Investigation of the oxygen exchange mechanism on Pt|yttria stabilized zirconia at intermediate temperatures: Surface path versus bulk path

Highlights

► Oxygen exchange kinetics of Pt on YSZ investigated by means of Pt model electrodes. ► Two different geometry dependencies of the polarization resistance identified. ► At higher temperatures the oxygen exchange reaction proceeds via a Pt surface path. ► At lower temperatures a bulk path through the Pt thin film electrode is discussed.

Abstract

The oxygen exchange kinetics of platinum on yttria-stabilized zirconia (YSZ) was investigated by means of geometrically well-defined Pt microelectrodes. By variation of electrode size and temperature it was possible to separate two temperature regimes with different geometry dependencies of the polarization resistance. At higher temperatures (550–700 °C) an elementary step located close to the three phase boundary (TPB) with an activation energy of ∼1.6 eV was identified as rate limiting. At lower temperatures (300–400 °C) the rate limiting elementary step is related to the electrode area and exhibited a very low activation energy in the order of 0.2 eV. From these observations two parallel pathways for electrochemical oxygen exchange are concluded.

The nature of these two elementary steps is discussed in terms of equivalent circuits. Two combinations of parallel rate limiting reaction steps are found to explain the observed geometry dependencies: (i) Diffusion through an impurity phase at the TPB in parallel to diffusion of oxygen through platinum – most likely along Pt grain boundaries – as area-related process. (ii) Co-limitation of oxygen diffusion along the Pt|YSZ interface and charge transfer at the interface with a short decay length of the corresponding transmission line (as TPB-related process) in parallel to oxygen diffusion through platinum.

1. Introduction

The mechanism of the oxygen exchange reaction O₂ + 4e⁻ ⇌ 2O²⁻ on the system platinum|solid oxide electrolyte is a highly important issue in solid state electrochemistry since it plays a fundamental role in several electrochemical devices and research areas: (i) In voltammetric oxygen sensors (often called lambda probes) the oxygen exchange reaction is essential for the electrochemical equilibration of gas phases and oxide ion conducting electrolyte. Therefore, the oxygen exchange reaction between surrounding gas phase and electrolyte is inevitable for the generation of the Nernst potential [1]. (ii) In solid oxide fuel cells (SOFCs) the relatively slow kinetics of O₂ reduction can cause a substantial cathodic overpotential, which to a significant part contributes to the total polarization of a SOFC and thus limits its efficiency [2]. The same is true for the reverse situation of O²⁻ oxidation in solid oxide electrolysis cells (SOECs). Even though Pt is not used as a typical cathode material in such devices, it offers an excellent model system for fundamental investigations in SOFC/SOEC research. (iii) Anodic oxide ion oxidation at (noble) metal electrodes often leads to spill-over of adsorbed oxygen species across the metal surface causing a change of the work function of the metal. This phenomenon – usually referred to as non-faradaic electrochemical modification of catalytic activity (NEMCA) – can strongly change the catalytic properties of the metal and is thus a highly interesting effect in the field of surface catalysis [3,4]. (Please note: Since in equilibrium both O₂ reduction and O²⁻ oxidation occur with equal reaction rates, these terms as well as the term oxygen exchange are used synonymic throughout the text. The same is true for adsorption and desorption as well as for oxygen incorporation and release.)

Because of this outstanding importance, the kinetics of oxygen exchange on solid oxide ion conductors was investigated from the beginnings of solid state electrochemistry. However, despite this long history of research the reaction mechanism of oxygen reduction on the system platinum|yttria stabilized zirconia (YSZ) is still not as well understood as in aqueous systems [2,5–22]. This makes it a highly interesting system for fundamental electrochemical research. In general, Pt|YSZ is assumed to be a surface path system (owing to the very low solubility and diffusivity of oxygen in bulk platinum [23]). This means that all elementary steps of oxygen exchange are believed to take place on the Pt (or YSZ) surface and the electrochemically active zone of oxygen incorporation into YSZ is generally assumed to be the three phase boundary (TPB) region (where O₂, Pt and YSZ meet) [2,5,24]. Experiments in the higher temperature range of 500–900 °C indeed revealed the TPB to be the zone of oxygen incorporation into YSZ and thus verified the surface path as being the dominant reaction path, at least in this temperature range [6,12,25]. However, Auger electron spectroscopy studies on sputter deposited Pt thin films (10–100 nm thick) indicated that thin polycrystalline Pt films were not as impermeable for oxygen as generally assumed [26,27]. Moreover, ab-initio calculations revealed that oxygen (via interstitial sites) preferentially diffuses along Pt grain boundaries [28]. In a recent ¹⁸O-tracer incorporation study we also found indication for oxygen transport through Pt thin film electrodes [29] and in the very recent work in Ref. [30] the authors also suggest an oxygen transport through polycrystalline Pt electrodes to explain their experimental results.

The goal of this work was the investigation of oxygen exchange on the system Pt|YSZ in the temperature range of 300–700 °C. In particular, information on the existence or non-existence of a reaction pathway of oxygen exchange through the Pt thin film (in parallel to the common surface path) was gained from the geometry dependency of the rate determining step. Electrochemical impedance measurements on geometrically well-defined Pt thin film electrodes were performed and by variation of the electrode size as well as by variation of the temperature mechanistic conclusions were drawn.

2. Experimental

2.1. Preparation of Pt thin film electrodes

Platinum thin films were prepared by sputter deposition (MED 020 Coating System, BAL-TEC, Germany) of Pt (99.95% pure, ÖGUSSA, Austria) onto polished YSZ (1 0 0) single crystals (9.5 mol% Y₂O₃, Crystec, Germany). In contrast to the related study in Ref. [25] the YSZ substrate was not externally heated during the deposition and the chamber pressure was set to 2.0 ± 0.1 × 10⁻² mbar argon. The nominal film thickness of 350 nm was controlled during the sputter process by means of a quartz micro-balance. Micro-structuring of the Pt films was performed by lift-off photolithography (ma-N 1420 negative photo resist and ma-D 533S developer for photo resist, both: micro resist technology, Germany). The photo mask (Rose, Germany) allowed the preparation of circular-shaped microelectrodes with different diameters (10–200 μm) on each sample. As a counter electrode Pt paste (Gwent Electronic Materials, UK) was applied onto the back side of the YSZ single crystals. The samples were subsequently annealed at 750 °C for 2 h. An optical micrograph after the annealing step is shown in Fig. 1a. The film thickness of the microelectrodes was also measured by means of a confocal microscope (AXIO CSM 700, Zeiss, Germany) – a 3D image of a 100 μm electrode is shown in Fig. 1b. A height profile along the cross section plane (indicated as transparent red plane in Fig. 1b) is given in Fig. 1c. From this height profile an electrode diameter of 100.2 μm and a thickness of the Pt film of about 300 nm were determined. This is in acceptable agreement with the nominal diameter and the thickness of 350 nm obtained by means of the quartz micro-balance during the sputter process.

Fig. 1.

