Impedance of an Oxygen Reducing Gas-Diffusion Electrode

Dietrich Wabner*, Rudolf Holze, Peter Schmittinger Arbeitsgruppe Angewandte Elektrochemie im Institut für Anorganische Chemie der Technischen Universität München und Institut für Physikalische Chemie der Universität Bonn Dedicated to Professor Dr. Wolf Vielstich on the occasion of his 60th birthday Z. Naturforsch. 39b, 157—162 (1984); eingegangen am 24. August 1983 Nernst-Impedance, Fuel Cell Electrode, Oxygen Reduction, Gas Diffusion Electrode, Teflon Bonded Electrode The impedance of teflon bonded electrodes was measured in the frequency domain. These electrodes based on activated carbon as electrocatalyst were developed for fuel cell applications. When feeding the electrode with air or oxygen the impedance spectra could be explained by two Nernst diffusion processes and a small charge transfer process. Two methods for separating the measured impedance into partial impedances related to differ­ ent steps of the electrode reaction are presented. A least square fit procedure is described which has been applied successfully to the impedance analysis of porous electrodes.

List of symbols 1. Introduction Symbol Dimension The measurement of the electrode impedance is a A diffusion factor VT c concentration of diffusing species at mol/dm3 useful method to investigate the kinetics of electrode electrode surface processes. With this method it is possible in many cD double layer capacity mF/cm2 cases to identify the processes, e.g. diffusion, ad­ d diffusion layer thickness ^m D diffusion coefficient cm2/s sorption or heterogeneous reaction of products and f frequency Hz reactands, which cause the total electrode overpo­ F Faraday constant As/mol tential. The overpotential of the working electrode current density i mA/cm2 can be separated into parts associated with these pro­ Im(Z) imaginary part of the complex Q or Q • cm impedance Z cesses. The Faradaic impedance mostly consists of a j imaginary quantity V~1 - series connection of several part-impedances e.g.: R resistance Q or Q ■cm T> ^ o .im p sum of the resistive parts of the Q or Q • cm' Zf = ZD -I- Zdl + Zd2 -I- Zx (1) Faradaic impedance with R o ,i/s slope of the potential vs. current Q or Q ■cm' density curve at the point of the im­ Zf = Total Faradaic impedance pedance measurement ZD = Charge transfer impedance R -do diffusion resistance Q or Q ■cm' Zdi, Z d2 = Diffusion impedance R d charge transfer resistance (equiva­ Q or Q ■cm lent to Rct) Zx = Residual impedance, e.g. caused by cristalliza- Re(Z) real part of the complex impedance Q ox Q ■ cm tion, adsorption or heterogeneous reaction. 2 In this paper impedances will be treated consisting Rei electrolyte resistance Q only of two diffusion impedances and a charge trans­ zd diffusion impedance Q or Q ■cm ZD charge transfer impedance f i o r f l ■ cm' fer impedance (equivalent to Zct) z, residual impedance ß o r ß - cm' Zf = Zdl + ZD -I- Zd2 (2) Y electrochemical equivalent mol/As which were derived from measured electrode impe­ CO angular frequency (a> = 2 jtF) Hz dances by a correction process. We have measured the impedance of a porous tef­ lon-bonded gas-diffusion electrode using activated * Sonderdruckanforderungen an Privatdozent Dr. Diet- carbon as electrocatalyst. These electrodes are used rich Wabner, Arbeitsgruppe Angewandte Elek­ as oxygen reducing cathodes in fuel cells, metal-air trochemie im Institut für Anorganische Chemie der batteries etc. Technischen Universität München, Lichtenbergstraße 4, D-8046 Garching. The aim of our work was to separate the overpo­ 0340-5087/84/0200-0157/$ 01.00/0 tential of the working electrode into amounts attri- 158 D. W abner et al. • Impedance of an Oxygen Reducing Gas-Diffusion Electrode

