Double layer capacity curves

The electrochemical behaviour of stainless steel has not been worked out completely, although the measured data are available. However, one aspect of the behaviour, based on the measured double layer capacity data, seems to be susceptible to interpretation. The capacity-potential curves are determined by the state of the metal surface and by the ionic environment. In this work, it has been assumed that the ionic environment is a constant. This means that the double layer capacity-potential curves should reflect the nature of the metal surface just as, say, an electron energy spectrum in surface science. Stainless steel has a complicated electrochemical behaviour. In previous work [22] an attempt has been made to compare the double layer capacity curves measured during dissolution and passivation of the stainless steel with that of the pure components. It seems that all the data in the high frequency regime can be fitted to eqn. (70) with the Warburg coefficient set equal to zero. 

Fig. 12. Rotating (45 Hz) ruthenium dioxide/titanium dioxide electrode (35%w/w ruthenium dioxide) in 1.0 M NaCl solution, (a) Standard rate constant-potential curve assuming a constant Tafel slope of 70mV. Dcl = 5 x 10 6cm s-1, Dc = 7 x 10 6cm s-1, E° = 1050mV SCE, and R = 0.8 ohm cm2. (b) Standard rate constant-potential curve assuming a constant Tafel slope of 40mV. DC1 = 5 x 10 8cm s 1, Z)ct2 = 7 x 10 8cm s 1, E° = 1050mV SCE, and R = 0.8ohm cm2. (c) Common experimental and calculated current-potential curve using the parameters of Fig. 12(b). (d) Double layer capacity curve.

Figure 7. Comparison of (a, solid) electrochemical and (b, dashed) UHV measurements of the H, coverage/potentiaI differential versus potential on Pt(lll).1.) cathodic sweep (25 mV/s) voltammogram in 0.3 M HF from Ref. 20, constant double layer capacity subtracted, b.) dB/d(A ) versus A plot derived from A versus B plot of Ref. 26. Potential scales aligned at zero coverage. Areas under curves correspond to a.) 0.67 and b.) 0.73 M per surface Pt atom.

The effect of the supporting electrolyte on the fpzc of Au electrodes indicates specific affinity of either cations or anions of the dissolved salt to the given surface. For example, the studies performed by Hamelin [34] have shown the effect of the supporting electrolyte on the double-layer capacity - potential curves (see Table 3). 

If we register the second harmonic current vs. d.c. potential, this will have the same form as the second derivative of the voltammetric curve, as Fig. 11.11 shows. One of the advantages of the use of the second harmonic is that, since the double layer capacity is essentially linear, it contributes much less to the second harmonic than to the fundamental frequency and the calculation of accurate kinetic parameters is much facilitated. 

The PZC may also be seen on differential capacity curves when specific adsorption is absent and the electrolyte concentration is low (< 0.01 M). At this point the capacity of the diffuse part of the double layer is a minimum and can fall below that of the compact or inner layer. As a result the total double layer capacity may... 

Analytical applications of electrochemistry, where the objectives are well defined, have fared better. There is a long list of papers going back twenty years on the applications of computers and then microprocessors. Reviews of this subject appear in the Fundamental Reviews sction of Analytical Chemistry (see refs. 8 and 9). In general, the aim in electroanalytical methods is to avoid interfering effects, such as the ohmic loss and the double layer capacity charging, and to use the Faradaic response peak current-potential curve as an analytical tool. Identification of the electroactive species is achieved by the position of the response peak on the potential axis and "pattern recognition , and quantitative analysis by peak shape and height. A recent development is squarewave voltammetry [10]. 

In this work, the main aim has been to determine the steady-state behaviour behaviour by measuring the current-potential curve. In general, the steady state is the most important characteristic of an electrode reaction. Fortunately, most known electrochemical reactions have a steady state and are variations of the redox type of reaction. As shown above, the steady current-potential curve can be exactly interpreted for redox reactions. In order carry out a complete analysis, it is essential to measure the components of the steady state by impedance-potential measurements. In addition, impedance delivers information about the charging processes as they appear in the high-frequency double layer capacity-potential curve. This last parameter is the parameter which should connect electrochemistry and surface science. The unfortunate fact is that it is still not very well understood. 

Z(a>) - Ra Rct + (1 - jymo-w and produce an electrochemical "spectrum as charge transfer-potential, double layer capacity-potential, ohmic resistance-potential, and Warburg coefficient-potential plots. Together with the current-potential curve, these present a useful representation of the steady-state electrochemical behaviour. 

Fig. 5. Analysis of the experimental steady-state current—potential and impedance-potential data from E = — 650 mV to E = —150 mV for a titanium rotating-disc electrode (45 Hz) in a solution of 3.0 M sulphuric acid at 65°C. (a) Steady state current-potential curve. The potentials are the measured potentials, (b) High-frequency double layer capacity-potential curve. The potentials are the measured potentials.