(a) Optical micrograph of circular Pt thin film electrodes on a YSZ (1 0 0) single crystal. Nominal electrode sizes are (from top to bottom): 200, 100, 80, 50, 20, and 10 μm. The dark dots on the surface of the Pt electrodes were neither pores nor pinholes but bubbles which evolved during the annealing process (cf. Fig. 2d and e). (b) 3D image of a 100 μm electrode measured by confocal microscopy. The height information is color-coded with blue indicating low and red indicating high values (note that the height axis is strongly exaggerated). The “spikes” in the image were bubbles. The red plane across the electrode indicates the cross section plane for height profiling – the corresponding height profile is given in (c). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

2.2. SEM investigations

Scanning electron microscopy (SEM) investigations were performed on a Quanta 200 FEG (FEI Europe, The Netherlands) with Schottky emitter – some SEM micrographs are shown in Fig. 2. An image of the virgin Pt film (after sputter deposition, without any thermal treatment) is given in Fig. 2a. The virgin films exhibited a very homogeneous micro-structure with an average grain size between 20 and 30 nm. No indication for pores or pinholes was found. After the first heat treatment (750 °C, 2 h) a significant increase in grain size could be observed – cf. Fig. 2b. Additionally, the annealing step led to the formation of bubble-like structures within the thin film – see Fig. 2d and e. They were found to be hollow since they collapsed when touched by the contact tip in electrochemical measurements (cf. Fig. 2f). Bubble formation was also observed in Ref. [16], but under anodic polarization of the Pt thin film electrodes. Possibly, the bubble formation in our case was caused by the release of oxygen from YSZ due to an increase in non-stoichiometry at higher temperatures ($\text{nil}\rightleftharpoons 1/2{\text{O}}_2+{\text{V}}_{\text{O}}^{}+2e^{\prime }$) [31,32]. However, no indication was found that the intact bubbles affected the gas tightness of the thin films. Hence, a noteworthy influence on geometrical properties such as surface area and TPB-length of the electrodes was excluded in the present study.

Fig. 2.

(a) SEM image of the virgin sputter deposited Pt film on YSZ (1 0 0). The average crystallite size was between 20 and 30 nm. (b) Pt film after a 2 h heat treatment at 750 °C. The crystallite size was increased but neither cracks nor pores were visible. (c) Pt film after electrochemical measurements. Further crystal growth and some surface roughening were obvious. (d) Lower magnification of a Pt film comparable to that in (c) indicating bubble formation. The bubbles persisted also during electrochemical experiments. (e) Higher magnification of one single bubble. (f) Collapsed bubble.

After the electrochemical experiments, the thin film electrodes were again investigated by SEM to control their stability in terms of gas tightness during these measurements. In Fig. 2c the corresponding micrograph is shown. Further grain growth and some surface roughening but again no indication for the formation of gas leakage (like pores, pinholes or cracks) was found.

2.3. XRD characterization of the Pt thin films

X-ray diffraction (XRD) patterns were measured on an X’Pert PRO Diffractometer (PANalytical, Almelo/NL), PW 3050/60 goniometer with para-focussing Bragg-Brentano arrangement, copper anode (long fine focus, wavelength Cu-K_α1 = 1.5406 Å, Cu-K_α2 = 1.5444 Å), divergence slit 0.5°, Soller collimator with an axial divergence of 2.3° on primary and secondary side, secondary sided Ni–K_β filter and X’Celerator detector. The thin films were characterized after deposition of the Pt and after the 2 h annealing step at 750 °C.

In Fig. 3a a comparison of measured data with the results of the Rietveld calculations (software: Topas 4.2) for the virgin samples is shown. On this Pt thin film without any thermal treatment primarily reflexes corresponding to YSZ (1 0 0) and Pt (1 1 1) orientation could be observed. In addition, a very weak Pt (2 0 0) signal was found. In Fig. 3b the diffraction pattern of the Pt film on YSZ after an annealing step (2 h at 750 °C) together with its Rietveld refinement is shown. On this films the Pt (2 0 0) reflex could not be detected, the Pt thin films were exclusively (1 1 1) textured. Obviously the (1 0 0) oriented Pt was transformed into (1 1 1) oriented Pt during the annealing step. The peak heights as well as the peak integrals obtained on the virgin films were significantly lower than in case of annealed films. This might possibly be attributed to a slight inclination of the Pt columns in the film right after sputter deposition [33]. In Fig. 3d simulated diffraction patterns of ideal (1 1 1) textured Pt (upper orange curve) and slightly inclined Pt (1 1 1) (lower light blue curve) are compared. The lattice parameters and the crystallite sizes in this simulation were the same as in case of our samples. Obviously, the simulation obtained a comparable intensity ratio of the two Pt species as our measurements (compare Fig. 3c and d). In addition to the (1 1 1) textured Pt, traces of an unknown impurity phase were found on the annealed Pt film (with an intensity being orders of magnitude smaller than the strongest Pt reflexes). In the Rietveld analysis the impurity phase refined with strongly distorted textured copper. However, due to the very small amount of this impurity its nature could not be identified unambiguously. The crystallite sizes (Lorentzian) as well as the lattice parameters of the platinum films obtained by the refinement are summarized in Table 1. The crystallite sizes were in good agreement with the results from SEM investigations (cf. Fig. 2). The somewhat larger lattice parameter of the virgin Pt thin film might be attributed to internal strain due to the small crystallites. Rietveld calculations indeed yielded a significantly higher strain for the Pt films without thermal treatment.

Fig. 3.

(a) Diffraction pattern of the virgin Pt thin film (without any thermal treatment) and the corresponding Rietveld refinement as well as the YSZ blank (mirrored). (b) Diffraction pattern of the annealed Pt film together with its Rietveld refinement and the YSZ blank (mirrored). (c) Comparison of the measurements shown in (a) and (b). The reflexes corresponding to the Pt thin film are indicated by an asterisk. (d) Comparison of two simulated diffraction patterns: The simulation of an ideal Pt (1 1 1) diffraction pattern is shown by the upper orange graph, whereas the lower light blue graph depicts the simulation of a slightly inclined Pt (1 1 1) diffraction pattern. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Table 1.

Crystallite sizes and Pt lattice parameters of sputtered and annealed platinum films.

Thermal treatment	Crystallite size/nm	Lattice parameter/Å
None	40	3.936
2 h at 750 °C	160	3.922

2.4. ¹⁸O tracer incorporation experiments and ToF-SIMS measurements

For ¹⁸O incorporation experiments rectangular Pt microelectrodes (100 × 100 μm²) were used. The tracer (¹⁸O₂ gas, 97%, Cambridge Isotope Laboratories, UK) was supplied to a microelectrode by means of a quartz capillary and was incorporated by a cathodic dc voltage of −2.00 V (resulting electrode polarization η = −1.96 V) during 600 s of polarization. The incorporation experiment was performed at a temperature of 280 °C and the sample was quenched to room temperature after the incorporation procedure in order to minimize the diffusion of the tracer in YSZ [34,35]. More details on such experiments including a discussion on the reasons for the high polarization voltages and a sketch of the setup are given in Ref. [29].

Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) measurements were conducted on a TOF-SIMS⁵ instrument (ION-TOF, Germany). 2D ¹⁸O distribution images were recorded with a mode commonly called “burst alignment mode”. For measurements a pulsed Bi₁⁺ beam with energy of 25 keV was used. The cycle time was 100 μs/pixel and the distribution images were measured with a resolution of 512 × 512 pixels. The measurement beam diameter was about 200 nm. Depth profiles were recorded by sequential sputtering with 2 keV Cs⁺ ions (500 × 500 μm² area, ∼170 nA sputter beam current). For charge compensation a low energy electron shower (20 V) was employed. In addition, measurements with focus on positive secondary ions were performed to obtain information on the distribution of typical contaminants such as Si and alkali earth elements on the surface of YSZ.

