LSM solid oxide cell by parametric impedance analysis

Solid State Ionics 232 (2013) 80–96

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Polarization mechanism of high temperature electrolysis in a Ni–YSZ/YSZ/LSM solid oxide cell by parametric impedance analysis Eui-Chol Shin a, Pyung-An Ahn a, Hyun-Ho Seo a, Jung-Mo Jo a, Sun-Dong Kim b, Sang-Kuk Woo b, Ji Haeng Yu b, Junichiro Mizusaki a, 1, Jong-Sook Lee a,⁎ a b

School of Materials Science and Engineering, Chonnam National University, Gwangju 500-757, Republic of Korea Korea Institute of Energy Research, Daejeon 305-343, Republic of Korea

a r t i c l e

i n f o

Article history: Received 1 April 2012 Received in revised form 28 September 2012 Accepted 23 October 2012 Available online 23 December 2012 Keywords: Impedance spectroscopy Solid oxide electrolyzer cells Ni–YSZ/YSZ/LSM Stray impedance Gerischer impedance Gas-electrode polarization mechanism

a b s t r a c t Comprehensive modeling of the spectra of the state-of-the-art Ni–YSZ/YSZ/LSM solid oxide cells including the instrumental stray impedance allowed the systematic deconvolution of the four major polarization losses ranging over one order of impedance magnitude. The stray impedance can be successfully modeled as an inductor connected in parallel with a parasitic resistor whose resistance was shown proportional to the inductance. From the high frequency the ohmic losses, the ‘charge-transfer’ impedance of the Ni–YSZ electrode, the surface diffusion and reaction co-limited impedance of LSM electrode, and the gas phase transport impedance of Ni–YSZ electrode were successfully distinguished. The latter two were satisfactorily described by the ideal Gerischer impedance with two independent parameters, respectively. The gas-concentration impedance increases with electrolysis due to the gas density decrease with hydrogen production, while the LSM polarization decreases due to the increased oxygen activity. Compensation of the opposite polarization behavior of Ni–YSZ and LSM electrodes explains the apparently ohmic polarization over a wide electrolysis range until the upturn where exponentially increasing gas-concentration impedance of Ni–YSZ electrode prevails. Apparently being quite distinct from the fuel cell polarization behavior, the polarization of the high temperature electrolysis can be consistently explained by the chemical potential variations of the reactants and products, which is suggested to be general characteristic of the gas electrodes of solid oxide cells, co-limited by surface diffusion and reaction process. The finite-length Gerischer model constituted of series resistors, shunt resistors, and shunt capacitors, allows the evaluation of the surface diffusivity (ca. 2⋅ 10−4 cm2 s−1), reaction constant (ca. 103 s−1), and the utilization length (ca. 5 μm) among the LSM–YSZ composite functional layer of thickness of ca. 10 μm. The strong decrease in LSM polarization with electrolysis at the humidity of 30% can be contributed by the increase in surface diffusivity, chemical capacitance, and the surface reaction constant in the decreasing order, while the adsorption capacitance increases is mainly responsible for the polarization decreases at higher humidity condition of 50%. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Impedance spectroscopy is the standard and probably the only tool to distinguish different polarization contributions in the solid oxide cells for power generation or electrolysis. Indeed the impedance measurements have been performed in most of the related studies. It may be however surprising, reports on the parametric impedance analysis of the solid oxide cells can be hardly found. Theoretical difficulty lies in the presence of the multi-processes which considerably overlap each other. Symmetric cells or half cells with reference electrodes are thus often used for the investigation of the respective electrode processes which are however rather insufficient for describing the full cell response under operation. Current (i)–voltage (V) characteristics of solid oxide cells [1–3] clearly ⁎ Corresponding author. Tel.: +82 62 530 1701; fax: +82 62 530 1699. E-mail address: [email protected] (J.-S. Lee). 1 Professor Emeritus, Tohoku University, Japan. 0167-2738/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ssi.2012.10.028

indicate that the polarization behavior in electrolysis is quite distinct from that of fuel cell operation. Brisse et al. [3] also reported the characteristic impedance behavior upon electrolysis. The identification of the different polarization contributions of solid oxide cells has been only recently made [4–6]. The distributions of the relaxation times (DRTs) [4,5] or the derivatives of real impedance with respect to the logarithmic frequency (ΔŻ′) [6] were examined by varying the test conditions such as humidity, oxygen partial pressure and temperature, and the respective processes could be attributed to the specific components of the solid oxide cells. It should be mentioned that a parametrization or a modeling of the identified polarization mechanisms is further necessary in order to quantify the loss contributions and to obtain the mechanistic information e.g. from the temperature dependence of the parameters. It should be mentioned that the deconvolution successfully made in these reports [4–6] has been limited to the measurements under open circuit voltage (OCV) condition. There are only a few reports

2. Experimental The cermet-supported, thin-film electrolyte button cells were machined out of the flat tubular type NiO-YSZ supported cells. The flat tubular type NiO-YSZ supports were prepared by the extrusion process and pre-sintered at 1150 °C. YSZ electrolyte layer of 15–20 μm thickness was prepared by dip-coating and co-fired at 1400 °C. The details of the preparation of the flat tubular type cells can be found elsewhere [11]. The oxygen/air electrode of 0.28 cm2 area was prepared as multi-layer of 20–25 μm thickness all together with LSM current collecting layer on top of LSM–YSZ composite functional layer by spray coating and sintering at 1150 °C. LSM–YSZ composite functional layer was about 15 μm as indicated in the micrograph of Fig. 1 (Shimadzu SS-550, Japan). Commercial powders of La0.8Sr0.21Mn1.02O3 (LSM821, Rhodia E&C, USA), 8YSZ (TZ-8YS, Tosoh, Japan) and NiO (99.97% High Purity Chemicals, Japan) were used. The current collector was prepared by brushing the platinum paste (Engelhard No. 6926, USA) and annealing at 900 °C for 10 min. The button cells were mounted on a SOC test unit (Chino, FC5300, Japan). A pyrex ring of 1 mm thickness between bare YSZ electrolyte film and the alumina support tube was used for sealing the compartments. The O2 gas for the LSM electrode was supplied at 75 sccm using a multi-hole mullite tubing. The H2/H2O mixture to the Ni/YSZ electrode was guided through 1/8″ inch quartz tubing at 150 sccm in total. The NiO-YSZ composite was treated in pure H2 at 800 °C for 1 h for NiO reduction to Ni. A custom-made direct steam evaporator combined with a liquid flow meter (DV2MK-TL, ADrop GmbH, Germany), employed earlier in Risø National Laboratory [12,13], was used for the supply of H2/H2O gas mixture at different humidities. Note that in this work the hydrogen flow rates were adjusted so that the total flow

LSM+YSZ

[3,7,8] on the impedance measurements of the solid oxide cells in non-OCV operation condition which can be directly related to the energy efficiency of the devices. This may be rather a bizarre situation, since model-based parametric estimation with error analysis is the very essence of the impedance spectroscopy. Impedance spectroscopy can be applied to the nonlinear electrode processes in solid oxide cells by superimposing dc bias with the small ac signals [9,10]. The status is also indicated by the scarcity of the experimental report. This may be ascribed to the difficulty in obtaining well-behaved impedance data of the solid oxide cells at high temperatures under the turbulent flow of gas mixtures and often involving a substantial temporal change. In addition to these issues, this work will emphasize that the stray impedance is one of the major hurdles for practicing a parametric analysis of the high temperature solid oxide cells. Long wiring necessary for the high temperature measurements often results in the pronounced inductance. Since the high temperature solid oxide cells involve the area specific resistance (ASR) values as small as a few hundreds mΩ cm2, the ac response can be significantly affected by the stray impedance, especially at high frequency range. The electrode processes are however usually substantially overlapped with each other. Without a proper consideration of the stray impedance, the parametric analysis may be difficult even for partial information at low frequency range only. In this work the electrolysis performance of the state-of-the-art Ni–YSZ cermet supported solid oxide cells with strontium-doped lanthanum manganese oxide (LSM) top electrode is investigated by impedance spectroscopy as a function of the electrolysis currents. High quality impedance data suitable for the parametric analysis can be obtained when the cell EMF remains stable during the measurements. Major polarization contributions can be systematically deconvoluted by comprehensive modeling of the solid oxide cells including the stray impedance. The results clarify the details of the polarization mechanisms in high temperature electrolysis which are hardly retrievable from the i–V characteristics.

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LSM

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Fig. 1. SEM cross-section image of LSM electrode constituted of pure LSM and LSM–YSZ composite functional layer.

rate of hydrogen and steam was fixed at 150 sccm for different humidity conditions, e.g. for 30% humidity 45 sccm steam controlled by the liquid flow rate in the direct steam evaporator was carried by 105 sccm hydrogen controlled by a mass flow controller, for 50% humidity 75 sccm steam and 75 sccm hydrogen were used. This is not always the case in other reports. Usually the flow rates of the carrier hydrogen gas are fixed while the humidity is varied by the evaporator temperature, or high flow rate is required to carry the high vapor amount for high humidity condition. The electrode reactions are generally affected by the flow rates. The experimental method employed in the present work is expected to show the humidity effects more systematically. The impedance and i–V characteristics were measured in a 4-wire configuration in an Autolab PGSTAT 302 N FRA2 (Eco-Chemie BV, The Netherlands) using the platinum lead wire of 0.5 mm diameter and 80 cm length each and the gold mesh current collector. The electrolysis currents ranging from zero OCV condition to 0.56 A cm−2 were applied at the sweep rate of 2 or 4 mA s−1. The measurements of impedance spectra were made using ac current of 10 μA rms over the frequency range from 10 6 Hz to 0.1 Hz with 10 points per decade. Impedance data of a quality suitable for the fitting analysis were obtained when the voltage values of the cell became stable at selected fixed electrolysis currents, which usually took ca. 10 min. The numerical Kramers–Kronig test and the parametric analysis were performed using KK-test program provided by Prof. Boukamp and a commercial software Zview (Scribner Ass. Inc., USA), respectively.

