Standard rate constant impedance

These electron transfer reactions are very fast, among the fastest known. This is the reason that impedance methods were used originally to determine the standard rate constant,13,61 at a time when the instrumentation available for these methods was allowing shorter measurement times (high frequencies) to be reached than large-amplitude methods such as cyclic voltammetry. The latter techniques have later been improved so as to reach the same range of fast electron transfer kinetics.22,63... 

Sluyters and coworkers [34] have studied the mechanism of Zn(II) reduction on DM E in NaCl04 solutions at different water activity (uw) using faradaic impedance method. Dqx and E p were determined from dc polarographic curves. Hydration numbers of Zn(Il) ion were estimated from the dependence of E[p on In Uw The obtained standard rate constant was changing with a NaCl04 concentration and the slope of the dependence of In k on potential was changing with potential (see Fig. 1). Therefore, the following mechanisms were proposed ... 

Impedance-potential curve for a single electrode reaction with single electron transfer description by standard rate constant... 

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. 7. 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 hydrochloric acid, (a) Standard rate constant-potential curve calculated for the hydrogen evolution reaction on titanium assuming that DA = 7.5 x 10 5cm"1s 1 and E° = - 246 mV. The Tafel slope 6C = 211 mV and the measured ohmic resistance was 0.4 ohm cm2. The potentials are the "true potentials, (b) High-frequency double layer capacity-potential curve. The potentials are the measured potentials.

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. 

For interest, Figs. 18(b) and 19(a) show standard rate constant-potential curves obtained by analysing the same current-potential and impedance-potential data, but assuming that PdCl2 is the electroactive species, i.e. that the deposition-dissolution reactions occurs by the reaction scheme... 

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. 7 Logarithmic plots of the apparent standard rate constant of cyt. c as a function of a number of methylene groups of alkanethiol SAM. ( ) obtained by ER technique and (°) obtained by ac impedance technique. (Z.-Q. Feng,...

Figure 4.4.34. Bode impedance magnitude plots for Alloy-22 in 6.2m NaQ + 0.001 m HQ (pH = 3) at 80°C as a function of the standard rate constant for the dissolution of the passive film, calculated using the data listed in Table 4.4.6. Some experimental data are included for comparison. These data gave rise to the parameter values listed in Table 4.4.7 as determined by optimization of the PDM on the experimental data. The standard rate constant, k has units of mol° /cm .s, corresponding to a kinetic order for film dissolution with respect to H of 0.6.

Figures 19.4 and 19.5 show typical experimental electrochemical impedance spectra for the passive sulfide film on copper in a deaerated 0.1 M NaCl + 2 x 10 " M Na2S-9H20 solution at 25 °C. The best fit results, calculated from the parameters obtained from optimization of the proposed mechanism based on the modified PDM (Figure 19.3), as listed in Tables 19.2 and 19.3, are also included in these figures as solid lines. It can be seen that the correlation between the experiment and the model is fairly good, indicating that the proposed model can provide a reasonable account of the observed experimental data. It should be noted that the obtained parameters should not only reproduce the experimental impedance spectra but also deliver values that are physically reasonable. The obtained kinetic parameters, such as the standard rate constants, transfer coefficients and defect diffusivities listed in Tables 19.2 and 19.3, show no systematic dependency on the applied...

In 1982, Samec et al. studied the kinetics of assisted alkali and alkali-earth metal cation-transfer reactions by neutral carrier and conclnded that the kinetics of transfer of the monovalent ions were too fast to be measured [186]. In 1986, Kakutani et al. published a study of the kinetics of sodium transfer facilitated by di-benzo-18-crown-6 using ac-polarography [187]. They concluded that the transfer mechanism was a TIC process and that the rate constant was also high. Since then, kinetic studies of assisted-ion-transfer reactions have been mainly carried out at micro-lTlES. In 1995, Beattie et al. showed by impedance measurements that facilitated ion-transfer (FIT) reactions are somehow faster than the nonassisted ones [188,189]. In 1997, Shao and Mirkin used nanopipette voltammetry to measure the rate constant of the transfer of K+ assisted by the presence of di-benzo-18-crown-6, and standard rate constant values of the order of 1 cm-S were obtained [190]. A more systematic study was then published that showed the following sequence,, which is not in accordance with... 

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