3. Results and discussion

3.1. SIMS measurements

In Fig. 4a the ¹⁸O distribution in an YSZ (1 0 0) single crystal beneath a Pt microelectrode is shown resulting from cathodic polarization in ¹⁸O₂ tracer atmosphere (η = −1.96 V, T = 280 °C). The ¹⁸O intensity in this image is color-coded with low and high intensities being dark and white, respectively (cf. the vertical bar on the right hand side of Fig. 4a). The distribution was measured by means of ToF-SIMS after removal of the Pt electrode by wet chemical etching. For the calculation of a lateral tracer profile the intensity (Int) within the red boxes in Fig. 4a was summed up along the vertical (y) direction and a tracer fraction c(¹⁸O) was calculated by [36,37].

$$\text{c}{(}^{18}\text{O})=\frac{\text{Int}{(}^{18}\text{O})}{\text{Int}{(}^{18}\text{O})+\text{Int}{(}^{16}\text{O})}$$ (1)

Fig. 4.

(a) Distribution of ¹⁸O in YSZ measured by ToF-SIMS at a Pt electrode exposed to ¹⁸O₂ atmosphere during polarization (overpotential = −1.96 V, T = 280 °C; Pt electrode removed by wet-chemical etching). The size of the distribution image is 127 × 127 μm² with a resolution of 512 × 512 pixels. The green/blue frame shaped zone reflects high intensities of ¹⁸O close to the TPB region. The red boxes indicate integration areas. (b) Lateral profile obtained by integrating the intensity within the red boxes in (a) along the y-direction, converting it into a relative concentration (Eq. (1)) and plotting it versus the x-position. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

This relative tracer concentration was plotted versus the lateral position (x-axis) in Fig. 4b. (Please note that the increased intensity in the central region of the electrode was due to a damage of the thin film caused by the contact tip. This region was excluded in the calculation of the profile.) In the lateral profile relatively sharp peaks at the TPB, obviously resulting from the tracer incorporation via a surface path, are visible. The tracer fraction at the TPB was increased from 0.2% (natural abundance of ¹⁸O) to 2.5% on the left hand side and 2.1% on the right hand side of the electrode. These different peak concentrations might be caused by the non-symmetric supply of the tracer gas via the capillary. The shape of the peaks at the TPB appears to be slightly asymmetric, indicating some diffusion of oxygen along the Pt|YSZ interface. This is in agreement with findings of a similar study [29] where oxygen incorporation underneath the Pt took place in a narrow zone close to the TPB.

However, the decay length of this lateral interface diffusion is too short to explain the tracer content at the entire interface which was increased from 0.2% to ∼0.6%. The assumption of oxygen transport through the gas-tight Pt thin film along an electrochemical pathway competing with the surface path via the TPB is the most reasonable explanation for the increase of the tracer along the Pt|YSZ two phase boundary. In the study in Ref. [29] the same behavior was observed and was also interpreted as oxygen transport through the Pt electrode competing with the classical surface path.

From the increase in ¹⁸O surface concentrations (on average 1.0% at the TPB versus 0.4% at the electrode area) and the areas of the incorporation zones (∼1000 μm² TPB-area and 10000 μm² electrode area) it could be estimated that the ratio of the dc current via the surface path to the dc current via the bulk path (I_dc,TPB/I_dc,area) was about 0.25 for the given overpotential and temperature.

3.2. Impedance measurements

The Pt microelectrodes were electrically contacted by gold-coated steel tips (acupuncture needles, Pierenkemper, Germany) which could be accurately positioned under an optical microscope (Mitutoyo, Japan) by means of micromanipulators (Mitutoyo, Japan). For electrochemical characterization, the samples were placed onto a heating stage – a sketch of the experimental setup for impedance spectroscopy is shown in Fig. 5. The impedance between the Pt microelectrode and the Pt paste counter electrode was measured at set temperatures between 300 and 750 °C in ambient air using an Alpha-A High Performance Frequency Analyzer with a POT/GAL 30V 2A test interface (both: Novocontrol, Germany). The measurements were carried out in a frequency range of 1 MHz–20 mHz with a resolution of 10 points per decade, an ac voltage of 10 mV (rms) and at zero bias (i.e. around equilibrium conditions). For a given set temperature, microelectrodes of two different sizes (200 μm and 50 μm) were electrochemically characterized (3–5 of each size) and on each microelectrode 2–3 impedance spectra were recorded. After sweeping through the temperature range (starting with the highest set temperature of 750 °C and ending at 300 °C), again measurements at 750 °C were carried out. Since these results were within the experimental error of the very first measurements, the samples were assumed to be sufficiently electrochemically stable. Significant effects of irreversible changes of the samples during the impedance measurements were therefore excluded.

Fig. 5.

Sketch of the setup used for electrochemical impedance measurements. The symbols on the impedance analyzer CE, WE and RE denote counter electrode, working electrode and reference electrode, respectively. The meaning of capacitor C_{no_dc} is explained in the text (Section 3.2).

The electrochemical experiments were conducted in a pseudo 4-wire setup instead of a conventional 2-wire setup. Moreover, a variable capacitor was connected in series during measurements (see Fig. 5). Reasons for these modifications are explained in the following: Owing to the asymmetrical heating of the sample on the heating table and an additional cooling effect of the contacted microelectrode by the tip, a temperature gradient across the sample was generated. In a previous study, this temperature gradient was discussed to be responsible for a thermovoltage (usually in the range of 10–30 mV) between micro- and counter electrode [25,38]. Since the input resistance of the counter electrode (CE) connector versus the working electrode (WE) connector of the POT/GAL 30V 2A test interface is specified as virtually 0 Ω, the thermovoltage was short-circuited by the impedance analyzer. Hence, the resulting current – despite no external bias voltage was applied – led to a dc polarization of the electrode and consequently the impedance measurements could not be conducted under equilibrium conditions. To overcome this effect, the above mentioned capacitor (denoted as C_{no_dc} in Fig. 5) in series to analyzer and sample was introduced into the measurement setup. In a conventional 2-wire setup this capacitor would of course change the resulting impedance response (leading to a vertical line in the low frequency part of the Nyquist plot). In our pseudo 4-wire measurement, however, this capacitor is not “visible” in the measured spectrum (and neither are the inductances of the cables). A short-circuiting of the thermovoltage via the reference electrode connectors could be ruled out due to their input resistance of >10¹² Ω. Since the connection of the capacitor C_{no_dc} in series to the resistance of the sample R_samp acted as a filter for low frequency ac signals, the value of C_{no_dc} had to be individually adjusted for each measurement. It was chosen such that the characteristic angular frequency of the measuring system ω* ≈ 1/(R_samp·C_{no_dc}) was of the order of about 1–5 mHz. Consequently, before any impedance measurements, a delay time τ > 1/ω* was waited to charge the capacitor.

The measured impedance spectra depicted in Fig. 6a–c consist of a large arc in the complex impedance plane, a small shoulder at medium frequencies, and a high frequency intercept (for high temperatures) or onset of a high frequency arc (for lower temperatures). In accordance with Ref. [25] and many other studies on microelectrodes [39–43] the large arc can be assigned to the electrochemical oxygen exchange reaction at the microelectrode. Any influences of the porous counter electrode on the measured impedance spectra can be excluded since its polarization resistance is negligible compared to that of the microelectrode (due to its orders of magnitude larger size). At the highest measured temperatures the large arc is mostly visible within the frequency range under investigation (Fig. 6a). For lower temperatures, however, only a fraction of it was detected (Fig. 6c). Details on the analysis of the raw data and mechanistic interpretation will be given in the following.