buted to the electrode processes, and to get more necessary. Mathematical equation and frequency de­ information for further improvement of these elec­ pendence of a single diffusion impedance based on trodes. the assumption of a finite diffusion layer thickness d (called “Nernst impedance”, in contrast the impe­ 2. Experimental dance based on the assumption of an infinite diffu­ Electrodes were prepared from a teflon dispersion sion layer thickness is called “Warburg impedance”) (HOECHST) and activated carbon NORIT-BRX ac­ are well known in the literature [4—10]. cording to the procedure described in [1]. A silver A comprehensive equation of the Nernst impe­ wire net was pressed on one side of the electrode as dance is given by current collector. On the other side a porous teflon- foil was pressed to prevent electrolyte leakage even Z d = R do • f(jc) (3) without feed-gas overpressure. Recording potential containing the diffusion function vs. current density curves and impedance measure­ ments were done using the same plexiglas cell, fitted (sinh(;t) + sin(;t)) —j(sinh(x) —sin(x)) f(x) =- (3 a) with a screw-cap for simple replacement of the work­ x (cosh(;t) + cos(x)) ing electrode and a large-surface counter electrode 2 • d r _ (platinized platinum). The potential of the working with x = — 7 - - V o j or x = 2 ■ d ,resp. (4) electrode was measured versus a standard saturated V ^ D 2 D calomel electrode (SCE), mounted in a separate Function values of the diffusion function f(x) are compartment outside the cell (to prevent artefacts tabulated in [11]. The term due to stray capacities). To connect the cell electro­ lyte and the electrolyte in the reference electrode 2 • d A = - (5) compartment a small hole was drilled in the cell wall v T ^ d ending near the working electrode surface. The elec­ is called diffusion factor [11], In contrast to I.e. [12], trolyte was 6 M KOH solution prepared from KOH G. R. and MILLIPORE-water. The electrode was where a relaxation time r correlated to D and d was fed with unscrubbed air or pure oxygen at normal defined without having a physical meaning, we will use atmospheric pressure. the diffusion factor A as a characteristic quantity. The The cell was connected to a potentiostat (WENK- correlation between the diffusion layer thickness d and ING PCA 72 M) in the usual three electrode ar­ the current density i according to log d = f(log i) is rangement. A transfer-function-analyser 1172 (SO- derived in [13]. LARTRON-SCHLUMBERGER) was wired to the The diffusion resistance Rdo is given by potentiostat. All impedances and potential vs. cur­ R • T • d • y R • T rent density curves were measured potentiostatically. Rdo" -- r- _ reSP ‘ Rdod - (6) The impedances experimentally found were used n • F • c • D n* ■ F‘ • c • D to calculate the electrolyte resistance Rel and the Rdo is equivalent to the real part of the diffusion double layer capacity by an extrapolation method impedance at the low frequency limit [2], According to the procedure described in chap­ ter 3, Rel and CD were separated from the measured Rdo — lim R e(Zd) ( 6 a) impedance. The parameters of the charge transfer f->0 reaction and the other electrode processes were op­ The impedance plot in the complex plane at high timized assuming an adequate equivalent circuit and frequencies shows the typical behaviour of a Warburg a computer routine including the Marquardt-Leven- impedance. Starting with an angle of 45° with respect to berg algorithm. All calculations were done with an the real part axis the curve deviates from the Warburg IBM 168/360 computer. For details of the programs behaviour at lower frequencies and shows a maximum see [2, 3]. of the imaginary part at f(jc) = 2.25 (mostly at moderate 3. Theory of the Diffusion Impedance low frequencies), (see Fig. 1). Beyond the maximum the curve returns to the real part axis again, reaching 3.1. A single diffusion process the axis at the frequency zero with the intercept Rdo Before describing the analysis of complicated im­ (see Fig. 1). Analysis of the diffusion function and the pedances containing two or more diffusion impe­ impedances obtained by varying the independent dances in detail some summarizing remarks concern­ parameters D. d etc. reveals [14], that only the diffu­ ing the impedance of a single diffusion process are sion factor A (eq. (4) and (5)) affects the frequency D . W abner et al. - Impedance of an Oxygen Reducing Gas-Diffusion Electrode 159

