Conductivity dependence of the polarization impedance spectra of platinum black electrodes in contact with aqueous NaCl electrolyte solutions

Transcription

1 Colloids and Surfaces A: Physicochem. Eng. Aspects (003) 93/99 Conductivity dependence of the polarization impedance spectra of platinum black electrodes in contact with aqueous NaCl electrolyte solutions Mónica Tirado a, Constantino Grosse a,b, * a Departamento de Física, Universidad Nacional de Tucumán, Av. Independencia 1800, (4000) San Miguel de Tucumán, Argentina b Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, Argentina Abstract The polarization resistance and capacitance of platinum black electrodes in contact with aqueous NaCl solutions was investigated. A series of measurements were made at 59/0.1 8C in the 10 Hz to 10 MHz range using a HP 419A Impedance Analyzer. The measurement cell has flat parallel platinum electrodes 15 mm in diameter, with a continuously variable spacing from 0.5 to 9 mm. They were platinized prior to each measurement. The electrolyte solution conductivities were in the 0.004/0.6 S m 1 range. The data were analyzed using an equivalent circuit consisting in a constant phase element in series with a parallel connection of a resistance and another constant phase element. The characteristic parameters of the model are presented as a function of the electrolyte solution conductivity. # 003 Elsevier B.V. All rights reserved. Keywords: Platinum black electrodes; Electrode polarization; Constant phase element; Variable spacing technique; Dielectric spectroscopy 1. Introduction Dielectric measurements of conductive liquids always deal with the problem that the cell impedance depends on both the impedance of the sample and the polarization impedance of the electrodes. These contributions can be separated, in principle, using a cell with variable spacing [1]. Nevertheless, this method only leads to satisfactory results when the sample impedance is greater than, or at least comparable to, the impedance of * Corresponding author. Tel.: / x18. address: cgrosse@herrera.unt.edu.ar (C. Grosse). the electrodes []. This condition renders polished stainless steel or platinum electrodes unsuitable in many cases, due to their excessively high impedance. The best technique to reduce it, by up to two or three orders of magnitude, is to electro deposit a platinum black layer on platinum electrodes. In this work we measured the electric properties of platinum black electrodes, in order to determine the dependence of the polarization impedance with the conductivity of the electrolyte solution and with the frequency of the applied field. We show that the Fricke model can not represent the observed behavior and propose an alternative /03/$ - see front matter # 003 Elsevier B.V. All rights reserved. doi: /s (03)0045-0

2 94 M. Tirado, C. Grosse / Colloids and Surfaces A: Physicochem. Eng. Aspects (003) 93/99 model that reproduces the experimental data in the whole measured frequency range.. Materials and methods The electrodes were blackened following the method proposed by Schwan [1] using a 0.05 N HCl platinizing solution with 0.3% PtCl 4 and 0.05% PbAc ; current density of 30 ma cm during 40 min and 4 h setup time in distilled water with short circuited electrodes. The measurements were made using a Hewlett Packard 419A Impedance Analyzer. The measurement cell has flat 15 mm diameter electrodes with variable spacing ranging between 0.5 and 9 mm [3]. Itis connected to the instrument using coaxial cables in the five-terminal pair configuration [ /4]. The electrode impedance is traditionally determined using a cell with variable spacing from the ordinate of the impedance versus spacing plot [1]. The standard procedure involves a short and an open circuit calibration prior to each measurement, which leads to the following expression for the polarization impedance Z p : [Z c (d) Z Sh ](1 Z Sh Y Op ) Z p kd (1) 1 Z c (d)y Op where the asterisk denotes complex functions of the frequency, Z c (d) is the measured cell impedance, Z Sh the short circuit calibration impedance, and Y Op the open circuit calibration admittance. The coefficient k* is: k 1 ivo=s 1 1 (ivo=s) ss where s and o are the electrolyte solution conductivity and absolute permittivity, while S is the electrode area. Using linear regression at each frequency, (Eq. (1)) leads to the values of Z p and k*. However, the reliability of the measurements strongly improves if an additional standard load calibration is performed. Because of this, we used a more elaborate procedure in which the measurement cell filled with the electrolyte solution with known dielectric properties was used as this standard [5,6]. This leads to the expression: Z c (d) Z Sh 1 Z c (d)y Op Z p Q k Q d where Q* is an unknown function related to the quadrupolar representation of the instrument. Using linear regression at each frequency and the calculated value for k* leads to the values of Q* and Z p. All measurements were performed at 59/0.1 8C in the 10 Hz to 10 MHz frequency range, using the same pair of electrodes that were platinized prior to each measurement. The conductivities of the NaCl solutions used, measured at 1 khz with an Orion 160 Conductivity Meter with a four electrode cell, are given in the Table 1. Their permittivities were calculated using the equations given in [7]. The results obtained, normalized for a cell with two identical electrodes 1 m each, are represented in Figs. 1 and. 3. Discussion According to the Fricke s phenomenological model [8], the electrode polarization impedance is proportional to the angular frequency v raised to a frequency independent exponent: Z p (v)k p (iv) m () which leads to: v1m C p (v) (3) mp K p sin mp R p (v)k p cos v m (4) Figures 1 and show that this behavior is only approximately valid over limited frequency ranges. The traditional way to describe the observed behavior [9] consists in treating (Eq. (3)) and (Eq. (4)) independently from one another: C p (v)k c (v)v m c (v) R p (v)k r (v)v m r (v)