3. Results and discussion 3.1. i–V characteristics Fig. 2 shows typical i–V characteristics of electrolysis using Ni–YSZ/ YSZ/LSM solid oxide cells. The electrolysis currents are indicated as negative, indicating the opposite direction to the fuel cell load currents. The curves indicate a wide linear i–V region and an upturn of increasing polarization resistance. The linear region extends with increasing humidity. The OCV values are shown to decrease with the increasing humidity in accordance with the estimate of the Nernst potential according to the oxygen activity increase with the humidity. In the typical fuel cell performance curve, a linear region after the initial activation polarization is usually attributed to the ohmic electrolyte resistance contribution [14] (As will be pointed out later in this work, however, the electrolyte contribution to the ohmic resistance is often negligible in the state-of-the-art cermet supported thin-film electrolyte fuel cells.) The electrolysis performance curves as in Fig. 2 do not

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a

b

Fig. 2. Current (i)–voltage (V) characteristics at 30% and 50% humidity balanced by hydrogen at the constant total flow rate of 150 sccm. The guide lines indicate the linear i–V region, respectively. The closed symbols indicate the electrolysis current values for the impedance spectra shown in Figs. 3 and 4.

clearly indicate any activation polarization but linear i–V behavior immediately from the zero current OCV condition which extends to −0.5 A cm−2 for 30% humidity and to −0.7 A cm−2 for 50% humidity. The behavior appears typical electrolysis performance of Ni–YSZ/YSZ/ LSM solid oxide cells [1–3,15].

c

3.2. Impedance characteristics Impedance spectra as in Figs. 3 and 4 show the details of the polarization behavior under electrolysis operation at 30% and 50% humidity condition, respectively. From the spectral feature different relaxation processes may be distinguished for the spectra of Fig. 3(a) and (b) or Fig. 4(a), (b) and (c). The numbers for the closed data symbols are logarithmic frequencies. In addition to the high frequency ohmic resistance three distinct processes may be identified with the characteristic frequencies between 10 5 and 10 4 Hz, 10 3 and 10 2 Hz, and 10 and 1 Hz. It is also shown that the overall resistance of the impedance spectra is more or less constant in Fig. 3(a) to (c) for 30% humidity and in Fig. 4(a) to (d), in consistency with i–V characteristics shown in Fig. 2. In this apparently linear regime the impedance spectra clearly indicate a systematic variation of the respective polarization contributions with the electrolysis currents. The model-based parametric analysis is required for the systematic analysis leading to the identification of the physicochemical nature of these polarization processes. The impedance spectra should be of a sufficiently good quality for the parametric analysis with equivalent circuit models to be valid. This can be shown by Kramers–Kronig residuals in the insets of Figs. 3 and 4 (red circles) obtained numerically using the test program kktest.exe. The detailed algorithm can be found in Refs. [16] and [17]. It is shown that the KK residuals are limited to less than 1% for the frequency range presented, except for the spectrum of Fig. 4(d). Poor KK compliant data with residual errors ranging up to 3–4% as shown in Fig. 4(d) may still provide the parameters of a physical significance. This is a good example that a KK test is also very useful to see whether the poor description of the spectrum by a specific model is due to the unsuitability of the equivalent circuit model or due to the bad data quality. In the latter case efforts of a further improvement would be of little use.

d

Fig. 3. Impedance spectra at different electrolysis current densities with 30% H2O: (a) −0.03 A cm−2, (b) −0.09 A cm−2, (c) −0.33 A cm−2 and (d) −0.56 A cm−2. The solid line and dotted lines in the impedance spectra are simulated results from fit results using the equivalent circuit model shown in Fig. 7 with and without the stray impedance L–RSTR. The fit results are given in Table 1. Insets indicate the Kramers–Kronig test and the fit residuals, respectively.

E.-C. Shin et al. / Solid State Ionics 232 (2013) 80–96

a

b

83

In the spectra of Figs. 3 and 4 some high frequency data near 10 6 Hz are not shown, since the singularity and the large KK residuals clearly indicated the artifactual nature associated with high frequency measurements by electrochemical impedance analyzers. On the other hand, the quality of the low frequency data near 10−1 Hz was found to be directly related to the stability of the cell voltage values during the impedance measurements under galvanostatic condition. Good quality impedance data can be extended further to the lower frequency range as long as the cell voltage stays stable during the measurement. In addition to the equilibriation upon application of the electrolysis currents, the cell voltages can be strongly disturbed by small irregularity in the steam flow e.g. due to some condensation in the gas supply line. The intervals between the high oxygen activity bursts were reduced, when the temperature of the gas supply line was increased and/or the thermal insulation was made more thorough. 3.3. Stray impedance

c

d

Fig. 4. Same as in Fig. 3 but for the 50% humidity. Impedance spectra at different electrolysis current densities (a) −0.03 A cm−2, (b) −0.09 A cm−2, (c) −0.33 A cm−2 and (d) −0.56 A cm−2. The solid line and dotted lines in the impedance spectra are simulated results from fit results using the equivalent circuit model shown in Fig. 7 with and without the stray impedance L–RtSTR. The fit results are given in Table 1. Insets indicate the Kramers–Kronig test and the fit residuals, respectively.

Long lead wire necessary for the high temperature measurements induces a substantial inductance, which is usually modeled as an inductor connected in series to the solid oxide cell impedance components. The resistance of the lead wire, usually of platinum, can be also of a substantial contribution to the total resistance. The lead wire resistance is thus favorably subtracted via a 4-wire configuration. Such connection is also necessary for the i–V measurements as shown in Fig. 2 to represent the true cell characteristics, rather than the dominant contribution of the lead wire resistance. The 4-wire configuration is supposed to subtract the lead wire resistance but not the inductance. The L element in series produces the straight line response diverging at or parallel to the imaginary axis at high p frequencies, since the impedance of L eleffiffiffiffiffiffiffiffi ment is Z″ =jωL where j ¼ −1. The impedance spectra in Figs. 3 and 4 are notable for the extended fourth quadrant portion of the high frequency parts. In most publications only the first quadrant or only limited portion of the fourth quadrant data are presented, since the lead wire inductance is of little interest of investigation. The KK residuals shown in Figs. 3 and 4 clearly indicate that such a high frequency response is a valid response for the fit analysis using equivalent circuit models which are also KK compliant [18,17], whether originated from the electrochemical cell, from the electrical connection of the measurement setup, or from the electronics in the instrument. Since the artifact and the cell impedance do not distinguish clearly from each other, a comprehensive modeling of the solid oxide cell and the electrical artifact together is suggested necessary for the systematic analysis of the various polarizations. It can be easily seen that the high frequency inductive loops in Figs. 3 and 4 can be described by a L–RSTR parallel connection where the peak frequency corresponds to ω= RSTR/L. For an infinitely large RSTR, the model becomes the conventional series L only. To illustrate the interaction of the stray impedance and the cell impedance, equivalent circuit models shown in Fig. 5(a), model 1 and model 2, are considered. In the dashed box region of model 1, four loss contributions of a solid oxide cell (SOC) are indicated: RESR for the pure resistive components e.g. from lead wires, where ESR represents Equivalent Series Resistance, RYSZ for the resistance of the YSZ electrolyte, and RH and RL representing the polarizations from the electrode reaction. The L–RSTR parallel circuit for the stray impedance is connected in series to these circuits for the SOC impedance. Note that the parallel RSTR does not contribute to the dc resistance of the circuit. The spectrum at the bottom of Fig. 5(a) is for the SOC part of the model 1 (dashed box) using the values of the circuit elements given above. The numbers on the points of the spectrum represent the logarithmic frequency values. The high frequency limit (at frequencies approaching to the infinity) represents RESR including the lead wire and other electronic resistance, which is assumed as 0.1 Ω cm2. The first semicircular response at high frequency range represents the YSZ impedance which is modeled as RYSZ–CYSZ parallel circuit. RYSZ is

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a

b

μ μ Ω μ Ω Ω Ω

Ω μ Ω

Ω

Fig. 5. (a) Simplified equivalent circuit models for a solid oxide cell (SOC) constituted of the series resistance, YSZ electrolyte impedance, and two electrode reaction impedance, connected in series with the stray impedance of L–RSTR parallel network (model 1) and the modified one for the practical frequency range below 106 Hz (model 2). The simulated spectrum of the SOC part of the model 1 using the parameter values is shown below. (b) The evolution of the spectra of the SOC part of model 2 in the presence of the lead wire inductance and stray resistance in parallel.

given as 0.2 Ω cm2 for the purpose of illustration. In fact, for the state-of-the-art cermet supported thin film electrolyte solid oxide cells at high temperatures as in the present work the electrolyte resistance is negligibly small. The contribution of the YSZ electrolyte for the present experiments may be estimated as small as 0.008 Ω cm2. A substantial electrolyte contribution to the high frequency intercept may arise when operated at lower temperatures and/or from the thicker electrolytes as in the case of the electrolyte supported solid oxide cells. The geometric capacitance of the electrolyte layer CYSZ is assumed as 10 −10 F or 0.1 nF from the typical geometry factor of the thin film electrolytes. It should be noted that due to the small resistance values the peak frequency of the RYSZ–CYSZ parallel circuit of the electrolyte becomes as high as 1010 Hz. Since the frequency range of the electrochemical measurements is usually limited to 10 5 or 106 Hz, the YSZ contribution is usually included in the high frequency intercept or in the ohmic contribution. The ‘model 2’ represents the equivalent circuit of the solid oxide cells for such a practical experimental frequency range limited to 106 Hz, where the high frequency intercept is represented by ROHM. As discussed above, the YSZ contribution in the state-ofthe-art SOCs can be negligibly small and the high frequency intercepts are often erroneously taken as the electrolyte resistance. Electrode polarizations are represented by the two RC parallel components, RH–CH and RL–CL which may be considered idealized responses of the spectra of Figs. 3 and 4 with comparable resistance values and the time con−1 stants τ= ωPeak = RC. The spectra simulated in Fig. 5(b) illustrate how the stray impedance affects the spectra of the cell impedance discussed so far. First, the effect of the L component alone is considered. It is shown that with a sufficiently smaller L e.g. 0.05 μH, the high frequency intercept may still be taken as the ohmic resistance of ROHM of SOC with a negligible error (blue line).