Fig. 1. Calculated complex plane loci of two diffusion impedances with finite diffusion layer thickness: A l = 0.3 Vs~> Rdol — 0.2 Ohm, Rdo2 — 0.5 Ohm, variation of A2: (O) A2.1 = 0.03 Vs~> (x) A2.2 = 0.08 y/T, (•) A2.3 = 0.5 \/s~. behaviour of the diffusion impedance significantly. 3.2. Two diffusion processes According to eq. (4) the diffusion factor is correlated In most cases two or more diffusing species are with the frequency at the maximum of Im(Zd) by involved in the electrochemical reaction. Therefore a fmax-0.806/A2 or fmax = 0.403-D/d2, resp. (7) Faradaic impedance containing more than one diffu­ The diffusion layer thickness d and the diffusion sion impedance will be measured. Since Zdi = f(l/Cj), factor A, respectively, depend on the DC current two diffusion processes can be separated in an impe­ density applied to the electrode. With a known diffu­ dance spectrum only, if all values C; are in the same sion coefficient D the diffusion layer thickness d can be order of magnitude. Otherwise one diffusion process calculated from fmax or vice versa. may be neglected. The analytical application and the features of the Numerous impedances calculated by adding two single diffusion impedance concept (including the cal­ Nernst impedances have been presented in [11, 14]. A culation of the surface concentration of the diffusing favourable characterization of both diffusion proces­ species and a principal comparison of the Warburg and ses was achieved by assuming different values of Rdo Nernst impedance) are described elsewhere [14, 15]. (see Fig. 1 and Fig. 2, R dol = 0.2 Ohm, R do2 = 0.5

Fig. 2. Calculated complex plane loci of two diffusion impedances with finite diffusion layer thickness A l = 0.3 Vs”, Rdol = 0.2 Ohm, Rdo2 = 0.5 Ohm, variation of A2: (x) A2.4 - 0.8 y/s , (O) A2.5 = 2.5 Vs , (•) A2.6 = 5.0 Vs~- 160 D. W abner et al. ■ Impedance of an Oxygen Reducing Gas-Diffusion Electrode