3 M. Tirado, C. Grosse / Colloids and Surfaces A: Physicochem. Eng. Aspects (003) 93/99 95 Fig. 1. Polarization capacity at 5 8C of a cell with two identical electrodes 1 m each, in contact with different aqueous NaCl electrolyte solutions. The curves correspond, top to bottom, to the following conductivities: , 0.401, 0.88, 0.169, 0.096, 0.050, and S m 1. The frequency dependence of the exponents m c (v) and m r (v) is then determined from the slopes of the log[c p (v)] or log[r p (v)] versus log(v) curves. Since this interpretation is incompatible with Kramers-Kroning relations, it is not surprising that it can lead to values of m c (v) bigger than unity [9] and that condition m c (v)/m r (v)/1, which follows from (Eq. ()), is generally not fulfilled. An alternative interpretation can be formulated plotting the experimental data on the reactance versus resistance plane, Fig. 3(a, b). While Fricke s Fig.. Polarization resistance at 5 8C of a cell with two identical electrodes 1 m each, in contact with aqueous NaCl electrolyte solutions. The curves correspond, top to bottom, to the following conductivities: , 0.050, 0.096, 0.169, 0.88, 0.401, and Sm 1.

4 96 M. Tirado, C. Grosse / Colloids and Surfaces A: Physicochem. Eng. Aspects (003) 93/99 Fig. 3. (a) Experimental electrode polarization reactance vs. resistance data points at 5 8C for an aqueous NaCl electrolyte solution with a S m 1 conductivity, and fitted values (line) calculated using Eqs. (5) and (6). (b) Same as above but for a S m 1 conductivity. equation (Eq. ()) leads to a straight line in this representation, Fig. 4(a), our data show straight lines at low frequencies and depressed circles at high frequencies, which corresponds to the circuit represented in Fig. 4(c). Neither circuit 4(a) nor 4(c) includes the contribution of the faradaic current across the electrode /electrolyte solution interface, which is usually neglected in dielectric measurements in view of the low fields (of the order of 1 V cm 1 ) and relatively high frequencies involved [10,11]. However, this contribution can be taken into account considering the circuit 4(d), which is compatible both with our data and with the findings of McAdams and Jossinet [10]. These authors measured electrode impedances at very low frequencies: 10 4 /10 4 Hz and different ap-

5 M. Tirado, C. Grosse / Colloids and Surfaces A: Physicochem. Eng. Aspects (003) 93/99 97 Fig. 4. Different equivalent circuits used to represent the electrode polarization impedance and their corresponding behavior in the reactance vs. resistance plane: (a) Fricke, (b) McAdams/Jossinet, (c) model used in this work, (d) suggested full model. The impedances Z* represent constant phase angle elements, Eq. (1). Indexes h and l correspond to high and low frequency elements, respectively. Fig. 5. Experimental electrode polarization capacitance and resistance at 5 8C for aqueous NaCl electrolyte solutions with S m 1 (circles) and S m 1 (diamonds) conductivities. Lines represent fitted values, (Eqs. (5) and (6)).