In the typical high-temperature setup the inductance L can be as large as 0.5 μH. The case is indicated by red line in Fig. 5(b). It can be seen that the ohmic resistance is subject to a substantial error if taken from the high frequency intercept. Simultaneously the electrode reaction component of RH–CH is severely affected. With a higher L, e.g. 5 μH (green line), the high frequency intercept includes the electrode reaction polarization resistance RH as well. The simulations in Fig. 5(b) with the stray impedance L only as 0.05 μH (blue circle), 0.5 μH (red triangle), and 5 μH (green diamond), show that at frequencies high enough the spectra converge to the line parallel to the imaginary axis with real axis intercept at ROHM regardless of the inductance values. It should be emphasized that when the frequency range sufficiently covers the entire responses a nonlinearleast-squares fit analysis using the original ‘model 2’ in Fig. 5(a) yields the correct values of all the circuit parameters with negligible errors. Experimentally observed high frequency inductive loop behavior in Figs. 3 and 4 cannot be satisfactorily described by the L element alone, but by an additional parallel resistance RSTR as indicated by the simulated spectra in Fig. 5(b) with L of 0.5 μH and RSTR of 5 Ω (purple square) and with L of 5 μH and RSTR of 25 Ω (brown down-triangle), respectively. Similar modeling of the high frequency stray impedance has been also reported [19,20], but little explanation for the origin of RSTR has been given. As discussed above an L–R parallel circuit exhibits a circular loop with the peak frequency at ωPeak =R/L and the size of R. The experimental spectra measured would not exhibit the appreciable loop behavior if RSTR is sufficiently larger than ωmaxL where ωmax =2πfmax is the experimental maximum frequency. It should be mentioned that the electrochemical impedance spectroscopy for the power sources is instrumentally limited to 1 MHz and often performed only up to 0.1 MHz.

E.-C. Shin et al. / Solid State Ionics 232 (2013) 80–96

Fig. 6 represents RSTR and L values of the present work, labeled as SOC I, the numerical values of which are also presented in Table 1. The short-circuited empty cell constituted by Pt lead wires of 0.5 mm thickness and ca. 80 cm length were measured by different wiring configurations and ac applications indicated by the numbers 1 to 6. The highlighted data number 1 may be close to the experimental condition in view of the temperature (800 °C) and ac/dc current signals. The inductance value is close to the theoretical value for 80 cm length, which is much higher than those of SOC I. The response, however, significantly changed with temperature or probably with time as indicated by the data group numbered by 2 and 3. The data point of number 4 was measured by applying ac voltage while data indicated by 1, 2, and 3 were measured using ac/dc currents. The effects of the wire configurations and signal configurations were also examined. Theoretically, the 4-wire measurement is expected to provide the inductance value of the single lead wire of the configuration. For the ‘shorted 2-wire’ configuration the two lead wires of the respective polarities of the 4-wire configuration are shorted. The inductance of the shorted 2-wire configuration should be similar to that of 4-wire configuration. The simple ‘2-wire’ method differs from the ‘shorted 2-wire’ method by using single lead wires for the respective polarities. The inductance then becomes twice larger. The measurement by 2-wire configuration, indicated by the data number 6, indeed provided double the inductance of that by the 4-wire configuration, data number 4, but the absolute values are not consistent with the theoretical lead wire inductance. The result by the shorted 2-wire method, labeled as 5, close to that by 2-wire method is not consistent with other configurations. The data set 1 to 6, with the exception of number 3, indicates a linear relation between RSTR and L, which also encompasses the results of SOC I. The measurements indicated by SOC II to VI represent various experimental SOCs in a different setup. Specific details of the other SOCs are out of the present scope. It suffices to mention that these SOCs are

85

constituted of different electrode and electrolyte materials and the data were collected under an OCV condition by 4-wire method applying small ac voltages at different temperatures. The respective lead wires are ca. 60 cm. There are variations in L and RSTR values but smaller RSTR values than those of SOC I indicate the more prominent high frequency L–RSTR loop behavior if measured up to the same high frequency limit of 1 MHz as in the present work in Figs. 3 and 4. Pt wires of 0.5 mm thickness and 30 cm length were tested on the lab bench for comparison. The 4-wire configuration measurements, which are indicated by the number 7, resulted in much smaller inductance, regardless of ac and dc signals, than the shorted 2-wire measurements represented by the two data points indicated by the number 8, which is close to the theoretical value. The set of data points from 30 cm Pt wires can be represented by a linear relation RSTR/Ω = 16(±2)L/μH − 0.7(±0.2) (line in dark cyan) which the results of SOC II to VI also approximately follow. A systematic investigation of the stray impedance behavior was attempted by testing more dummy cells of electrical wires on the lab bench. The results of the measurements performed on the series of Cu or Al-based conventional electrical wires of different lengths (40 cm and 80 cm) and thicknesses (0.25 mm and 0.5 mm) are indicated by the number 9 to 12 in Fig. 6. The data set can be represented by the linear relation of RSTR/Ω= 16(±1)L/μH + 1.5(±1.3) as indicated by the solid line in black. It is notable that the L values were found to be close to the theoretical values as marked on top of the graph. The consistency is however rather exceptional. Data indicated by 13 to 18 were obtained by another set of Cu clad Al wires of 0.6 mm thickness and 80 cm length, similarly as the data numbered 9 and 10. Unlike the measurements represented by data numbered 9 and 10, data set numbered 13, 14, and 15 show that, regardless of magnitude of ac voltages, the inductance from 4-wire configuration is rather small as ~0.1 μH. The shorted 2-wire and single 2-wire method yield 0.9 μH and 1.7 μH, respectively, approximately meeting the theoretical ratio,

Fig. 6. Stray impedance components, L and RSTR from different SOCs with different cathode and electrolyte materials in two different setups and the dummy cells of the copper, aluminum, or platinum lead wires in varying lengths and thickness in various measurement configurations.

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Table 1 Fit results and the derived parameters of Ni–YSZ/YSZ/LSM cell under electrolysis represented in Figs. 9, 10, 11, and 12, as well as for the simulated spectra in Figs. 3 and 4. Variable

T

H2O

i

Unit

°C

%

A cm−2

800 800 800 800 800 800 800 800 800 800 800 800 800 800 800

30 30 30 30 30 30 30 50 50 50 50 50 50 50 50

0.003 0.03 0.09 0.16 0.33 0.56 0.56 0.03 0.03 0.033 0.09 0.09 0.16 0.33 0.56

Fig. 3(a) Fig. 3(b) Fig. 3(c) Fig. 3(d)

Fig. 4(a)

Fig. 4(b) Fig. 4(c) Fig. 4(d) RNi–YSZ

Err.

ANi–YSZ α −1

Ω

%

Fs

1.13 1.10 1.05 1.00 1.36 1.96 1.71 1.37 0.93 1.03 1.22 0.91 1.22 1.07 1.17

5.8 1.8 2.2 1.3 3.9 1.0 1.9 5.2 1.9 5.9 6.1 2.0 7.6 3.4 5.0

2.86E−04 2.80E−04 2.05E−04 1.60E−04 2.45E−04 3.47E−04 3.41E−04 1.71E−04 4.15E−04 7.75E−05 1.18E−04 4.25E−04 1.13E−04 9.94E−04 4.63E−04

Err.

χ2

3.53E−04 1.12E−04 1.04E−04 1.02E−04 1.15E−03 9.86E−05 2.54E−04 2.88E−04 1.75E−04 5.48E−04 4.10E−04 1.52E−04 4.60E−04 4.83E−04 1.54E−03 αNi–YSZ

% 17.9 8.2 9.2 7.7 21.5 4.8 8.5 14.4 9.6 21.5 16.7 9.9 17.4 16.3 25.5

Sum-sqr

0.62 0.63 0.66 0.69 0.66 0.66 0.67 0.62 0.63 0.72 0.66 0.64 0.66 0.57 0.65

3.32E−02 1.28E−02 1.00E−02 9.95E−03 1.22E−01 1.01E−02 2.49E−02 2.71E−02 2.09E−02 1.15E−01 4.06E−02 1.67E−02 4.38E−02 5.50E−02 1.57E−01

RSTR

Err.

L

Err.

ROHM

Err.

Ω

%

H

%

Ω

%

12.5 10.9 10.7 12.3 11.0 11.8 11.7 12.9 12.0 15.9 15.6 11.7 11.7 11.0 11.1

13.9 1.6 4.9 1.5 10.7 1.8 3.7 9.5 1.9 18.9 14.7 2.6 16.4 3.1 5.9

5.23E−07 4.91E−07 4.87E−07 4.78E−07 4.77E−07 4.71E−07 4.74E−07 5.12E−07 4.88E−07 5.20E−07 5.20E−07 4.88E−07 5.30E−07 4.93E−07 4.85E−07

2.0 0.4 0.8 0.3 1.5 0.3 0.5 1.8 0.4 2.2 2.2 0.5 3.1 0.7 1.1

0.31 0.37 0.41 0.46 0.45 0.49 0.45 0.21 0.36 0.30 0.22 0.36 0.19 0.32 0.38

16.8 3.7 4.4 1.8 6.6 1.0 1.7 29.0 2.7 16.7 28.7 3.0 42.2 5.8 5.4

Err.

GLSM

Err.

τG(LSM)

Err.

GNi–YSZ

Err.

τG(Ni–YSZ)

Err.

%

Ω

%

s

%

Ω

%

s

%

3.5 1.3 1.5 1.1 3.2 0.7 1.2 2.9 1.5 3.4 3.2 1.6 3.6 2.9 3.7

1.25 1.29 1.39 1.35 0.80 0.19 0.17 1.07 1.27 1.36 1.25 1.30 1.20 0.77 0.28

3.0 1.6 1.6 1.8 9.6 17.6 28.3 3.2 1.8 3.7 3.3 1.8 3.4 5.5 29.9

1.09E−03 1.13E−03 1.28E−03 1.37E−03 1.51E−03 1.34E−03 8.93E−04 8.07E−04 1.17E−03 1.20E−03 1.08E−03 1.25E−03 9.47E−04 1.61E−03 9.62E−04

2.41 1.30 1.37 1.63 7.76 12.90 19.28 2.54 1.50 3.18 2.76 1.50 2.81 4.22 21.33

0.36 0.37 0.43 0.47 0.91 2.60 1.41 0.27 0.32 0.35 0.35 0.35 0.29 0.58 0.99

39.0 17.1 22.9 29.4 12.9 2.6 3.6 57.4 7.7 17.3 18.9 7.7 19.9 7.9 10.5

5.80E−02 6.41E−02 6.29E−02 4.43E−02 9.82E−02 2.03E−01 1.30E−01 3.86E−02 6.21E−02 7.30E−02 5.17E−02 6.90E−02 4.86E−02 9.71E−02 9.95E−02