Fig. 6.

Comparison of three representative impedance spectra measured on 200 μm electrodes at three different temperatures with the results of the Kramers Kronig tests: (a) 615 °C, (b) 510 °C, (c) 424 °C. Below each impedance spectrum the respective residual plot is shown (cf. Eq. (2)): (d) 615 °C, (e) 510 °C, (f) 424 °C.

3.2.1. Kramers Kronig test

The impedance spectra were tested in terms of the Kramers Kronig (KK) relation to further exclude time dependent influences on the impedance data. Owing to the low ac voltage of 10 mV (rms), which is much lower than k_BT/e₀, we assumed a linear response of our system (k_B, T, and e₀ denote Boltzmann's constant, temperature, and elementary charge, respectively). For Kramers Kronig testing, the program “K-K test version 1.01” by B.A. Boukamp was used [44,45]. For an easy monitoring of KK-compliance, the relative differences – Δ_re,i and Δ_im,i – between the data and its KK-compliant fit were calculated. The residuals are defined by [44]

$${\Delta }_{re,i}=\frac{Z_{\text{re,i}}-Z_{\text{re,KK}}}{\left|Z_{\text{KK}}\right|};{\Delta }_{\text{im,i}}=\frac{Z_{\text{im,i}}-Z_{\text{im,KK}}}{\left|Z_{\text{KK}}\right|}$$ (2)

where Z_re,i and Z_im,i denote the real and imaginary part of the measured impedance data and Z_re,KK and Z_im,KK denote the real and imaginary part of the KK-transform, respectively. |Z_KK| is the magnitude of the KK-transform.

In Fig. 6 three representative impedance spectra (Nyquist plots) measured on 200 μm electrodes and the corresponding KK-transforms as well as their residuals are shown. Absolute impedance data and the corresponding KK-transform are given in Fig. 6a–c, while the respective residuals are plotted as a function of the frequency in Fig. 6d–f. KK-compliant impedance data (that means good match between data and KK-model) should only yield a scattering of the residuals around the log(f) axis [45]. In Fig. 6d (corresponding to 615 °C) indication of some trace was found. A possible explanation is a fluctuation in the thermovoltage which could also be observed when measuring this thermovoltage by a voltmeter (Keithley 2000, USA). However, the magnitude of data corruption is below 0.5%, which is far below the scatter of our experimental data when comparing measurements on different electrodes. At medium temperatures (510 °C, Fig. 6e), the traces become less pronounced but the scattering, especially in the low frequency range, was increased, indicating more noisy data in this frequency range. In case of the low temperature (424 °C), the residuals plot in Fig. 6f indicates KK-compliant behavior as well as quite low noise. In summary, only minor (if any) systematic errors in the data were found in KK analysis. Hence, artifacts such as variations in activation energy due to changes of the samples during measurements (for example caused by irreversible changes of the electrodes due to a thermovoltage-induced polarization) could be excluded.

3.2.2. Parameterization

For data parameterization the complex non-linear least squares (CNLS) fit program Z-View (Scribner, USA) was used. In a previous study on the system Pt|YSZ, an equivalent circuit exhibiting a capacitively blocked path in parallel to an R-CPE element was applied to fit the impedance data [25]. In that study, Pt electrodes were differently prepared including a high temperature deposition followed by a 48 h annealing step and measurements were only performed at set temperatures above 700 °C. In the present study, however, this circuit turned out to be applicable only to spectra obtained at the highest temperatures (above ∼650 °C). For spectra recorded at lower temperatures, the circuit in Ref. [25] did not lead to satisfying fit curves. Hence, the circuit in Fig. 7 (with two serial resistors representing the electrode reaction) was used instead for parameterization. One of the two resistors (R_rds) was always orders of magnitude larger than the other and therefore the resistance R_rds was almost identical to the total polarization resistance of the microelectrodes and represents the rate determining step of the electrode reaction (R_rds + R_B ≈ R_rds). To account for non-ideal capacitive behavior, constant phase elements (CPE_A and CPE_B) instead of ideal capacitors were employed. The complex impedance of a constant phase element Z_CPE is given by

$$Z_{\text{CPE}}=\frac{1}{{(i\cdot \omega )}^n\cdot Q}$$ (3)

where ω denotes the angular frequency, and n and Q are fitting parameters. The rather small resistor R_B as well as the constant phase element CPE_B were only included to obtain sufficient fit quality but will not be interpreted in a physical manner. The spreading resistance [46,47] of ion conduction in YSZ (R_YSZ) and the known conductivity of YSZ were used to calculate the effective temperature of each individual electrode. The corresponding procedure was described in detail in Ref. [25].

Fig. 7.

Equivalent circuit used for parameterization of impedance spectra. R_rds represents the resistance of the rate determining step. The elements R_B and CPE_B were only used to obtain satisfying fit results.

In Fig. 8 measured impedance data are compared to the results of the CNLS fit using the equivalent circuit in Fig. 7. Since at lower temperatures only the onset of a huge electrode arc is visible in the low frequency range – see Figs. 8d and 6c – it has to be proven that such a fragmentary semicircle can yield reliable fit results. Therefore, the high temperature spectrum in Fig. 8a was fitted in a reduced frequency range (omitting the lowest frequency points) – in Fig. 8b and c the frequency points used for this reduced range fit are indicated by the filled red circles. An extrapolation of the corresponding results is given in Fig. 8b by the blue dotted line and showed only about 10–15% deviation in the resistance compared to the fit using the full (measured) frequency range (cf. the extrapolations in Fig. 8a and b). This is still within the statistical scatter of measurements on different electrodes. An explanation for the rather low deviation is the “well-behaved” nature of the capacitor in parallel to R_rds. It can be quantified pretty well by a constant phase element (Eq. (3)) with a n-value of 0.88 ± 0.03 which stays almost constant over the entire temperature range. Accordingly, the depression of the corresponding arc in the complex impedance plane is almost the same for all examined temperatures and a small fraction of the arc is sufficient to get the whole information contained in the relaxation (i.e. the parameters R_rds, Q_A, and n_A). The capacitance of the arc can be calculated from the constant phase element CPE_A and the resistance R_rds by [48].

$$C_{\text{A}}={({R_{\text{rds}}}^{1-n_{\text{A}}}\cdot Q_{\text{A}})}^{1/n_{\text{A}}}$$ (4)

Fig. 8.

Impedance spectra measured at different temperatures on 200 μm electrodes compared with the results of the CNLS fit using the equivalent circuit in Fig. 7. (a) Measured impedance data at 615 °C electrode temperature (open diamonds) compared to the fit result (solid green line). The fit was extrapolated to very low frequencies (dotted green line) to indicate the dc resistance at this temperature. (b) Comparison of the measured data (open diamonds) with the extrapolated fit result (dotted blue line) when using only a reduced frequency range of the spectrum in the CNLS-fit (red filled circles). (c) Magnification of the medium frequency part of the spectrum in (b) indicating the reduced fit range. (d) Low frequency part of the spectrum measured at 424 °C (open circles) as well as the fit result (solid orange line). The extrapolation of the fit is shown in (e) with the orange dotted line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

An Arrhenius plot of the resulting capacitance is shown in Fig. 9. Even though capacitance C_A shows about 50% relative standard deviation, it did not strongly change with decreasing temperature despite the fact that smaller and smaller parts of the arc were used in the fit. Hence, CNLS-fits of spectra measured at lower temperatures (fragmentary semicircles) can still be regarded as being quite reliable. In Fig. 8d a representative spectrum and its fit curve are shown for a lower measurement temperature; Fig. 8e shows the corresponding extrapolation.