However, the active dissolution of titanium depends markedly on temperature in acid solution. At lower temperatures, the picture is not so clear. It is necessary to have a quantitative measure of the rate of the hydrogen reaction and the titanium dissolution reaction. The complete set of current-potential and impedance-potential data has been tested against the theory given above. The best strategy seems to be to fit to a single electrode reaction and then to look for deviations from the expected behaviour for a perfect redox reaction. A convenient way of doing this is to represent the electrochemical data as a standard rate constant-potential curve in conjunction with a double layer capacity-potential curve [21]. 

Fig. 6. Analysis of the experimental steady-state current-potential and impedance-potential data from E = -1300 mV to E = -600 mV for a titanium rotating-disc electrode (45 Hz) in a solution of 2 M perchloric acid, (a) Standard rate constant-potential curve calculated for the hydrogen evolution reaction on titanium assuming that DA = 7.5 x 10-5cm s and E° = —246 mV. The Tafel slope bc = 120 mV and the measured ohmic resistance was 0.3 ohm cm2. The potentials are the "true potentials, (b) Standard rate constant-potential curve calculated for the hydrogen evolution reaction on titanium assuming that DA = 7.5 x 10-5 cms-1 and E° = — 246mV. The Tafel slope bc = 211 mV and the measured ohmic resistance was 0.3 ohm cm2. The potentials are the "true potentials, (c) High-frequency double layer capacity-potential curve obtained from the impedance data. The potentials are the measured potentials.

Fig. 10. Double layer capacity-potential curves for different metal rotating-disc electrodes (45 Hz rotation speed) in the given acid solutions, (a) Nickel in 1M HC104 (b) electropolished nickel in 1M HC104 (c) nickel in lM HC1 (d) chromium in 1M HC104 (e) iron in 1M HC104 and (f) stainless steel (304 L) in 1M HC104.

Two solutions, 1M hydrochloric acid + 0.01 M PdCl2 (A) and O.lM hydrochloric acid + 0.91 M perchloric acid + 0.01 M PdCl2 (B), have been analysed in Fig. 17(a) and (b) by impedance-potential measurements, to give standard rate constant-potential, double layer capacity-potential, and current-potential curves for a particular reaction mechanism, in this case for the PdCl+ complex... 

The graphs [Fig. 17(a) and (b)] show the large increase in standard rate constant as the potential goes negative, suggesting that the palladium electrode is much more active for the deposition reaction at potentials less than about 100 mV. This effect is also reflected in Fig. 17(c) and (d) in which the double layer capacity-potential curves are reproduced. These show that the double layer capacity sharply increases with negative potential. The main reason for this effect is, undoubtably, an area increase as palladium metal is deposited. Figure 17(e) and (f) show the associated log current-potential curves (corrected for ohmic resistance). These curves are also reproduced by calculation from the measured impedance-potential curves. 

Fig. 17. Analysis of current-potential and impedance-potential data for the active deposition-dissolution of palladium in solutions of 1M hydrochloric acid + 0.01 M PdCl2 (A) and 0.1 M hydrochloric acid + 0.91 M perchloric acid + 0.01 M PdCl2 (B). (a) Standard rate constant-potential curve calculated according to the reaction scheme (78) using experimental data obtained for palladium in solution A with the parameters i>a = 220 mV, 6C = 60 mV, and E° = 575 mV. (b) Standard rate constant-potential curve calculated according to the reaction scheme (78), using experimental data obtained for palladium in solution B with the parameters i>a = 220 mV, bc = 60 mV, and ° = 575 mV. (c) Double layer capacity-potential curve for solution A. (d) Double layer capacity-potential curve for solution B. (e) Current-potential curve for solution A. (f) Current-potential curve for solution B.

Fig. 20. Typical result of measuring the characteristics of dissolution of a dental amalgam (Dispersalloy, electrode 37 HD) in 2/3 strength Ringer s solution. The measurements are almost in the steady state at 60 s per potential point, (a) Charge transfer-potential curve (b) Current-potential curve, also showing the return potential sweep and (c) double layer capacity-potential curve.

A comparison of the development of the SER intensity with the changes of the true surface area, represented by the double-layer capacity, is shown in Figs. 3 and 4. The two examples measured under similar conditions demonstrate the scattering of the general shape of Raman-time and capacitance-time plots. The good correlation in the shape of the curves found in the experiments leads to the assiunption of a proportionality relation between the SER intensity and the true area of the surface. 

As discussed in Section 8.3.4, the presence of a finite double-layer capacity results in a charging current contribution proportional to dEldt (equation 8.3.11) and causes /f to differ from the total applied current, /. This effect, which is largest immediately after application of the current and near the transition (where dE/dt is relatively large), affects the overall shape of the E-t curve and makes measurement of r difficult and inaccurate. A number of authors have examined this problem and have proposed techniques for measuring T from distorted E-t curves or for correcting values obtained in the presence of significant double-layer effects. 

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