12.4 5.3 9.1 13.0 10.6 6.6 4.9 13.7 6.3 14.7 17.1 6.5 17.6 6.8 9.7

however. A linear relation between the parallel stray resistance and inductance can be found as RSTR/Ω= 33(±1)L/μH − 3.1(±0.2) (solid line in pink). Data 16, 17, and 18 are analogous measurements but using ac current signals instead of voltage. Similar variation depending on the wire configuration was observed, but the absolute values of the inductances differed. Another linear relation was found as RSTR/Ω= 19.3(±0.9)L/μH + 0.4(±0.8) represented by the olive line. It should be noted that the L values in the respective measurements are well-defined with the fit errors usually less than 0.1%. However, the absolute L values change significantly depending on the cell and device configurations, not quite in a reproducible and construable manner. The OCV and the resistance of the SOCs, which are absent in dummy cells, may also affect the stray behavior. For some of wire dummy cells several impedance analyzers of autobalance bridge type and frequency response analyzers have been tested in addition but the theoretical inductance values could not be obtained. Often a much larger value of a few μH was observed, indicating the stray impedance mainly originates from the internal electronics of the devices. On the other hand, very low inductance of the order of ten nH was also observed for some instruments. An electrochemical impedance analyzer of a different brand, for example, resulted in the inductance values of the order of ten nH for lead wires of 60 cm, 80 cm and 100 cm, respectively, indicated by the data 19, 20, and 21, respectively, under various ac and dc signals. A certain instrumental compensation mechanism seems present, which, however, is not explicitly given. In conclusion, the investigations did not allow a fundamental understanding of the high frequency stray impedance behavior. The accurate measurement of the lead wire inductance turns out non-trivial. However, the results summarized in Fig. 6 demonstrate clearly the presence of RSTR in a linear correlation with the inductance values whatsoever measured. Using the simulations in Fig. 5, for example, it can be easily

shown that the fit analysis of the spectra conventionally with the cut-off high-frequency region without a proper modeling of the stray impedance leads to the inaccurate estimation of the fit parameters and the inadequate description of the overall spectral behavior which is indicated by a large χ2 value. It should be emphasized that the information loss and uncertainty is not likely limited to the ohmic resistance at high frequency. The measurements and the analysis of the spectra covering a wide frequency range including the artifact are recommended for a more correct (in view of the mechanistic model) and a more accurate (in view of the parameter values) description of the electrochemistry in solid oxide cells. Fig. 5 also shows that the stray impedance distorts the originally ideal RC semicircular response apparently to a depressed circle or even an asymmetric arc. The real situation can be rather unambiguous, since the cell response itself indeed generally needs distributed elements as discussed below. 3.4. Equivalent circuit model for SOC The electrode polarization impedance in the real solid oxide cells can be rarely described by ideal RC circuits as assumed in Fig. 5, but requires so-called ‘distributed’ elements with power-law frequency exponents such as constant phase elements (CPEs) of complex capacitance A(iω)α−1 (or Q elements), Gerischer, Warburg, etc. either simply due to the inhomogeneity or from a specific mechanistic origin. A working impedance model of Ni–YSZ/YSZ/LSM solid oxide cells as shown in Figs. 3 and 4 is suggested in Fig. 7. It is similar to the schematic model 2, in Fig. 5, but includes three, rather than two, electrode reaction processes for the three impedance ‘bumps’ well-distinguished in the experimental impedance spectra of Fig. 3(a) and (b) or Fig. 4(a), (b) and (c).

E.-C. Shin et al. / Solid State Ionics 232 (2013) 80–96

G

G

Fig. 7. Equivalent circuit model to fit impedance spectra of Ni–YSZ supported solid oxide cells with LSM top electrode as shown in Figs. 3 and 4.

They are represented in the decreasing frequency order by an R–Q parallel circuit for a Cole–Cole element and two Gerischer elements, G, of an asymmetric spectral shape with the slope one at high frequencies. The RNi–YSZ–QNi–YSZ parallel circuit represents the ‘charge-transfer’ reaction at Ni–YSZ electrode. GLSM represents diffusion–reaction co-limited impedance in LSM electrode. GNi–YSZ is the impedance resulted from the gas phase transport in the Ni–YSZ electrode compartment. The details will be presented in the following sections. The numerical values of the fit results are given in Table 1. The peak frequencies of the respective components confirm the assignment of the frequency response order. In Figs. 3 and 4 the deconvoluted three electrode processes are indicated separately in (blue) solid lines. The dotted lines represent the simulated overall spectra with the stray impedance subtracted. As illustrated in Fig. 5(b), the stray impedance is shown to significantly affect the Cole–Cole type RNi–YSZ–QNi–YSZ response. Without a proper modeling and a sufficient coverage of the response from the stray impedance, the RNi–YSZ as well as ROHM is subject to large errors. Since the RNi–YSZ–QNi–YSZ component considerably overlaps with the lower frequency component, and this again overlaps with the lower one and so on, the poor analysis would propagate through the whole frequency range down, if the high frequency stray impedance were not properly taken into account. The mechanistic assignments in the present work are consistent with the recently reported clarification from ΔŻ′ behavior in Ni– YSZ/YSZ/LSM solid oxide cells under OCV condition [6] or by the

a

87

analysis of DRTs (distributions of the relaxation times) in lanthanum strontium (cobalt) ferrite or LS(C)F/Ni–YSZ solid oxide cells [5] under the variation of test conditions. It was also found a less oxidative atmosphere in LSM electrode such as nitrogen and static air increases GLSM and generates additional ‘gas-conversion’ impedance at lower frequencies, in accordance with the previous reports [5,6]. The details will be reported elsewhere. Five or six processes may be deconvoluted from the spectra shown in Figs. 3 and 4 similarly as Refs. [5,6,21]. The spectra could be overall more nicely described by introducing more circuit components and/or the distributed elements with free adjustable power-law exponents. It should be noted that the distributed elements with power-law exponents cover a wide frequency range and thus affect the impedance response far away from the characteristic frequency values. An inappropriate application of distributed elements therefore often leads to the unsystematic separation of the individual contributions. In that case the associated physical mechanisms are difficult to identify, if not completely lost. It should be also noted that KK-valid impedance data can be perfectly simulated using as many RC, RQ, or L as required. This is also the principle of the numerical Kramers–Kronig test which is not mechanism-based [16,17]. A good spectra fitting does not necessarily guarantee the physical plausibility of the model analysis. In this work, therefore, only four clearly distinguished major loss contributions are separated. 3.5. Gerischer model The Gerischer model is chosen as the simplest model which describes the essential features of electrode reaction of LSM and Ni– YSZ electrodes in the middle and low frequency range, respectively, as also previously suggested in the literature [5,22–25]. A straightforward insight into the Gerischer model, as shown by the model ‘G’ in Fig. 8(c), may be obtained by considering the transmission line model modified from the ordinary diffusion case. The ordinary

c ωτ

ωτ

ωτ

α

α

FLW

FLWα

FLG

FLGα

α

b

α β ωτ

α

α

β

ωτ

β α

α

β

G

β ωτ

α β

ωτ α β

Gα α

β

α

β

HNαβ

Fig. 8. (a) Gerischer impedance in comparison with Warburg impedance in the ideal and generalized form represented as the transmission line models in (c) of an infinite and finite length where shunt capacitance C is replaced by Q. (b) Havriliak–Negami impedance: symmetric arcs for β = 1 and asymmetric arcs for β ≠ 1. Ideal semicircular response of RC parallel circuit (α= β = 1) and Gerischer impedance (α = 1; β = 0.5) with peak frequencies according to Eq. (8). (c) Equivalent circuit models for the impedance spectra in (a) and (b). See the text for explanation.

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diffusion process can be represented by a rS–cP transmission line model or Warburg model, as represented in Fig. 8(c), top. The rS elements represent the transport properties such as conductivity or mobility and cP elements represent the (electro)chemical storage process. Then (rScP) −1 is the (chemical) diffusion coefficient, D, of the Fick's law, ∂c ∂2 c ¼D 2: ∂t ∂x

ð1Þ

The Gerischer model is a transmission line model by adding rP element in transverse direction, which from the general equation of the infinite transmission line with z longitudinal impedance and y transverse admittance, results in the characteristic impedance as

reaction zone (ERZ) [28,29], the penetration depth [4] or the utilization length [24]. The generalization of shunt capacitors cP into constant phase elements qP =a(iω)α−1 in these transmission line models allows the description of the realistic impedance response with the slope of the high frequency spectrum deviating from one as indicated in Fig. 8(a). The generalized finite-length short-circuited Gerischer impedance, indicated as FLGα in Fig. 8, can be written as Z FLGα

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   RS α ¼ tanh RS R−1 P þ ðiωÞ A −1 α RP þ ðiωÞ A

ð6Þ

where the reaction constant k corresponds to (rPcP) −1 [26]. The extra rP in Gerischer model then represents the co-existing reaction (or recombination) process during the diffusion [22,24,26,27], which plays a role of a ‘sink’ of the transport species. Therefore, the proper analysis of the Gerischer function can provide both the diffusion and reaction kinetics for the processes occurring within the quasihomogeneous medium including the porous structure. The situation should be distinguished from the case where the reaction is concerned with the in/excorporation at the sample boundary only and the governing equation is the conventional Fick's equation, Eq. (1) for the Warburg impedance. It should be noted that the Gerischer impedance is in fact a two-parameter function, i.e.

where QP =LqP =A(iω)α−1. Note that with rP →∞, the expressions of Eqs. (2), (5) and (6) become the Warburg impedance in the infinite length, and finite length in the ideal form (FLW) and in the generalized form (FLWα), respectively. It should be also noted that the time constant τ of the short-circuited finite-length transmission line of Eqs. (5) and (6) is a function of rS as well as rP and cP. It may be a useful information that a very generalized finite length transmission line model with a symmetrically shortcircuited terminals can be now conveniently employed for the nonlinear-least-squares analysis using Jamnik–Maier–Lai–Lee model (DX-19) implemented in a commercial fitting software Zview 3.2c and later version [30–32]. The transmission line models for the SOC electrode impedance with asymmetric boundary condition in Fig. 8(c) are equivalent to the half of the symmetric transmission line model of DX-19 (or Jamnik–Maier model (DX-15) with ideal capacitors [33]). With DX-19 model, arbitrary rS, rP, a and α can be simulated. Due to the short-circuiting nature of rP elements, however, the parameters become strongly correlated for rS ≫ rP and the short-circuited boundary condition in DX-15 or DX-19 models. As also previously noted [27], the (generalized) Gerischer model, Gα, is a special case of Havriliak–Negami function, originally suggested to describe complex permittivity of dielectric system [34], more generally than Cole–Cole dielectric model [35]. The Havriliak–Negami function in impedance plane can be expressed as

RG ffi Z G ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ jωτ G

Z HN ¼

rffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi z rS ¼ ZG ¼ : y r −1 P þ iωcP

ð2Þ

The model can describe co-limited diffusion and reaction process of the equation, 2