Fig. 9.

Capacitance C_A calculated by Eq. (4) from the constant phase element CPE_A, which in the equivalent circuit is in parallel to the resistance representing the rate determining step. Values were determined from the data of 200 μm (black diamonds) and 50 μm electrodes (blue dots). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

The capacitor C_A exhibited an average value of about 600 μF/cm² which is too high to be interpreted in terms of a double layer capacitor [49]. Contributions by a chemical capacitance might explain such high values which could possibly originate from oxygen in Pt grain boundaries or PtO_x/impurities at the Pt|YSZ interface [22,25,50]. A detailed mechanistic interpretation, however, cannot be drawn from the present data.

3.2.3. The geometry dependence of the electrode polarization resistance

The inverse values of R_rds (obtained from CNLS-fits) are plotted in an Arrhenius diagram (see Fig. 10a). The data points already suggest two temperature regimes with different slopes in the Arrhenius plot and thus two processes with different activation energies. Since the slope (i.e. the activation energy) in the higher temperature range was obviously higher than for lower temperatures, a parallel connection of two processes is an appropriate description of such a situation. This can be understood from the model calculations in Fig. 11, where the temperature dependent inverse resistances of two different electrode processes are sketched. Since they exhibit very different activation energies, their parallel or serial combination are both characterized by a changing slope in the Arrhenius diagram. However, only the parallel connection (red dotted curve) can lead to a situation with higher activation energy at higher temperature [20]. A serial connection (blue dotted curve) is unavoidably reflected by a lower activation energy at higher temperature and thus contradicts our results. Consequently, the Arrhenius diagram does not only give information on the activation energies of the processes (the slopes of the two parts of the resulting curve), but also on the type of connection of the involved resistive processes: parallel connections result in a concave shape and serial connections lead to a convex shape. We therefore analyzed the results in terms of two parallel oxygen exchange reaction paths of different activation energy.

Fig. 10.

Arrhenius plot of the inverse polarization resistance representing the rate determining step. (a) Raw data of 200 μm (black squares) and 50 μm electrodes (blue triangles). Further the resulting fit curves using Eq. (5) are shown – 200 μm: solid black line; 50 μm: dashed blue line. (b) Fit results of 200 μm and 50 μm data related to the TPB-length of the electrodes. Obviously the steeper branches of the curves fall together. (c) Plot of area-related fit results; in this case the shallow branches fall together. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 11.

(a) Equivalent circuit describing two parallel resistive electrochemical processes (capacitive processes not shown). Resistor 1 represents the surface path with a rate determining step located close to the TPB. Resistor 2 symbolizes the rate determining process of the pathway through the Pt electrode. (b) Equivalent circuit with two slow serial electrochemical processes (capacitances again neglected). (c) Expected Arrhenius diagram (in a.u.) for the situations in (a) and (b) assuming different activation energies for the two processes.

To avoid an arbitrary definition of the transition range between the two activation energies the entire data set instead of two parts of the curve was fitted. For a parallel connection of two Arrhenius activated processes the fit equation for 1/R_rds = Y_rds reads

$$Y_{\text{rds}}=Y_1^0\cdot e^{(-E_{\text{a},1}/k_{\text{B}}T)}+Y_2^0\cdot e^{(-E_{\text{a},2}/k_{\text{B}}T)}$$ (5)

Therein the pre-exponential factors Y₁⁰ and Y₂⁰ as well as the activation energies E_a,1 and E_a,2 were fitting parameters; k_B and T denote Boltzmann's constant and temperature, respectively. For an appropriate fit a weighting function w (different from one as in case of a linear fit equation) had to be defined and

$$w={\left(\frac{1}{{}^{\text{fit}}Y}\right)}^2$$ (6)

was used which leads to a minimization of the relative deviation of the measured values from the fit results according to:

$${({}^{\text{meas}}Y-{}^{\text{fit}}Y)}^2\cdot w={\left(\frac{{}^{\text{meas}}Y-{}^{\text{fit}}Y}{{}^{\text{fit}}Y}\right)}^2=\text{Min}!$$ (7)

The fit results for 200 μm and 50 μm electrodes are given in Fig. 10a by the solid black line and the dashed blue line, respectively. The resulting activation energies (c.f. Eq. (5)) are summarized in Table 2; on average 1.6 eV and 0.2 eV are found for the high and low temperature regime, respectively. It becomes obvious from the scattering of data points in Fig. 10a that the value of 0.2 eV has a high relative error and should more be taken as indication of very little activation than as an exact value.

Table 2.

Activation energies of the processes responsible for the rate determining step of the electrode reaction obtained by fitting the measured data in Fig. 10a using Eq. (5).

Electrode size/μm	Ea,1/eV	Ea,2/eV
200	1.55	0.22
50	1.57	0.13
Average	1.6	0.2

For the investigation of the geometry dependence of 1/R_rds, both fit curves were related to the length of the TPB (calculated from the electrode diameter d_ME by π·d_ME) as well as to the area of the electrodes (π·d_ME²/4). In Fig. 10b the fit curves related to the TPB-length are shown. In this diagram the branches with the higher activation energy (at higher temperatures) fall together, indicating a rate determining process at or close to the TPB in this temperature regime. In the plot of the area-related fit results – Fig. 10c – the shallow branches (at lower temperatures) coincide. In this temperature range, the rate determining step was obviously related to the area of the electrodes. This different geometry dependence of the two parts of the fit curves clearly indicates a change of the geometry dependence of the polarization resistance and thus of the rate determining step. Moreover, the shape of the curve (higher E_a at higher temperatures and lower E_a at lower temperatures) can only be interpreted in terms of a parallel connection of these two processes (cf. Fig. 11). Altogether, the observed behavior suggests two different reaction pathways connected in parallel.

It was frequently discussed in literature that a co-limitation of two processes rather than only one single elementary step could be responsible for the polarization resistance of Pt electrodes on YSZ [2,14,19,20]. Situations potentially leading to co-limited kinetics typically include a diffusion process (e.g. surface diffusion of adsorbed oxygen) and a reaction perpendicular to the diffusion direction (e.g. adsorption/desorption on the surface). Such a situation is sketched in Fig. 12a – the corresponding equivalent circuit (transmission line; capacitances neglected) is shown in Fig. 12b. However, also such a situation cannot explain the observed temperature dependence: For a stripe-shaped electrode with only one TPB being electrochemically active, the polarization resistance of co-limited kinetics is given by [24]

$$R_{\text{co}}=\sqrt{\frac{1}{{\sigma }_{\text{lat}}{Y}_{\text{perp}}}}\cdot \text{coth}\left(b\sqrt{\frac{Y_{\text{perp}}}{{\sigma }_{\text{lat}}}}\right)$$ (8)

Fig. 12.

(a) Schematic illustration of two electrode processes potentially leading to a co-limited polarization resistance. (b) Equivalent circuit corresponding to the situation in (a) – capacitances were neglected. (c) Arrhenius diagram of the conductances of the two individual processes and the resulting co-limitation with the lateral diffusion process having a higher activation energy than the perpendicular reaction (E_a,lat > E_a,perp). (d) Resulting Arrhenius diagram with E_a,lat < E_a,perp.