6 98 M. Tirado, C. Grosse / Colloids and Surfaces A: Physicochem. Eng. Aspects (003) 93/99 Table 1 Fitted parameter values Conductivity (S m 1 ) K l (kv Hz ml ) m l K h (kv Hz mh ) m h R h (kv) plied voltages. Their data described a depressed circle so they proposed an equivalent circuit made of a constant phase angle element in parallel with a non-linear faradaic charge transfer resistor, Fig. 4(b). Our measurements correspond to the small circle and just the tip of the large one, which appears as a straight line. On the contrary, McAdams and Jossinet only measured the large circle and did not detect the presence of the small one. We, therefore, analyzed our data using the equivalent circuit represented in Fig. 4(c) since, in the frequency range accessible to our instrument and for the applied voltage values, it is not possible to detect the curvature of the low frequency circle. The equations used to fit the data are: ml p R p (v)k l cos v m l K h R h K h R h v m h R h vm h Kh R h v m h ml p X p (v)k l sin v m l K h R h vm h R h vm h Kh R h v m h mh p cos mh p cos K h mh p sin cos mh p K h (5) (6) where the lower indexes h and l correspond to the high and low frequency elements, respectively. The values obtained for the different parameters appear in the Table 1. Figures 4(a, b) and Fig. 5 show examples of the experimental data and the fitted curves. 4. Conclusion In this work we present experimental data of platinum black electrode impedance parameters for broad frequency and electrolyte solution conductivity ranges. We show that our data cannot be described using the traditional Fricke model. However, a more elaborate model, Fig. 4(c), made it possible to describe the observed behavior in the frequency range from 10 Hz to 10 MHz. Our results, together with those of McAdams and Jossinet [10], suggest that over an even broader frequency range extending from 10 4 Hz to 10 MHz, the polarization impedance of platinum black electrodes should be well described by the model presented in Fig. 3(d), which includes the faradaic charge transfer effect. Acknowledgements This work was partially supported by CON- ICET, Argentina, PIP 465/98, and FONCYT, Argentina, PICT 03/ We gratefully acknowledge economic help provided by ELKIN 00, Cracow, Poland.

7 M. Tirado, C. Grosse / Colloids and Surfaces A: Physicochem. Eng. Aspects (003) 93/99 99 References [1] H.P. Schwan, in: W.L. Nastuk (Ed.), Physical Techniques in Biological Research, vol. 6, Academic, New York, [] C. Grosse, M. Tirado, J. Non-Crystall. Solids 305 (00) 386. [3] M. Tirado, F. Arroyo, A. Delgado, C. Grosse, J. Colloid Interf. Sci. 7 (000) 141. [4] M. Honda, The Impedance Measurement Handbook. A guide to Measurement Technology and Techniques, Hewlett Packard, Yokogawa, Japan, [5] C. Grosse, M. Tirado, in: M.F. Iskander, J.O. Kiggans, J.C. Bolomey (Eds.), Microwave Processing of Materials V, vol. 430, Proceedings of Symposium Mater. Res. Soc., San Francisco, CA, USA, 8 /1 April 1996, M.R.S., Pittsburg, PA, 1996, p. 87. [6] C. Grosse, M. Tirado, IEEE Trans. Instrum. Measure. 50 (5) (001) 16. [7] A. Stogryn, IEEE Trans. Microwave Theory Tech. MTT 19 (1971) 733. [8] H. Fricke, Philos. Mag. 14 (193) 310. [9] B. Onaral, H.P. Schwan, Med. Biol. Eng. Comput. 0 (198) 99. [10] E.T. McAdams, J. Jossinet, Annual International Conference on IEEE Eng. Med. Biol. Soc. 13 (1991) 178. [11] M. Scott, R. Paul, K.V.I.S. Kaler, in: A. Hubbard (Ed.), Encyclopedia of Surface and Colloid Science, M. Dekker, New York, 00, p