∂cðx; t Þ ∂ cðx; t Þ þ kðcðx; t b 0Þ−cðx; t ÞÞ ¼D ∂t ∂x2

ð3Þ

ð4Þ

where the dc resistance RG and the characteristic time constant τG(= k − 1) correspond to (rSrP) 1/2 and rPcP, respectively. The three parameters, rS, rP, and cP cannot be independently determined. The transverse admittance or the leakage rP leads to a finite dc resistance RG of the infinite length transmission line. RG is thus a function of the reaction kinetics rP as well as the transport properties rS. The impedance representation of a Gerischer element is shown in Fig. 8(a) and (b). It can be easily shown that the peak frequency ωG of thepasymffiffiffi −1 metric spectrum of the Gerischer impedance corresponds to 3τG . As indicated in Fig. 8(a), the spectral feature of Gerischer impedance is thus quite similar to that of rS–cP transmission line model with the finite-length short-circuited or absorbing boundary condition, as represented by the model ‘FLW’ for Finite-Length Warburg in Fig. 8, top. Note that a similar, intermediate response results when the Gerischer element ‘G’ is short-circuited in finite length, as indicated by the transmission line model ‘FLG’ in Fig. 8 for Finite-Length Gerischer with impedance function, Z FLG ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   RS tanh RS R−1 P þ iωC P −1 RP þ iωC P

ð5Þ

where RS =LrS, RP =rP/L, and CP =LcP for the transmission line of a finite length L. The finite-length with the open terminus is represented by cotangent hyperbolic function. The hyperbolic functions the ffi pffiffiffiffiffiffiffiffiffiffiffiffi pofffiffiffiffiffiffiffiffiffiffiffi finite-length Gerischer elements have the variable R =R =r ¼ L= r S P P S. pffiffiffiffiffiffiffiffiffiffiffi The ratio lδ ¼ r P =r S can thus represent the length of the effective

RHN ð1 þ ðiωτHN Þα Þβ

ð7Þ

where β exponent fixed to 0.5 corresponds to the Gerischer function. Havriliak–Negami impedance was thus also expressed as ‘double fractal’ Gerischer impedance [25,27]. With arbitrary β the function represents the general asymmetric arcs as shown in Fig. 8(b). The low-frequency-limiting frequency power-law exponent or log–log slope is α, and the high-frequency limiting slope is −αβ. The peak frequencies of Havriliak–Negami impedance indicated in Fig. 8(b) can be estimated as [36]   1=α π ωHN τ HN ¼ tan 2ðβ þ 1Þ

ð8Þ

pffiffiffi which becomes 3 for Gerischer impedance. Note that with β = 1 Havriliak–Negami function becomes a Cole– Cole function for a depressed semicircle or symmetric arc, in impedance plane, which may be represented by a circuit model of R–Q parallel connection, although Q is not a proper electrical component but just a notation of the element by convention after Ref. [37]. An ideal semicircular response results for the case α = β = 1, which is represented by non-distributed, lumped elements of R and C. Note that Havriliak–Negami element, a ‘double-fractal’ function with two arbitrary α and β exponents cannot be graphically represented. The ideal Gerischer model used in the present work may be replaced or generalized by other analogous transmission line models [4,23,25,27]. The electrode thicknesses are generally very thin but the effective reaction zone can be even thinner than the real electrode

E.-C. Shin et al. / Solid State Ionics 232 (2013) 80–96

89

thickness [20]. Boukamp et al. suggested the finite-length Gerischer (FLG) model of Eq. (5) or (6) containing a tangent hyperbolic function should be a more proper description of the electrode reaction at the porous Ni–YSZ electrodes [25]. The finite-length condition and/or the generalization increase the number of fit parameters. Such a more exhaustive approach may reduce the fit residuals indicated in Figs. 3 and 4 to the level of KK residuals. However, substantially overlapping responses as shown in Figs. 3 and 4 cannot be systematically distinguished, since the response of the distributed elements can cover a wide frequency range, depending strongly on the small changes in the power-law exponents. As illustrated in Fig. 8 the spectral features of these different transmission lines do not differ substantially. A two-parameter ideal Gerischer model should be considered the simplest choice to represent the essential features of the experimental spectra. The equivalent circuit model of Eq. (7) employing two Gerischer elements systematically separated the individual polarization components of the spectra in Figs. 3 and 4 in consistence with the graphical intuition. 3.6. Polarization Mechanisms for Electrolysis Figs. 9, 10, 11 and 12 display graphically the fit and derivative parameters from the non-linear least squares fitting analysis using the equivalent circuit in Fig. 7 as a function of the electrolysis currents for two humidity conditions 30% and 50%. The guidelines are drawn by polynomial fitting weighted by measurement errors. For clarity the lines are shown only for the data at 30% humidity. The numerical results of the direct fit parameters are provided in Table 1. The simulated spectra using the fit results are presented with the experimental spectra in Figs. 3 and 4. Note that the polarization resistance values in Fig. 9 are given in the logarithmic scale in order to represent the resistance values differing by up to one order of magnitude. ROHM represents the series resistance which includes the ohmic resistance of the electrolyte and electrode materials as well as residual lead wire resistance. It is shown that they contribute to ca. 10% of the total ASR or ~0.1 Ω cm2 and almost independent of the electrolysis currents. The ohmic contribution is thus attributed to the residual resistance of lead wire and zirconia electrolyte. The electrolyte contribution, however, is estimated to ca. 0.01 Ω cm2, only 10% of

a

Fig. 10. ANi–YSZ and αNi–YSZ values of QNi–YSZ as a function of the dc electrolysis current densities in 30% and 50% H2O atmosphere.

the ohmic resistance. The simulated spectra without the stray impedance in Figs. 3 and 4 clearly illustrate that ROHM from the model analysis including the stray impedance can be substantially smaller than the high frequency intercepts of the spectra conventionally taken as ohmic resistance. The electrolyte contribution obtained from the high frequency intercepts in SOCs is likely to have been overestimated. 3.6.1. ‘Charge-transfer’ impedance of Ni–YSZ electrode The ‘charge transfer’ impedance of Ni–YSZ cermet modeled as the RNi–YSZ–QNi–YSZ parallel circuit overlaps substantially with L–RSTR response in the frequency range of 104 and 106 Hz. The conventional analysis without proper consideration of the stray impedance would lead to a substantial underestimate of RNi–YSZ, which is in correlation

b

Fig. 9. The polarization resistances as a function of the dc electrolysis current densities in 30% H2O (a) and 50% H2O (b) atmosphere.

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E.-C. Shin et al. / Solid State Ionics 232 (2013) 80–96

Fig. 11. Time constants for the three relaxation processes: τNi–YSZ for RNi–YSZ–QNi–YSZ and τG's for GLSM and GNi–YSZ, respectively, as a function of the dc electrolysis current densities in 30% and 50% H2O atmosphere.

with the overestimate of ROHM as discussed above. The interference of the stray impedance with the RNi–YSZ–QNi–YSZ component with the adjustable power-law frequency exponent α resulted in large relative errors in some of RSTR, ROHM and ANi–YSZ values as indicated in Figs. 9 and 10. See also Table 1. The α values for the non-ideal double layer capacitance of QNi–YSZ element ranged between 0.6 and 0.7. Fig. 10 suggests a strong correlation between the parameter ANi–YSZ and α. The variation in ANi–YSZ and α with the electrolysis current density in the opposite direction is expected to compensate the frequency dependence of impedance. Indeed, as shown in Fig. 11, the time constant uNi–YSZ obtained as (RNi–YSZANi–YSZ) 1/α, which is the inverse of the peak frequency of the Cole–Cole plot, show a monotonic increase with the electrolysis current

Fig. 12. Effective capacitances from the relaxation times τ's and polarization resistance R values of the three relaxation processes. Cdl for RNi–YSZ–QNi–YSZ, and CLSM forGLSM and Cgas for GNi–YSZ.

density, which is considered physically significant. The τNi–YSZ values between 10 −6 and 10−5 s are also consistent with the assignment of the ‘charge transfer’ reaction in the frequency range 104 and 106 Hz where the stray impedance also co-exists. The effective double layer capacitance Cdl obtained as τNi–YSZ/RNi–YSZ, shown in Fig. 12 increased from ca. 1 μ F to 10 μF (or ca. 4 μF cm−2 to 30 μF cm−2) at high electrolysis currents (Fig. 12). More than 10-fold values have been previously reported for the double layer capacitance of Ni–YSZ electrodes under similar experimental condition [38–40]. The large double layer capacitance values have been attributed to the enlargement of the effective Ni/YSZ interface area in the porous electrode structure. Rather low estimates of double layer capacitance in the present work compared to the literature may be ascribed to the smaller Ni/YSZ interface area of the particular cermet electrodes or may be due to the difference in the deconvolution method. The aspect needs a further investigation. The capacitive effects are shown little affected by the humidity change between 30% and 50%. The ‘charge transfer’ resistance RNi–YSZ, shown in Fig. 9 is usually of a prime interest and quite often provided by dc measurements by applying anodic or cathodic bias using a reference electrode. In the dc measurements, however, the effect of additional polarization mechanisms, such as gas concentration impedance discussed below in Section 3.6.2, may not be completely excluded. The deconvoluted ‘charge transfer’ resistance RNi–YSZ in Fig. 9 is shown to first decrease and then increase with electrolysis currents. Here, the term ‘charge-transfer’ is maintained in quotation for the simple designation of the polarization component in reference to literature employing the terminology. The initial decrease may be considered activation polarization under the electrolysis bias. The increase of RNi–YSZ at high electrolysis currents become moderate when the humidity was increased to 50% (b) from 30% (a), indicating the effects of gas compositions. There seems not yet generally accepted kinetic mechanism of H2/H2O/Ni/YSZ electrodes [41]. Note that ‘charge-transfer’ reaction is a concept borrowed from the liquid electrochemistry where the electronic equilibrium of the solvated ions in the electrolyte with electrons in the metallic electrode is slow and often rate-determining. The activated polarization is represented by Butler– Volmer equation. Although the i–V characteristics of gas electrodes of SOCs often exhibits a Butler–Volmer type relation, the relation can be also described by chemical-reaction controlled kinetics, since the overpotential for the activation polarization indicates the gas activity. Unlike with the liquid electrolyte system the electronic equilibrium between solid electrolyte and (solid) electrode can be easily attained. Since the electrolysis current increases the hydrogen activity and decreases humidity, the behavior of RNi–YSZ is qualitatively consistent with the previously reported reaction mechanism of H2,H2O/Ni/YSZ electrodes [4,42], where the hydrogen activity or anodic polarization increases, while the steam activity or cathodic polarization decreases the charge-transfer polarization. Gas activity dependence can be explained by the adsorption/desorption and surface diffusion controlled electrode reaction [42,43]. Here, the term ‘charge-transfer’ is maintained in quotation for the simple designation of the polarization component in reference to literature employing the terminology. The mechanism was in fact suggested much earlier and well-established for O2, Pt [24,44,45], which can be similarly applied to O2, LSM electrodes discussed later in Section 3.6.3. As described in Section 3.5, the Gerischer impedance can be applied for the polarizations in gas electrode with a finite length L co-limited by surface diffusion and ad/desorption reaction [24]. The model can be applied to gas electrodes of metal/YSZ such as Pt/YSZ and Ni/YSZ as well as LSM/YSZ. The application to the polarization of LSM electrode is described in Section 3.6.3. For the Ni–YSZ cermet electrodes, the series resistors are modeled as the ionic paths of zirconia and the electronic path of nickel network [4,28]. When the YSZ constitutes the sufficiently conducting network through the cermet structure which ensures sufficiently short surface diffusion distance of oxygen from YSZ to Ni, the migration pathways