Ohm). The influence of different values of the diffu­ 4. Analysis of Measured Impedances sion factor A is demonstrated by varying A 1 keeping To check if the total Faradaic impedance R 0 includ­ A 2 fixed and vice versa. This method is hypothetical, ing all part impedances has been measured, the sum of since in reality a change of A means a change of d, and all polarization resistances (i.e. the sum of the real this is connected with a change of i and c. Both i and c parts at the frequency zero) have to be compared with affect Rdo. In Figs. 1 and 2 characteristic complex the slope of the potential vs. current density curve at plane plots are presented. The complex impedance at the point of the impedance measurement. If R 0.imP < each frequency was obtained by adding real parts and R 0 i ^ one or more part impedances have been omitted. imaginary parts of both diffusion impedances. In the This demonstrates the importance of impedance complex plane plot the curves start always with a slope analysis at low frequencies, since only sufficiently low of 45°. Two limiting cases are observed: The sum of two frequency values give a reliable extrapolation of R o imp impedances looks like one impedance or the curve in the complex plane plot. exhibits two maxima (each at a value of f(*) = 2.25 for Usingacomputerroutinedescribedin [2] Rcl andCD both diffusion processes). Curve shape and frequency are subtracted from the measured electrode impe­ dependence are only affected by the diffusion factors. dance. The resulting Faradaic impedance contains the Since the separation of the diffusion impedances de­ charge transfer resistance according to pends on the ratio of the diffusion factors, three gener­ RD = limRe(Zf) (9) al cases of the ratio Abig/Asmau will be discussed: From the Randles plot of the Faradaic impedance (plotted after subtraction of RD at each frequency) Ab/As < 1.5 the value of fmax of the lower frequency maximum is The impedance spectrum looks like the spectrum of ascertained. Taking the value of A calculated from a single diffusion impedance (Fig. 1 ,0 —O). With only fmax and Rdo obtained from Remax(Z) or Immax(Z) ac­ one impedance spectrum measured no distinction be­ cording to eq. (7) —( 8 ) a Nernst impedance is com­ tween a single diffusion impedance or the sum of two puted and subtracted from Zf at each frequency. The residual impedance should show the behaviour of diffusion impedances is possible. If Rdoi =£ R do2 the Z x value Immax (Z) obtained with eq. ( 8 ) is smaller, com­ a single diffusion impedance. This procedure can be pared with the single diffusion impedance; e.g. in carried out by a computer program. Another ap­ Fig. 1, 0 —0 proach is done by optimizing the parameters RD, A l, Rdoi, A 2 and R do2 describing the assumed Im max (Z di + zd2) = 0.391 (Rdoi + Rdo2) (8) Faradaic impedance until the calculated impedance fits well to the Faradaic impedance obtained from 1.5 < A^As < 5 the measured impedance. For details see [2, 3], The impedance spectrum shows one turning point, e.g. in Fig. 1, x—x and Fig. 2, x—x. 5. Results and Discussion In Fig. 3 the potential vs. current density curves of the electrode fed with air and oxygen are plotted. Ab/As > 5 Impedances were measured at current densities be­ The impedance spectrum shows three extrema, e. g. tween 5 and 50 mA cm2. Two examples of Faradaic Fig. 1, # - # , Fig. 2, 0 - 0 , • - # . impedances obtained from the measured impedances If two diffusion impedances can be separated the by subtraction of Rcl and CD are shown in Fig. 4 (x) diffusion characterized with a smaller value of A ap­ and Fig. 5 (x), (during further interpretation of the pears at higher frequencies. If the ratio Ab/As is big measured impedances the results of de Levie [20] enough even in the case of extreme Rdol/R do2 ratios and Drossbach [21] concerning porous electrodes both processes appear clearly separated in the spec­ and their behaviour in impedance measurements trum. have been taken into account). As can be seen from Examples of impedance spectra containing two Table I the values of R0.imp and R0.1(? are in good Nernst impedances were published [12, 15—18], but agreement, indicating that all processes contributing no kinetic data were given, except some estimated to the electrode overpotential are included in the diffusion coefficients. impedance experimentally found. D. W abner et al. • Impedance of an Oxygen Reducing Gas-Diffusion Electrode 161

dance is caused by the diffusion of the reaction pro­ ducts from the electrode into the bulk electrolyte. Taking into account the results of investigations on oxygen electrochemistry at various carbon electrodes this product was identified as H 0 2_ [22]. The surface concentration of H 02” at the reaction sites can be calculated from the diffusion resistance Rdo) accord­ ing to eq. ( 6 ), the results are:

A 1 Rdo 1 C 0.261 Vs”0.285 Q ■ cm2 3.4 10_8 m ol-dm - 3 (Fig. 4) 0.158 Vs~0.108 Q- cm2 1.4 10_7 m ol-dm ~ 3 (Fig. 5)

Table I. Results of the analysis of the impedances present­ ed in Fig. 4 and Fig. 5 (values in parantheses give the rela­ Fig. 3. Potential vs. current density curves for oxygen re­ tive part of each part impedance). duction at an activated carbon electrode, 6 M KOH elec­ trolyte, air and pure oxygen athmospheric pressure, iR- 4) (Fig. 5) corrected. (Fig- 2 C d 9.73 9.5 mF/cm f Amaxl 8.2 37.7 Hz The correlation of the diffusion processes with the A l 0.261 0.158 VT two diffusion impedances contained in the Faradaic R d o l 0.285 (23.5%) 0.108 (23.3%) Ohm •cm2 fmax2 0.13 0.071 Hz impedance is obvious, because one impedance A2 2.69 2.923 (characterized by A 2 and Rd 02) is clearly depending R d o 2 0.875 (72.2%) 0.302 (65.2%) Ohm •cm2 on the oxygen partial pressure in the feedgas. There­ Rd 0.052 (4.3%) 0.053 (11.5%) Ohm • cm2 D fore this impedance is attributed to the oxygen diffu­ o.imp 1.212 (100%) 0.463 (100%) Ohm • cm2 1.12 0.49 Ohm •cm2 sion to the reaction sites. The residual smaller impe­

