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Impedance of an Oxygen Reducing Gas-Diffusion Electrode VT Cd

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Impedance of an Oxygen Reducing Gas-Diffusion Electrode VT Cd 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].
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