E.-C. Shin et al. / Solid State Ionics 232 (2013) 80–96

may be represented by the physical network of the ionic conductors, rather than the surface diffusion of oxygen on porous Ni surface. As in the treatment by Sonn et al. [4] rS is constituted by the ionic resistance of the percolating YSZ network since the electronic path of Ni network is sufficiently conductive. Under the assumption, a more definite interpretation may be made regarding the ‘charge transfer’ impedance of Ni– YSZ deconvoluted in this work. Since the ionic resistance rS is constant for the measurements at constant temperature 800 °C, RNi–YSZ, correpffiffiffiffiffi sponding RG in Eq. (4), to r P . Since τNi–YSZ ≈ωG−1 pffiffiffi pffiffiffi is thus proportional 2 corresponds to τG = 3 ¼ ðrP cP Þ 3, τNi–YSZ/RNi–YSZ is proportional to cP, which is represented in Fig. 13(a). The guide lines are produced by a weighted polynomial fitting procedure. Although qualitatively similar to Cdl = τNi–YSZ/RNi–YSZ in Fig. 12, the cP exhibits a clear tendency of saturation with increasing electrolysis. It is also notable that the humidify effects not appreciable in Cdl are indicated in cP. The faster saturation to a higher cP values is indicated for 50% humidity than for 30% humidity. Another parameter inferable is the utilization pffiffiffiffiffiffiffiffiffiffiffi length or penetration depth which can be defined as lδ = r P =rS for Gerischer diffusion model. The dependence of lδ on humidity and electrolysis currents can pffiffiffiffiffi be seen in RNi–YSZ ∝ r P with constant rS. RNi–YSZ presented in Fig. 9(a) and (b) for 30% and 50% humidity is thus shown in Fig. 13(b) for direct comparison. It is shown that the utilization length decreases slightly with electrolysis currents at the lower level but increases at higher electrolysis current, especially at the lower humidity condition of 30%. The magnitudes of cP and lδ exhibit an opposite humidity dependence at the electrolysis condition. Apparently humidity-independent of Cdl shown in Fig. 12 can be understood as the compensation by the two parameters in Cdl ≡ cPlδ. 3.6.2. Gas-concentration impedance of Ni–YSZ electrode The lowest frequency response indicated in the spectra of Figs. 3 and 4 is attributed to the Ni–YSZ electrode as well, which is modeled as a Gerischer impedance, GNi–YSZ in Fig. 7. As indicated by the time constant τG(Ni–YSZ) in Fig. 11, the response time is slower by four orders of magnitude than the charge transfer reaction discussed above. The intermediate

τNi-YSZR-2Ni-YSZ /Ω-2⋅cm-4⋅s

a

-3.5

-4.0

-4.5

30% H2O 50% H2O

-5.0

-5.5

0.0

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

Current density /A⋅cm-2

b R Ni-YSZ /Ω⋅cm2

0.6 0.5 0.4 0.3 0.2

0.0

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

Current density /A⋅cm-2 Fig. 13. The behavior of the finite-length Gerischer model parameters of Ni–YSZ electrode polarization assuming rS as the ionic conductor network: (a) cP proportional to 2 τNi- YSZ/RNi -YSZ and (b) lδ utilization length proportional to RNi–YSZ at humidity levels of 30% and 50%.

91

process in the spectra between RNi–YSZ–QNi–YSZ and GNi–YSZ originates from LSM electrode, discussed in the following section. As also indicated in Fig. 9 the polarization loss of GNi–YSZ is very small under OCV condition, comparable to the ohmic loss ROHM. The resistance, however, increases strongly with the electrolysis current. Note that almost linear plot in logarithmic scale in Fig. 9 represents an exponential increase of the polarization resistance with the electrolysis currents. The large contribution of this component is illustrated in the impedance spectrum of Fig. 3(d). The humidity increase from 30% to 50% is shown to moderate the polarization rise of GNi–YSZ for the similar electrolysis currents. Using the characteristic time constant τG(Ni–YSZ) and the polarization resistance values shown in Fig. 9, the effective capacitance C pgas ffiffiffi = τG(Ni–YSZ)/GNi-YSZ is estimated as shown in Fig. 12. (The factor 3 difference between the peak frequency and the time constant shown in Fig. 8 can be neglected for the present discussion.) The gas capacitance change with electrolysis currents may be considered negligible, especially when compared to the exponential increase of the polarization resistance, GNi–YSZ. There seems no significant dependence on the humidity, either. According to the previous work the Gerischer impedance, GNi–YSZ, can be attributed to the temperature-independent gas-phase diffusion and gas convection processes at Ni–YSZ electrode [4–6,46,47], which has been termed as ‘gas concentration’ impedance [47]. The modeling and simulation studies by Bessler [47] on the gas-phase transport in stagnation point flow geometry of typical laboratory button-cells explain consistently all the experimental features of the present work. The gas chamber at the Ni–YSZ anode side acts as a bulk chemical capacitor, causing an RC-type impedance spectrum and large apparent capacitances 0.1–1 F cm−2, which remains constant for the given cell geometry and depends only on the (total) flow rate, as indicated by Fig. 12. At high ac frequencies, the diffusional wave does not have time to penetrate into the whole gas chamber, causing the Warburg-type high-frequency behavior. As illustrated in Fig. 8(a), the ideal Gerischer model employed in this work is one of the simplest model to successfully describe the essential feature and distinguish systematically the overlapping individual components. The resistance increase with the electrolysis currents can be explained by the increasing H2 concentration and decreasing H2O concentration. The effects result from a change of the gas density due to electrochemical conversion of a heavy species, H2O to a light species, H2, a necessary consequence of mass flow density conservation, which should be distinguished from the gas concentration or activity effects on the ‘charge-transfer’ reaction discussed in the previous section. It should be emphasized that the separation of the two polarization contributions in the Ni–YSZ anodes, and those from the LSM polarization discussed in the following section, is essential to understand polarizations in solid oxide cells. It should be noted that not only in the planar stacks but also in many laboratory single cells a channel geometry of the gas flow system is used. The behavior of gas-concentration impedance appears somewhat different from that of stagnation point flow geometry of button cells as in the present work [47,48]. The present results clearly show that the gas concentration impedance is responsible for the polarization upturn at high electrolysis current in the typical i–V characteristics of Ni–YSZ/YSZ/LSM solid oxide electrolyzer cells as shown in Fig. 2. The gas concentration impedance itself increases exponentially. A considerable extension of linear regime as indicated in Fig. 2 is understood by the compensation by the oppositely varying polarization resistance of the LSM electrode discussed below. A new design of hydrogen/steam electrodes is recommended for the high performance high-temperature-electrolysis. Thick Ni–YSZ electrode design in the state-of-the-art SOFCs is detrimental for the electrolysis. 3.6.3. Diffusion–reaction impedance of LSM electrode Fig. 9 shows that the diffusion–reaction polarization at LSM electrode, GLSM, is the major polarization contribution together with the

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‘charge-transfer’ resistance at Ni–YSZ electrode RNi–YSZ at OCV and at low electrolysis currents for the present experimental condition. The polarization appears to increase slightly at small electrolysis currents. No indication of the activation polarization can be seen, while the ‘charge-transfer’ resistance of Ni–YSZ electrode, RNi–YSZ exhibited a decrease initially, as discussed above in Section 3.6.1. At higher electrolysis currents, while RNi–YSZ and GNi–YSZ exhibit a weak and much stronger increase, the resistance of LSM electrode dramatically decreases. It can be seen that the decrease in LSM polarization with electrolysis is as large as the increase in the gas concentration impedance of Ni–YSZ electrode, GNi–YSZ, discussed in the previous section. The two compensating effects thus explain the apparently linear i–V behavior over a wide electrolysis current range shown in Fig. 2, until LSM polarization becomes negligibly small at high electrolysis currents and the exponentially increasing gas concentration impedance of Ni–YSZ electrode dominates. LSM electrode reaction kinetics still remains uncertain and a challenging subject in SOFC applications, which was strongly emphasized in the review published in 2004 [24]. Unlike the mixed-conduction dominated features of the next-generation electrode materials such as LSCF and LSC, the surface catalytic reaction mechanism, similarly as for the metallic electrodes such as Pt [44,45], is known to dominate at low overpotentials or near OCV. The bulk reaction path becomes appreciable under strongly reducing, high overpotential, SOFC operation conduction. Although most of the mechanistic studies of the LSM electrode reaction have focused on the SOFC applications, investigations under anodic bias are relevant to the electrolysis operation. From the examination of the bias dependence using well-defined LSM microelectrodes [49,50] it has been shown that the surface reaction mechanism becomes more dominating under anodic bias, while the cathodic bias corresponding to SOFC operation condition tends to enlarge bulk paths. Surface reaction mechanism becomes more prominent in porous electrode structure. The bias effect can be understood as the oxygen activity enhancement by Nernst potential. It is well known a lower oxygen activity such as static air or nitrogen increased the LSM resistance. It is worth mentioning that a considerably large LSM polarization in a reducing atmosphere at a lower operation temperature abruptly decreased above the certain electrolysis current level. Details of the experiments are beyond the scope of the present work. Drastic decrease in the polarization at high electrolysis currents presented here can be thus attributed to the high oxygen activity induced by the electrolysis currents. High oxygen pressure established by electrolysis is considered responsible for the detrimental delamination of the oxygen electrode [21,51]. In the microcontact experiments with dense LSM microelectrodes oxygen bubble formation was observed at LSM/YSZ interface under high anodic bias [49]. Although electrode material with higher oxygen ionic conductivity such as LSCF and LSC has been suggested to be better candidates, high oxygen activity at the interface from the electrolysis may similarly decrease the ionic conductivity in LSCF and LSC. Moreover, these materials require a GDC intermediate protecting layer due to their reactivity with YSZ and the long-term stability needs to be further tested. On the other hand, LSM is a well-established electrode material for SOFC application. Since the catalytic activity of the LSM electrode is shown substantially increased by the electrolysis, LSM electrodes are suggested to be a promising electrode material for the high temperature electrolysis and the development may be made to further optimize the microstructure to minimize the delamination problem. As also suggested in the previous section, SOCs supported on oxygen electrodes or cathodes of SOFC may be beneficial for the electrolysis operation, in view of the enhanced activity of oxygen electrode and large gas concentration impedance of Ni–YSZ cermets. When the diffusion–reaction Gerischer model discussed in Section 3.5 is applied to LSM material without a significant bulk oxygen ion conductivity, D and k in Eq. (3) should represent the surface oxygen diffusion coefficient and the oxygen desorption reaction constant, respectively. Note that the units for D and k are cm2 s−1 and s−1, respectively for

