentration of point defects, i.e. the reacting species.
Second, despite the possibly existing electrostatic potential difference χ = ϕ ode −ϕ ads between the electrode bulk (ϕ ode ) and the adsorbate layer (ϕ ads ), an applied overpotential does not directly translate to a change of this surface potential. If χ is caused by charged adsorbates, any overpotential driven change of this surface potential is correlated with a change in adsorbate concentration, and the resulting χ − η relation can become quite non-trivial. S3 Owing to these differences, a modified approach is required to describe the current-voltage characteristics of electrochemical reactions at solid electrode|gas interfaces. In the following we deduce such a model, i.e. a rate equation, for an exemplary mechanism and this can then be generalized. This mechanism is not necessarily the most realistic one, rather it is chosen for the sake of clarity.
Let us assume that the reaction consists of a reductive adsorption of molecular oxygen to form adsorbed O -2 (2), followed by dissociative incorporation into the electrode (3) and S-5 reduction to oxide ions (4), and let steps (2) and (4) be sufficiently fast compared to step (3), such that (3) is the rate determining step (rds).
Equations (2) and (4) include holes (h ) in the valence band but could also be formulated with electrons (e ' ) from the conduction band, due to equilibrium of (2) and electron hole formation. The reaction rates of the rate limiting forward ( − → r ) and backward ( ← − r ) ion transfers are then given by S-6 Here, χ = ϕ ode − ϕ ads is the electrostatic potential difference between electrode bulk and adsorbate layer, µ 0 i is the standard chemical potential and z i is the charge number of species i (z O -2 = −1 and z h = 1). K 1 and K 3 are the purely chemical equilibrium constants of the preceding and succeeding equilibria without the factor due to the equilibrium surface potential. Combining equations (9), (10) with equations (5) and (6) yields The rate determining transfer of O -2 from the adsorbate layer to the electrode bulk can be considered a jump of the O -2 ion over a spatial energy barrier, where initial and final state are at different electrostatic potentials ϕ ads and ϕ ode , respectively. S4 The activation barrier for this ion jump consists of a purely chemical term ( − − → E eq a,c and ← − − E eq a,c ) and an additional component due to the potential difference between the two phases (αz O -2 eχ and − (1 − α) z O -2 eχ). The surface potential χ = χ 0 + ∆χ includes the equilibrium surface potential χ 0 and its deviation under current ∆χ; α reflects the symmetry of the energy barrier, see figure S5. Thus, we get S-7 with the pre-exponential factors − → k 0 and ← − k 0 of the forward and backward ion transfer. As sketched in figure S5, the change in surface potential upon current ∆χ = χ − χ 0 modifies the equilibrium activation barriers by αz O -2 e∆χ and − (1 − α) z O -2 e∆χ for the forward and backward reaction, respectively; a possible χ dependence of α is neglected. Combining equations (11) to (14) leads to Thus, we get a,c kT . One peculiar feature of this specific mechanism is the fact that forward and backward reaction have the same surface potential dependency, i.e both reaction rates decrease with increasing surface potential.
The reason for this behavior is that in forward direction, the thermodynamic term of the preceding equilibrium (−eχ 0 , −e∆χ) adds to the kinetic term of the rate limiting ion transfer (αeχ 0 , αe∆χ) resulting in the same surface potential dependency as the kinetic factor of the backward reaction ((α − 1) eχ 0 , (α − 1) e∆χ). The succeeding equilibrium does not contribute a surface potential dependency since no charge is transfered between the two phases. Equal surface potential dependencies of forward and backward rate can occur if a preceding equilibrium involves a charge transfer with the opposite direction of the charge transfer in the rate determining step. In general, however, different dependencies of − → r and ← − r result. Figure S5: The incorporation of an O -2 ion can be considered an ion jump over an activation barrier. Under equilibrium this energy barrier consists of a purely chemical energy contribution (1) with the activation energies − − → E eq a,c and ← − − E eq a,c and an electrostatic potential term (eχ 0 ) due to charged adsorbates (2). This potential term causes a modified energy barrier (4) with activation energies −→ E eq a = − − → E eq a,c − αeχ 0 and ←− E eq a = ← − − E eq a,c + (1 − α)eχ 0 . Under current flow, the surface potential changes from its equilibrium value (3), and this further modifies the energy barrier (5) and leads to activation energies of − → E a = − − → E eq a,c − αeχ 0 − αe∆χ and ← − E a = ← − − E eq a,c + (1 − α) eχ 0 + (1 − α) e∆χ for the forward and backward reaction.