Fig. 4. Impedance of an oxygen reduc­ ing activated carbon electrode (com­ plex plane plot), obtained after sub­ traction of Rel and CD, current density i = 50 mA • cm-2, air-fed, 6 M KOH electrolyte, x = measured, — fitted.

Fig. 5. Same as Fig. 2, but elec­ trode fed with pure oxygen, cur­ rent density 50 mA • cm~2, x = measured, — - fitted. 162 D. W abner et al. ■ Impedance of an Oxygen Reducing Gas-Diffusion Electrode

Due to the relative low current density of tion demonstrates the high importance of transport 50 mA • cm “ 2 the peroxide concentration is low, but processes in porous gas diffusion electrodes. Further still it causes severe damage to the electrode and discussion of these results and practical implications limits the electrode performance as well as the are published elsewhere [ 2 2 ]. lifetime [3]. Therefore the practical importance of carbon electrodes containing no catalyst decompos­ ing the peroxide is rather small. The relative mag­ Financial support of the Deutsche Forschungs­ nitude of the diffusion resistance, which is equal to gemeinschaft, Fonds der Chemischen Industrie and an adequate diffusion overpotential, compared with Studienstiftung des Deutschen Volkes is gratefully the charge transfer resistance of the oxygen reduc­ acknowledged.

[1] W. Vielstich, Fuel Cells, London, Wiley-Interscience, [12] A. H. Zimmermann, M. R. Martinelli, M. C. Janecki, New York, 1970. p. 42. and C. C. Badcock, J. Electrochem. Soc. 129, 289 [2] R. Holze. Thesis, Bonn 1983. (1982). [3] R. Holze and W. Vielstich, paper to be presented at [13] N. Ibl, Y. Barruda, and G. Trümpler, Helv. 37, 1624 the Fall Meeting of the Electrochemical Society, (1954). Washington. Oct. 1983. [14] D. W. Wabner. Habilitationsschrift, München 1978. [4] T. R. Rosebrugh and W. Lash Miller, J. Phys. Chem. [15] D. W. Wabner and P. Bertsch. Z. Naturforsch. 38b, in 14, 81 (1910). press. [5] J. Llopis and F. Colon, Eighth Meeting of the CITCE, [16] J. Thonstad, Electrochim. Acta 15, 1581 (1970). 1956, Butterworth, London 1958, p. 414. [17] H. Hoff, Thesis, München 1965. [6] J. H. Sluyters. Thesis, Utrecht 1959. [18] P. Bertsch. Thesis, München 1969. [7] J. H. Sluyters, Rec. Trav. Chim. Pays-Bas 82, 100 [19] P. Schmittinger and D. W. Wabner. Metalloberfläche (1963). — Angew. Elektrochemie 26, 262 (1972). [8] P. Drossbach and J. Schulz, Electrochim. Acta 9, 1391 [20] R. de Levie, Electrochim. Acta. 8 , 751 (1963); 9, 1231 (1964). (1964). [9] A. B. Izermans, Thesis, Utrecht 1965. [21] P. Drossbach. ibid. 13, 2089 (1968). [10] D. Schumann. C. R. Acad. Sei. Paris 262C, 624 [22] R. Holze and W. Vielstich, submitted to J. Elec­ (1966). trochem. Soc. [11] D. W. Wabner. Thesis. München 1971.