the transport and reaction on the surface in Eq. (3). Fig. 14(a) schematically illustrates the electrode polarization mechanism in electrolysis co-limited by the surface diffusion and desorption. As represented by the distributed rp the surface reaction process occurs along the diffusion process. The parameters D, k, and lδ can be derived from the three parameters rS, rP, and cP of the Gerischer element. However, only two of them are independent in the Gerischer model. Similarly done for the charge-transfer and gas-concentration impedance of Ni–YSZ electrode, the effective capacitance of the relation τG(LSM) ≈GLSMCLSM can be obtained as indicated in Fig. 12. Note that τG =rPcP =k−1 according to the Gerischer expression in Eq. (2). Fig. 11 indicates a weak variation in τG(LSM) with electrolysis currents. Consequently, CLSM in Fig. 12 is shown to strongly increase at high electrolysis currents, essentially reflecting the variation of GLSM shown in Fig. 9. The decrease in resistance and the increase in capacitance is almost exponential above a ‘cut-off’ electrolysis current of 0.1–0.2 A cm − 2. The effective capacitance CLSM of the LSM polarization corresponds pffiffiffiffiffiffiffiffiffiffiffi to cP r P =r S ¼ cP lδ which can be compared to cPL of the total capacitance of a transmission line model of the electrode layer thickness of L. The utilization length lδ indicates a ‘compromise’ between surface reaction kinetics and surface diffusion [24]. The application of the ideal Gerischer model does not allow the unambiguous description of the polarization parameters, since there are only two independent parameters as a function of rS, rP, and cP.

pffiffiffiffiffiffi A relation RG ¼ RTW=4F 2 cads = kD may be derived similarly as for the prefactor of the Warburg impedance, where cads represents the equilibrium surface concentration and R, T, F, and W are gas constant, temperature, Faraday constant and the thermodynamic factor, respectively [27]. With the unknown W assumed to be 1, the relation results in too high diffusivity values of minimum 10–100 cm 2 s −1 for a theoretical maximum cads ≈ 10 15 cm −2 corresponding to the crystallographic density of oxygen in LSM crystal structure. In fact, there exist a big variation and uncertainty in the theoretical and experimental estimation of D and consequent lδ parameter as also addressed in the recent theses dedicated to the oxygen reduction mechanism on Pt and LSM electrodes [52,53], respectively. A recent theoretical study also reports on the detailed atomistic mechanism of oxygen incorporation in LSM electrode involving various oxygen adsorbate species and sites depending on temperature and oxygen partial pressure as well as the crystallographic planes [54].

3.6.4. Application of three-parameter Gerischer model A direct experimental determination of rS, rP, and cP can be made when the finite-length Gerischer model (FLG) with a fixed length parameter L is applied, rather than the ideal Gerischer model as discussed in Section 3.5. The spectral difference between Gerischer and finite-length Gerischer element is illustrated in Fig. 8(a). The necessity has been emphasized of employing the two-parameter ideal Gerischer model for the systematic deconvolution of the strongly overlapped polarizations as shown in Figs. 3 and 4. In the same vein, to avoid the risk of the over parametrization leading to the unsystematic and unstable fitting the fit parameters for the other responses of ROHM, RNi–YSZ, and GNi–YSZ, were fixed as evaluated using the original model in Eq. (7) presented in Table 1 and the ideal Gerischer model for GLSM was replaced by the three-parameter finite-length Gerischer model with an open-circuit terminus. The analysis can be performed using DX-11 or DX-12 Bisquert model in Zview. The procedure provided successfully independent parameters of rS, rP, and cP as presented in Table 2 and Fig. 15 when the electrode thickness is assumed to be 10 μm, which describe the spectra feature similarly well as shown in Figs. 3 and 4. It should be noted that the application of the Gerischer element with the closed-circuit terminus was not successful as rS and rP parameters become strongly correlated with the short-circuit terminal condition.

E.-C. Shin et al. / Solid State Ionics 232 (2013) 80–96

93

a rS

YSZ

desorption

rP

-Z''

cP

surface diffusion LSM Z'

b

YSZ

LSM+YSZ functional layer

c

LSM current collecting layer

bulk diffusion excorporation rS

YSZ

-Z''

cP

Z'

Fig. 14. (a) LSM electrode kinetics co-limited by surface diffusion and desorption, respectively, which is represented by the Gerischer impedance where the transmission line model and the spectrum are shown on the right. (b) Electrode reaction in LSM–YSZ composite functional layer with sub-microcrystalline grains with current collecting layer of pure LSM. (c) Oxygen transport through the dense membrane with thickness L co-limited by the chemical diffusion with diffusivity Dchem through the mixed conducting electrodes and surface ex-corporation reaction with the reaction constant ks. The electrochemical impedance model and spectrum were shown for a predominantly electronically conducting mixed conductor.

Fig. 15 presents the three fit parameters rS, rP and cP (a, b, c) and there from derived parameters of D, k and lδ (d, e, f). All the parameters except lδ are represented in the logarithmic scale in the range of the magnitude two. The guide lines are constructed by fitting the data with appropriate functions such as polynomial or exponential by taking the errors indicated into consideration. It is shown that rS and rP decrease and cP increases above the electrolysis current of ca. 0.2 A cm−2. Humidity effects are indicated in rS and cP. The decrease in rS is stronger at 30% humidity than 50%, while the increase in cP is stronger for 50% than for 30%. The physicochemical parameters D, k, and lδ can be directly evaluated as (rScP)−1, pffiffiffiffiffiffiffiffiffiffiffi (rPcP)−1, r P =r S , respectively, and thus present the corresponding variations with electrolysis and humidity. While all the derived parameters tend to increase at high electrolysis for 30% humidity, they become more or less constant for 50% humidity as the effects indicated in rS, rP

and cP compensate each other. Although the data for 50% humidity are rather scattered and the data at the high electrolysis current of 0.56 A cm−2 is associated with a large error, it has been clearly shown that increasing humidity tends to level off the electrolysis current dependence [55]. The dashed lines indicate the average values for all the data of 50% humidity which are also consistent with the values of 30% humidity at low electrolysis level. The diffusivity is estimated as ca. 2⋅ 10−4 cm2 s−1, k ca. 103 s−1, and lδ ca. 5 μm. Based on the new analysis the origin of the decrease in polarization loss of LSM electrode, RG(= GLSM), can be discussed in a more pffiffiffiffiffiffiffiffiffi concrete and definite manner. Since RG ð¼ GLSM Þ ¼ r S r P , both rS and rP contribute to the decrease in GLSM indicated in Fig. 9. It is shown that the contribution of rS is more significant than that of rP at low humidity. In terms of the physicochemical parameters, GLSM can be

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Table 2 Fit results for the finite-length Gerischer model for LSM polarization with the electrode layer thickness fixed at 10 μm. χ2

Variable

T

H2O

i

Unit

°C

%

A cm−2

800 800 800 800 800 800 800 800 800 800 800 800 800 800 800

30 30 30 30 30 30 30 50 50 50 50 50 50 50 50

0.003 0.03 0.09 0.16 0.33 0.56 0.56 0.03 0.03 0.033 0.09 0.09 0.16 0.33 0.56

Fig. 3(a) Fig. 3(b) Fig. 3(c) Fig. 3(d)

Fig. 4(a)

Fig. 4(b) Fig. 4(c) Fig. 4(d)

Sum-Sqr

5.33E−04 8.80E−05 6.58E−05 8.78E−05 1.96E−04 1.58E−04 1.36E−03 5.18E−04 1.60E−04 1.11E−03 1.16E−04 5.29E−04 4.33E−04 4.32E−04 2.68E−03

6.03E−02 1.05E−02 6.65E−03 9.04E−03 1.63E−02 1.91E−02 1.78E−01 6.27E−02 2.00E−02 1.34E−01 1.33E−02 5.66E−02 4.80E−02 5.31E−02 3.57E−01

pffiffiffiffiffiffi −1 represented as cP kD . The surface diffusion, surface reaction rates, and chemical or pseudo-capacitance of oxygen adsorption contribute to the decreasing polarization loss at high electrolysis currents. For 30% humidity, the contribution of the surface diffusivity is shown to be larger than that of the surface reaction constant and similar to that of the chemical capacitance. On the other hand, for 50% humidity the decrease in polarization at high electrolysis can be mostly attributed to the increase in the chemical capacitance. The effects on the electrolysis can be firstly ascribed to the increased oxygen activity in LSM electrodes due to the oxygen evolution by the electrolysis. Mizusaki et al. derived the oxygen activity dependence of the polarization loss based on the chemical-reaction controlled kinetics and successfully applied for the electrode polarization kinetics of porous Pt oxygen electrode on YSZ when the overpotential measured with respect to the reference electrode is considered to represent the Nernst potential [44,45]. A quantitative evaluation of the oxygen activity is, however, difficult, since the splitting of the overpotential applied to the each electrode is not a trivial problem. The humidity effects on the LSM electrode reaction clearly shown in Fig. 15 are not to be understood in a straightforward manner, either. The humid gas is supplied nominally in Ni–YSZ electrode only. Since

Err.

rP

Err.

cP

Err.