Therein R_co denotes the resulting polarization resistance of co-limitation, σ_lat the lateral “conductivity” (e.g. of surface diffusion), Y_perp a constant quantifying the kinetics of the process perpendicular to the diffusion process (e.g. adsorption/desorption) and b the width of the electrode stripe. In Fig. 12c the resulting Arrhenius plot is sketched with the lateral diffusion exhibiting higher activation energy than the perpendicular reaction (E_a,lat > E_a,perp); Fig. 12d shows the opposite situation (E_a,lat < E_a,perp). In both cases Arrhenius curves with higher activation energy at lower temperature are found.

Even though Eq. (8) is exactly valid only in case of stripe-shaped electrodes (with only one electrochemically active TPB) and should be modified for circular electrodes, it still allows a qualitative estimation of the temperature dependence of co-limited reaction kinetics on thin film electrodes. We can thus conclude that co-limited reaction kinetics in the entire investigated temperature range contradicts our result of a lower activation energy at lower temperatures. Indeed, two parallel pathways have to be assumed. A co-limitation being responsible for only one branch of the measured Arrhenius curve, however, would still be in accordance with the measured results.

3.3. Mechanistic discussion of oxygen exchange

It remains to be discussed which detailed reaction paths and rate determining steps are in accordance with our experimental results. We thus have to search for kinetic situations where two parallel paths are possible for oxygen exchange, one path having a rate determining step located close to the TPB while the other one exhibits an area-related rate determining step. The activation energies of the rate limiting elementary steps are about 1.6 eV and 0.2 eV for the TPB- and area-related paths, respectively. In order to limit the possible kinetic scenarios, the following assumptions are made:

• (i)Close to equilibrium conditions, oxygen reduction and incorporation into YSZ was assumed to only take place underneath the Pt electrode. Consequently, ionization of oxygen by electrons from YSZ and subsequent incorporation at the free electrolyte surface is not considered at equilibrium conditions.
• (ii)Moreover, it should be noted that the electrochemical oxidation/reduction of an oxygen containing phase at the Pt|YSZ interface (e.g. PtO_x or O₂ in bubbles) would also exhibit a polarization resistance scaling with the area of the electrode. However, this resistor would be capacitively blocked by the chemical capacitance of the oxygen containing phase – i.e. the amount of oxygen stored in it. Since such a capacitively blocked pathway cannot carry a faradaic dc current, it would not be visible in the ¹⁸O tracer incorporation experiments. Further, a capacitively blocked path could be separated from a pure faradaic path by means of impedance spectroscopy [25]. Consequently we can exclude PtO_x or oxygen filled bubbles to be responsible for the area related polarization resistance observed at lower temperatures.

Regarding these assumptions three pathways of oxygen exchange are taken into account in the following discussion: a bulk path through the electrode (I), a surface path along the Pt electrode (II) and an alternative surface path along the free YSZ surface (III). In Fig. 13a a sketch of this situation is shown. In the remaining part of the paper we discuss which combinations of these paths and which rate determining steps are compatible with our experimental observations.

Fig. 13.

(a) Possible reaction pathways assuming fast Pt surface diffusion and negligible oxygen reduction/incorporation on free YSZ. The gray dotted path along the Pt|YSZ interface would only be accessible in case of fast interface diffusion. (b) Reaction pathways in (a) with oxygen adsorption on Pt being the area-related rate limiting step and co-limitation of adsorption and surface diffusion on YSZ (with a short decay length) being the slowest TPB-related elementary step. (c) Situation with oxygen diffusion through Pt (along grain boundaries) being the area related rate determining step in parallel to co-limitation of oxygen diffusion along the Pt/YSZ interface and charge transfer at the interface with a short decay length being the TPB-related rate limiting step. (d) Alternative to the situation in (c) with diffusion of an adsorbed species through an impurity phase as the TPB-related rate limiting process.

3.3.1. Slow oxygen adsorption on Pt in parallel to co-limitation of oxygen adsorption and surface diffusion on free YSZ

One possible scenario is slow adsorption on the entire Pt surface as area-related process, followed by fast transport through Pt (I) or along the Pt surface (II) and fast incorporation of this oxygen along the Pt|YSZ interface or close to the TPB. Slow TPB-related processes can only be in parallel to such an assumed adsorption step if they are associated with the free YSZ surface (path III in Fig. 13a). For example, a co-limitation of oxygen adsorption on YSZ and surface diffusion of the adsorbed species with a short decay length would reflect such a situation (Fig. 13b).

At temperatures >150 K oxygen adsorbs dissociatively on platinum (1 1 1) surfaces forming p(2 × 2) layers with the resulting atomic species covalently bonded in the threefold hollow site [51,52]. The mechanism of oxygen adsorption on Pt (1 1 1) is believed to proceed via molecular physisorbed or chemisorbed (superoxo- or peroxo-) precursor species [51,53,54] – cf. Fig. 14. For a (simplified) mechanism, a sticking coefficient S can be defined

$$S=\frac{r_{\text{a}}}{2\cdot P_{\text{tot}}}$$ (9)

where r_a denotes the adsorption rate of dissociatively bound atomic oxygen per unit area and P_tot the rate per unit area at which the adsorptive (O₂) strikes the surface. From adsorption kinetics the electrochemical polarization resistance of adsorption can be calculated (see Appendix A) to be

$$R_{\text{ac,eq}}=\frac{k_{\text{B}}T}{8e_0^2}\cdot \frac{1}{S\cdot P_{\text{tot}}}$$ (10)

Fig. 14.

Sketch of the possible reaction paths of oxygen adsorption on Pt (1 1 1) [54]: (a) Physisorbed molecular species. (b) Chemisorbed molecular species. (c) Dissociatively chemisorbed oxygen.

In Eq. (10) e₀ denotes the elementary charge. The total impinging rate

$$P_{\text{tot}}=\frac{N}{2V}\sqrt{\frac{k_{\text{B}}T}{M}}$$ (11)

can be obtained by kinetic gas theory [55]; N denotes the number of oxygen molecules within the volume V and M is the molecular mass of O₂. The sticking coefficient shows Arrhenius type behavior at temperatures above 200 K [51]. Depending on the kinetic energy of the impinging oxygen molecule, activation energies E_s of the sticking coefficient between 0.04 and 0.13 eV were reported [51,53,54]. Consequently, the temperature dependence of the inverse polarization resistance is dominated by the temperature dependence of the sticking coefficient. Since the activation energy of the area related exchange rate (0.2 eV) is close to the values of E_s, the area-related polarization resistance could be attributed to an adsorption/desorption process.

However, despite the promising accordance in activation energy, adsorption kinetics is not believed to be rate limiting due to the following considerations: The resulting polarization resistance of the adsorption process can be calculated by Eq. (10). For impact energies of oxygen molecules corresponding to 650 K gas temperature typical sticking coefficients are between 0.05 and 0.2 [51,53,54]. At this temperature, P_tot for oxygen in ambient air (200 mbar partial pressure) can be calculated from Eq. (11) to be 1.1 × 10²⁷ m⁻² s⁻¹. Assuming the worst case scenario with S = 0.05 Eq. (10) yields an electrochemical adsorption resistance of 7.9 × 10⁻¹⁰ Ωm². For a 200 μm microelectrode a polarization resistance of 2.5 × 10⁻² Ω is thus predicted for adsorption under equilibrium conditions. This is far below the values measured on 200 μm electrodes at 650 K in this study (∼10⁹ Ω) and hence we conclude that the area-related polarization resistance is not caused by adsorption limited kinetics.