%

Ω cm

%

F cm−1

%

2649 2854 2953 2917 1120 134 166 2132 2911 2716 2893 2072 2384 1521 358

14.4 5.9 5.0 6.6 19.6 20.1 59.9 13.4 7.4 16.8 6.5 11.6 12.2 17.2 95.0

5.71E−04 5.58E−04 6.24E−04 5.99E−04 2.97E−04 1.33E−04 1.11E−04 5.36E−04 5.34E−04 6.29E−04 5.60E−04 6.85E−04 5.80E−04 3.73E−04 1.35E−04

11.5 4.9 4.1 5.4 14.2 5.9 23.6 10.1 6.3 13.0 5.4 7.4 9.2 13.0 56.0

1.794 1.930 1.923 2.179 2.664 4.517 3.586 1.426 2.069 1.792 2.119 1.304 1.479 3.948 9.506

15.5 6.3 5.4 7.1 21.5 15.7 56.5 14.6 7.8 18.2 6.9 12.7 13.2 18.7 103.1

b

-3.0

c

2.0

-3.5

Log (cp /F / ⋅cm-1)

there is little humidity effect on the LSM polarization near OCV, the leakage may not be responsible. Such indifference of the polarization to the humidity in the hydrogen electrode was the criterion for the polarization to be assigned to the oxygen electrode in the recent reports [5,6], on which the present work is also based on. The humidity effects become significant at high electrolysis currents. It is notable the larger cP and the smaller lδ of LSM electrode for the higher humidity condition shown in Fig. 15(c) and (f) are qualitatively similar to the direct humidity effects on the Ni–YSZ electrode reaction as shown in Fig. 13. Since the humidity affects the overall overpotential and therefore the corresponding variation in the overpotential and the gas activity may be responsible for the variation in the LSM polarization. On the other hand, it seems difficult to imagine the difference in the effective oxygen activity when the same flux of oxygen is supplied by the electrolysis currents regardless of the humidity or overpotential. The observations suggest that the electrode polarizations of the solid oxide cells under operation may not be properly represented in the half-cell electrode polarization investigated using the symmetric cell configurations or reference electrodes, or polarizations at OCV condition as usually assumed. The deconvolution and exhaustive analysis of the electrode polarizations of the full-cell under

Log (rp /Ω⋅cm)

a

rS Ω cm−1

1.5

3.0 2.5 30% H2O

2.0

-0.4

-2.5

-5.0

-0.6

Current density /A⋅cm-2

d

30% H2O

30% H2O

4.0

50% H2O -3.0 -3.5

0.0

-0.2

-0.4

30% H2O 50% H2O

-0.2

0.5

-0.4

-0.6

Current density /A⋅cm-2

f

3.5 3.0

0.0

-0.2

-0.4

-0.6

Current density /A⋅cm-2 16 12

30% H2O 50% H2O

8 4

2.5

-4.0 0.0

50% H2O

1.0

0.0

-0.6

Current density /A⋅cm-2

e Log(k/s-1)

Log(D /cm2⋅s -1)

-0.2

-4.5

30% H2O

50% H2O

50% H2O 0.0

-4.0

lδ /μm

Log (rs /Ω⋅cm-1)

3.5

0 0.0

-0.2

-0.4

-0.6

Current density /A⋅cm-2

0.0

-0.2

-0.4

-0.6

Current density /A⋅cm-2

Fig. 15. The fit parameters of the polarization of LSM electrode using a finite-length Gerischer element for GLSM with L = 10 μm: rS (a), rP (b) and cP (c) and the derived parameters of D (d), k (e), and lδ (f). The humidity levels represent the atmosphere in the Ni–YSZ electrode.

E.-C. Shin et al. / Solid State Ionics 232 (2013) 80–96

operation as this work have not been precedented so far. Further investigations are therefore necessary to clarify the possible correlation between electrode polarizations of the solid oxide cells in operando. While the model for the gas electrode polarization illustrated in Fig. 14(a) assumes the three-phase boundary reaction, the utilization length lδ of ca. 5 μm estimated above (Fig. 15(f)) is much larger than the LSM grain size. The real active electrode next to the electrolyte membrane is constituted of LSM and YSZ composites as shown in the micrograph in Fig. 1, which is schematically represented in Fig. 14(b). The electrode reaction co-limited by diffusion–reaction mechanism should be extended over the assemblage. The composite layer can reduce the electrode polarization by better adhesion of LSM and electrolyte layers and by increasing the triple phase boundaries due to the percolating network of zirconia. The latter aspect is well-known for the Ni–YSZ cermet electrodes. In Section 3.6.1 Gerischer model was applied to Ni–YSZ electrode reaction where rS element represents the ionic path by the zirconia network. Similar effects should exist in the electrode reaction of the LSM–YSZ composites, extending the effective reaction zone or utilization length. The variation of rS with of the electrolysis currents and humidity in correlation with rP and cP parameter, as indicated in Fig. 15, suggests that the diffusion–reaction co-limited electrode polarization model is applicable and the parameters can represent the effective values for the LSM and YSZ composite structure. Generally, the connectivity of YSZ network in LSM–YSZ composite electrode is expected to be to a less degree than in Ni–YSZ electrode. The analysis provides the estimation of the utilization length of ca. 5 μm at low electrolysis currents for low humidity or regardless of the electrolysis at high humidity, which is less than the thickness of the functional layer. Kenney et al. [52] showed that the decrease in the polarization with the increase of the composite functional layer thickness saturates at the function layer thickness of e.g. 5–6 μm, even with further increase in the composite functional layer thickness. The utilization length appears to increase with electrolysis thickness close to the assumed electrode thickness of 10 μm at high electrolysis current at lower humidity. The co-limited diffusion and reaction mechanism in the porous gas electrodes should be distinguished from the co-limited transport in dense membrane as illustrated in Fig. 14(c). The surface reaction only occurs at the surface, x = L, and the surface reaction rate in Eq. (3) is dependent on the surface concentration only. The serial process of the bulk diffusion and the surface reaction is represented by the rc transmission line model with rS and cP (without rP), i.e. finite length (short-circuited) Warburg impedance (FLW) and a RC parallel circuit where Rsurf ∝ks−1. For the predominantly electronic conductor with negligible electronic resistance, the rS and cP of the transmission line −1 model represent the ionic conductivity σion ∝ Rion and the chemical capacitance Cchem, from which Dchem = L2/RionCchem can be estimated [31–33,56–59]. The configuration shown in Fig. 14(c) has been applied for the oxide ionic conductivity and chemical diffusivity of LSM [50]. It is noteworthy that the configuration was successfully applied to extract the mixed conduction even in the ‘porous’ lanthanum titanate hydrogen/steam electrodes [32]. The titanates are so poorly catalytic and thus the gas phase reaction is negligible and the surface reaction essentially occurs at the platinum electrodes. 6. Conclusion Comprehensive modeling of the impedance spectra of high temperature solid oxide cells including the instrumental artifact successfully deconvoluted multiple polarization contributions, which systematically varied with the electrolysis currents. It has been shown the stray impedance due to the lead wire exhibits the high frequency inductive loop which can be modeled as an inductor–resistor parallel circuit. The accurate and reproducible assessment of the lead wire inductance effects turned out non-trivial. The stray parallel resistance was found to be proportional to the lead wire inductance whatsoever measured. Four major loss contributions of Ni–YSZ/YSZ/LSM SOC were distinguished which

95

are in the order of the lowering frequencies ohmic losses, ‘charge-transfer’ impedance of the Ni–YSZ electrode, diffusion–reaction co-limited impedance of LSM electrode, and gas concentration impedance of Ni–YSZ electrode. The latter two impedance were firstly modeled using the ideal Gerischer function with two fit parameters, which allows the systematic deconvolution of the polarization components as well as satisfactorily describe the spectra. The strong polarization rise at high electrolysis currents can be mainly attributed to the gas-concentration impedance of Ni–YSZ electrode due to the gas flow density decrease due to the hydrogen production. The ‘charge transfer’ polarization of Ni–YSZ electrode also increases upon hydrogen production and steam consumption by electrolysis which is attributable to the diffusion–reaction co-limited electrode process. Assuming a constant series resistor contribution from the YSZ network in the Gerischer model, the behavior of chemical or adsorption capacitance, cP, and the utilization length, lδ, can be deduced. The cP increases with electrolysis to a saturation level while lδ appears to increase further with electrolysis. The polarization of the LSM electrode was found to decrease strongly with electrolysis currents, which thus compensates the increase in the gas concentration impedance of Ni–YSZ electrode, resulting in an apparent ohmic behavior up to a considerable electrolysis level. LSM polarization was further analyzed using a finite-length Gerischer element with three independent parameters of rS, rP, and cP, which allows a more definite statement on the effects of electrolysis currents and humidity of Ni–YSZ electrode on the surface diffusivity D, ad/desorption coefficient k and the utilization length lδ in relation to the electrode polarization. The pffiffiffiffiffiffi −1 pffiffiffiffiffiffiffiffiffi , decrease in the LSM polarization, represented as r S r P or cP kD can be ascribed to the increase in cP, D and k. The decrease in the polarization is contributed by the increase in D and cP and to a less degree in k for the lower humidity of 30%. For the higher humidity of 50%, the decrease can be mainly attributed to the increase in cP. The diffusivity is estimated as ca. 2⋅10−4 cm2 s−1, k ca. 103 s−1 and lδ ca. 5 μm, which represents the effective values of the LSM–YSZ composite function layer of thickness of about 10 m. The polarization mechanism for the high temperature electrolysis is apparently quite distinct from that of the fuel cell mode, but the gas activity dependence appears generally applicable to the variation in gas concentration impedance and gas-electrode reaction co-limited by chemical-reaction and surface diffusion-controlled mechanism. A new SOC design may be developed for the high performance electrolysis operation, which reduces the gas-concentration impedance of Ni–YSZ electrodes and makes the best of the enhanced activity of LSM electrodes. The evaluation of the Ni–YSZ/YSZ/LSM solid oxide cells in the reversible SOFC/SOEC modes [55] and as a function of temperature and the porosity of Ni–YSZ electrode [60] are under progress and will be reported in forthcoming publications. Acknowledgment This research (paper) was performed for the Hydrogen Energy R&D Center, one of the 21st Century Frontier R&D Program, funded by the Ministry of Science and Technology of Korea. This work was also partly supported by the World Class University (WCU) program (R32-2009-000-20074-0) through the National Research Foundation of Korea. J.-S. Lee thanks Derek Johnson at Scribner Associates for implementing the generalized transmission line model (DX-19) in the software package ZView and for valuable discussions in application of the fitting models. References [1] A. Hauch, S.H. Jensen, S. Ramousse, M. Mogensen, J. Electrochem. Soc. 153 (2006) A1741. [2] M. Laguna-Bercero, R. Campana, A. Larrea, J. Kilner, V. Orera, J. Electrochem. Soc. 157 (2010) B852.

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