3.3.2. Oxygen diffusion through Pt in parallel to a path with charge transfer close to the TPB

Another rate limiting step with a reaction rate proportional to the electrode area would be diffusion through the Pt thin film – most likely along Pt grain boundaries [26,28]. Gas diffusion through any pores in the Pt films can safely be excluded as a possible rate limiting step even though it would indeed lead to a small temperature dependence: First, such pores are not found in our SEM studies and second, even if there were some residual pores this would only slightly enhance the TPB length. Moreover, gas diffusion through pores would be connected in series with a TPB process which also contradicts our experimental results. In Ref. [28] the activation energy of 0.68 eV for grain boundary diffusion of oxygen in Pt was calculated by ab-initio methods. The inverse polarization resistance 1/R_diff of a diffusion limited electrode reaction close to equilibrium (assuming one dimensional diffusion through the Pt thin film) reads

$$\frac{1}{R_{\text{diff}}}=\frac{{(z{e}_0)}^2}{k_{\text{B}}T}\cdot \frac{D\cdot {\text{c}}_{\text{O}(\text{gb})}}{d}$$ (12)

with d being the film thickness, D the diffusion coefficient and c_O(gb) the equilibrium concentration of the diffusing oxygen species in the Pt grain boundary next to the surface [1]. The temperature dependence of D is given by Arrhenius’ equation

$$D=D^{\prime }\cdot e^{(-E_{\text{diff}}/k_{\text{B}}T)}$$ (13)

with D′ denoting the pre-exponential factor and E_diff the activation energy of the diffusion process. The gas phase and the oxygen in the surface near grain boundary are assumed to be in thermodynamic equilibrium and for low concentrations c_O(gb) is given by mass action law:

$$\frac{1}{2}{\text{O}}_2\rightleftharpoons {\text{O}}_{(\text{gb})}$$ (14)

$$K=\frac{{\text{c}}_{\text{O}(\text{gb})}}{\sqrt{p_{{\text{O}}_2}}}=K^{\prime }\cdot e^{(-{\Delta }_{\text{r}}g/k_{\text{B}}T)}=K^{\prime }\cdot e^{((-{\Delta }_{\text{r}}h-T{\Delta }_{\text{r}}s)/k_{\text{B}}T)}=K^{″}\cdot e^{(-{\Delta }_{\text{r}}h/k_{\text{B}}T)}$$ (15a)

$$c_{O(\text{gb})}=\sqrt{p_{{\text{O}}_2}}\cdot K^{″}\cdot e^{(-{\Delta }_{\text{r}}h/k_{\text{B}}T)}$$ (15b)

In Eqs. (15a) and (15b) $p_{{\text{O}}_2}$ denotes the partial pressure of oxygen in the gas phase, K is the equilibrium constant, K′ its pre-exponential factor, and K″ the modified pre-exponential factor (K″ = K′ · e^(Δ_rs/k_B)); Δ_rg, Δ_rh, and Δ_rs are Gibb's free reaction enthalpy, reaction enthalpy, and reaction entropy for the reaction in Eq. (14), respectively. The reaction enthalpy of this reaction can be calculated from the binding energy of the O₂ molecule, which is 4.91 eV per O atom and the binding energy of the oxygen species in the Pt grain boundary, which is in the range of 3.97–4.60 eV [28] and a value between −0.31 and −0.94 eV results for Δ_rh. Inserting Eqs. (13) and (15b) in (12) yields

$$\frac{1}{R_{\text{diff}}}=\frac{{(z{e}_0)}^2}{k_{\text{B}}T\cdot d}\cdot D\text{'}\cdot e^{(-E_{\text{diff}}/k_{\text{B}}T)}\cdot \sqrt{p_{{\text{O}}_2}}\cdot K\text{'}\text{'}\cdot e^{(-{\Delta }_{\text{r}}h/k_{\text{B}}T)}$$ (16)

The effective activation energy E_a of the corresponding inverse polarization resistance can therefore be estimated by

$$E_{\text{a}}\approx E_{\text{diff}}+{\Delta }_{\text{r}}h$$ (17)

and is in the range of 0.37 and −0.26 eV. This is an unusually low activation energy value for electrode reactions in solid state electrochemistry. Hence, rate-limiting oxygen diffusion along Pt grain boundaries might indeed be responsible for the little activated (0.2 eV) area related process observed at low measurement temperatures. However, from the data available so far Pt grain boundary diffusion of oxygen cannot be identified unambiguously as the rate limiting step responsible for the polarization resistance observed at temperatures below 450 °C.

Since adsorption was shown in Section 3.3.1 to be a very fast elementary step, a co-limitation of adsorption and surface diffusion on Pt with a short decay length can also be excluded as rate limiting TPB-process by the following argumentation: Adsorption limited to a rim of 1 nm width at the edge of a circular 200 μm electrode would correspond to a polarization resistance of ∼2.5 kΩ at 650 K which is still orders of magnitude below the measured value. Moreover, it was demonstrated in Ref. [56] that surface diffusion of oxygen on Pt (1 1 1) is significantly faster than desorption. In this study the authors showed that an anodic oxygen release (U_set = +0.2 V; 400 °C) led to a front of adsorbed oxygen moving from the TPB along the entire Pt surface.

However, a charge transfer step at the TPB would be a realistic rate determining step of path II. More precisely – since the electrochemical reaction is assumed to take place at the Pt|YSZ interface – co-limitation of oxygen diffusion along the Pt|YSZ interface and charge transfer at this interface with a short decay length of the corresponding transmission line would be a possible TPB-related rate limiting elementary process (an equivalent circuit is sketched in Fig. 13c). Such a short decay length, however, only results in case of slow interface diffusion. For fast interface diffusion the polarization resistance would not scale with the length of the TPB. An alternative TPB-related rate limiting step in parallel to oxygen diffusion through Pt would be oxygen diffusion through an impurity phase at the TPB (cf. Fig. 13d). Such impurity phases (particularly SiO₂ containing) were frequently discussed in the past to deteriorate the exchange rates of TPB-active electrodes [17,50,57–59]. In ToF-SIMS measurements we could indeed identify impurity elements such as Si and Ca at TPBs of strongly polarized high temperature deposited [25] Pt electrodes – cf. Fig. 15. However, so far we could not unambiguously proof the existence of sufficient amounts of these impurities also under equilibrium conditions. Hence, a final conclusion on the rate limiting TPB process is not possible yet and it should further be noted that the two combinations discussed above only represent the most likely mechanistic situations, but other interpretations of the observed electrochemical behavior are still possible.

Fig. 15.

Distribution images (intensity plots) obtained by ToF-SIMS showing impurities on the YSZ surface. The high temperature deposited rectangular Pt electrode in the center was strongly polarized (overpotential η = −2.22 V at 303 °C for 10 min), the neighboring electrodes – above and below – were not polarized during the experiment. (a) Accumulation of Si at the TPB of the polarized electrode. (b) Calcium distribution on the YSZ surface.

3.3.3. Comparison with electrode “conductivities” in literature

A comparison of the TPB-length related inverse polarization resistances (electrode “conductivities”) of the present study with values found in literature is shown in Fig. 16. Most activation energies and also several absolute values from other studies are in good agreement with the TPB-length related data of our results [7,8,18]. Moreover, it becomes obvious that the electrodes used in our previous study [25] exhibited a significantly lower “conductivity” than the electrodes in the present study. As already mentioned above the electrodes in Ref. [25] were deposited at much higher temperature and deviations could possibly be attributed to impurities at the TPB: The high temperature deposition procedure of the Pt thin films as well as the longer annealing times in Ref. [25] might influence the amount of impurities accumulated at the TPB and therefore the polarization resistance of oxygen exchange [58–60].

Fig. 16.

Comparison of the Arrhenius curves from the present study with electrode “conductivities” from literature.

Pt electrodes exhibiting higher “conductivity” values than ours were found in Refs. [6,9,17]. In Ref. [17] silicon contaminations were demonstrated to tremendously affect the oxygen exchange kinetics of Pt electrodes. The Pt electrodes with the highest “conductivity” (Ref. [17], Si-free in Fig. 16) were shown to be free of these contaminations. In the study on porous Pt electrodes in Ref. [57], however, SiO₂ impurities only deteriorated the electrode performance when being located at the Pt|YSZ interface. Traces of SiO₂ on the surface of Pt even decreased the electrode polarization resistance. This effect was discussed in terms of a change in adsorption kinetics of oxygen on platinum. A change in oxygen surface concentration would also affect a polarization resistance caused by an elementary step subsequent to adsorption on Pt (such as charge transfer or oxygen diffusion through an impurity phase at the TPB). Taking the strong effect of SiO₂ impurities into account the scenario in Fig. 13d seems to be the most realistic one to explain our results.

An area-related rate determining reaction step with a quite low activation energy of 0.2 eV was not reported so far. This might be attributed to the aspect ratio of our electrodes (50–200 μm diameter, 350 nm thickness) which – compared to Pt particles in porous paste electrodes – favours a bulk path. Also the quite small grain sizes of our electrodes (150–200 nm) and the consequently very high number of grain boundaries lead to a higher conductance of a diffusive path along Pt grain boundaries.

4. Conclusions

The oxygen exchange kinetics of sputter deposited platinum electrodes on YSZ was investigated by means of impedance spectroscopy at temperatures between 300 and 700 °C. By varying the size of geometrically well-defined electrodes, the geometry dependence of the polarization resistance was analyzed. In the higher temperature range (550–700 °C) a TPB-length dependent rate limiting step with an activation energy of about 1.6 eV could be observed. This is in good agreement with previous results from literature. At lower temperatures (300–400 °C), however, a different reaction regime was found exhibiting an area-related rate limiting step with very low activation energy of about 0.2 eV. From the shape of the Arrhenius curve it could be concluded that two parallel reaction paths have to be involved.

A more detailed discussion of kinetic situations yielded two possible combinations of TPB- and area-related elementary steps explaining the experimentally obtained Arrhenius plot and geometry dependence: (i) Oxygen diffusion through the Pt thin film – most likely via Pt grain boundaries – as area-related process in parallel to oxygen diffusion through an impurity phase at the TPB. (ii) Oxygen diffusion through the Pt thin film in parallel to co-limitation of oxygen diffusion and charge transfer along the Pt|YSZ interface with a short decay length being responsible for the TPB-related polarization resistance.

Appendix A.

Neglecting any effects of the physically adsorbed molecular species (cf. Fig. 14a), the adsorption reaction via a (molecularly chemisorbed) intrinsic precursor can be described by [51–54]

$${\text{O}}_{2(\text{g})}\rightleftarrows O_{2(\text{ad})}\underset{r_{-\text{a}}}{\overset{r_{\text{a}}}{\rightleftharpoons }}2{\text{O}}_{(\text{ad})}$$ (A1)

with a very fast first molecular adsorption step; r_a denotes the rate of dissociation, and r_−a the rate of reaction from the atomically adsorbed state into the molecularly adsorbed state. For such an adsorption process, a sticking coefficient S can be defined

$$S=\frac{r_{\text{a}}}{2\cdot P_{\text{tot}}}$$ (A2)

where P_tot denotes the total impinging rate of O₂ per unit area. Further, under equilibrium conditions

$$r_{\text{eff}}=r_{\text{a,eq}}-r_{-\text{a,eq}}=r_{\text{a,eq}}-k_{-\text{a}}\cdot {\Theta }_{\text{eq}}=0$$ (A3)

holds, where r_eff denotes the effective (net) reaction rate of the rate limiting dissociation step, k_−a the rate constant of reaction from the atomically adsorbed state into the molecularly adsorbed state, and Θ_eq the equilibrium coverage of atomically adsorbed oxygen. If the equilibrium is disturbed (e.g. by the ac signal of an electrochemical impedance experiment) the coverage of the atomically adsorbed species is changed by ΔΘ and therefore the effective reaction rate changes to

$$r_{\text{eff}}=r_{\text{a,eq}}-k_{-\text{a}}\cdot \Theta =r_{\text{a,eq}}-k_{-\text{a}}\cdot ({\Theta }_{\text{eq}}+\Delta \Theta )=r_{\text{a,eq}}-r_{-\text{a,eq}}-k_{-\text{a}}\cdot \Delta \Theta$$ (A4a)

$$r_{\text{eff}}=-k_{-\text{a}}\cdot \Delta \Theta$$ (A4b)

Since atomically adsorbed oxygen is the electrochemically active species [5,56,61], the trapping of oxygen from the gas phase into the precursor state is virtually not affected. Consequently, also the rate of dissociative adsorption r_a is not affected by electrochemical manipulation (r_a = r_a,eq). The resulting current I_eff is given by

$$I_{\text{eff}}=z{e}_0\cdot r_{\text{eff}}=-z{e}_0\cdot k_{-\text{a}}\cdot \Delta \Theta$$ (A5)

where z is the number of transferred electrons. The change in coverage is coupled to the electrode overpotential η by Nernst's equation

$$\eta =\frac{k_{\text{B}}T}{z{e}_0}\ln \left(\frac{\Theta }{{\Theta }_{\text{eq}}}\right)=\frac{k_{\text{B}}T}{z{e}_0}\ln \left(\frac{{\Theta }_{\text{eq}}+\Delta \Theta }{{\Theta }_{\text{eq}}}\right)=\frac{k_{\text{B}}T}{z{e}_0}\ln \left(1+\frac{\Delta \Theta }{{\Theta }_{\text{eq}}}\right)$$ (A6)

The change of the coverage thus depends on the voltage via

$$\Delta \Theta ={\Theta }_{\text{eq}}(e^{(z{e}_0\eta /k_{\text{B}}T)}-1)$$ (A7)

and the current – given in Eq. (A5) – reads

$$I_{\text{eff}}=-z{e}_0\cdot k_{-\text{a}}\cdot {\Theta }_{\text{eq}}(e^{(z{e}_0\eta /k_{\text{B}}T)}-1)$$ (A8)

The inverse polarization resistance of adsorption kinetics at equilibrium conditions 1/R_ac,eq is given by the slope of the current–voltage-curve at η = 0 V

$$\frac{1}{R_{\text{ac,eq}}}={\left|\frac{d{I}_{\text{eff}}}{d\eta }\right|}_{\eta =0}=z{e}_0\cdot k_{-a}\cdot {\Theta }_{\text{eq}}\cdot \frac{z{e}_0}{k_{\text{B}}T}$$ (A9)

After inserting Eqs. (A3) and (A2) as well as z = 2 for O_(ad) in Eq. (A9)

$$R_{\text{ac,eq}}=\frac{k_{\text{B}}T}{4e_0^2}\cdot \frac{1}{r_a}=\frac{k_{\text{B}}T}{8e_0^2}\cdot \frac{1}{S\cdot P_{\text{tot}}}$$ (A10)

results for the polarization resistance.