Faradaic reactions plots

Figure 5.4 Current response for a 12.5 pm platinum microelectrode modified with a [Os(bpy)2 py(p3p)]2+ monolayer following a potential step where the overpotential rj was —100 mV the supporting electrolyte is 0.1 M TBABF4 in acetonitrile. The inset shows ln[fp(f)] versus f plots for the Faradaic reaction when using a 12.5 pm (top) and 5 pm (bottom) radius platinum microelectrode. Reprinted with permission from R. J. Forster, Inorg. Chem., 35, 3394 (1996). Copyright (1996) American Chemical Society...

Figure 4.27. a Ladder structure for electrochemical systems known as Faradaic reactions involving one adsorbed species (Model D23) b Nyquist plot of a ladder structure for the Faradaic reaction involving one adsorbed species, over the frequency range 1 MFIz to 1 mHz (Model D23 Rd = 200 Q, Rct = 400 Q, R3 = 600 Q, Cd, = 0.0001 F, C2 = 0.01 F)... 

If double-layer charging is the only process taking place in a given potential region (this would be the case for an ideally polarizable interphase) and one cycles the potential between two fixed values, the results should be such as shown in Fig. 2L(a). Plotting Ai = i - i = 2 i as a function of v, as shown by line 1 in Fig. 2L(b), one can obtain the value of the double-layer capacitance from the slope. If a faradaic reaction is taking place, a result such as shown by line 2, from which C can still be obtained (cf. Fig. 14G), might be observed. 

The reason for the linear response at high frequency can be seen in the Lissajous plot of surface overpotential as a function of applied potential, given in Figure 8.8. At low frequencies, the surface overpotential is large and is scaled by Rt/(Rt + Re), whereas at high frequencies the surface overpotential tends toward zero. It is interesting to note that, at low frequencies, the surface overpotential is influenced by the nonlinearity associated with the faradaic reaction. 

The admittance format is not particularly well suited for analysis of electrochemical and other systems for which identification of Faradaic processes parallel to the capacitance represents the aim of the impedance experiments. When plotted in impedance format, the characteristic time constant is that corresponding to the Faradaic reaction. When plotted in admittance format, the characteristic time constant is that corresponding to the electrol5rte resistance, and that is obtained only approximately when Faradaic reactions are present. 

Figure 28. Complex plane plots in the presence of a constant phase element (a) ideally polarizable electrode and (b) in the presence of a faradaic reaction.

In the presence of the faradaic reaction, assuming that the faradaic impedance can be expressed as a simple equivalent resistance, the complex plane plots represent a rotated semicircle p ig. 28(b)], instead of a semicircle centered on the Z axis. Similarly, the double-layer capacitance in the presence of the faradaic reaction may be obtained as... 

Fig. 8.14 Complex plane plots for faradaic reaction with R t = 250 cm in various Hull cells cell parameters as in Fig. 8.13, (impedances are in Q., imaginary part is negative) (From Ref. [354], copyright (2007), with permission from Elsevier)...

Figure 8.8 j/E plots obtained at different sweep rates, for a system having a Faradaic current in addition to the double-layer charging current. Using the difference, Aj, rather than the individual values of jan or ja eliminates most of the error due to the Faradaic reaction. 

The presence of a Faradaic electrode reaction of any kind competing with the double layer charging presents a problem in determining the purely capacitive current needed to calculate the surface charge. From a plot of 1 vs. (/ = total electrode current) with a fixed concentration of the ions of the electrode metal dissolved in solution, the surface charge can be obtained [65Butl]. (Data obtained with this method are labelled TC). 

The mass spectrometric currents follow largely, but not completely the faradaic current signals. The contributions to the respective faradaic currents resulting from complete oxidation to CO2, which are calculated using the calibration constant K (see Section 13.2), are plotted as dashed lines in the top panels in Fig. 13.3. For the calculations of the partial reaction currents, we assumed six electrons per CO2 molecule formation and considered the shift in the potential scale caused by the time... 

Similarly, the m/z = 60 ion current signal was converted into the partial current for methanol oxidation to formic acid in a four-electron reaction (dash-dotted line in Fig. 13.3c for calibration, see Section 13.2). The resulting partial current of methanol oxidation to formic acid does not exceed about 10% of the methanol oxidation current. Obviously, the sum of both partial currents of methanol oxidation to CO2 and formic acid also does not reach the measured faradaic current. Their difference is plotted in Fig. 13.3c as a dotted line, after the PtO formation/reduction currents and pseudoca-pacitive contributions, as evident in the base CV of a Pt/Vulcan electrode (dotted line in Fig. 13.1a), were subtracted as well. Apparently, a signihcant fraction of the faradaic current is used for the formation of another methanol oxidation product, other than CO2 and formic acid. Since formaldehyde formation has been shown in methanol oxidation at ambient temperatures as well, parallel to CO2 and formic acid formation [Ota et al., 1984 Iwasita and Vielstich, 1986 Korzeniewski and ChUders, 1998 ChUders et al., 1999], we attribute this current difference to the partial current of methanol oxidation to formaldehyde. (Note that direct detection of formaldehyde by DBMS is not possible under these conditions, owing to its low volatility and interference with methanol-related mass peaks, as discussed previously [Jusys et al., 2003]). Assuming that formaldehyde is the only other methanol oxidation product in addition to CO2 and formic acid, we can quantitatively determine the partial currents of all three major products during methanol oxidation, which are otherwise not accessible. Similarly, subtraction of the partial current for formaldehyde oxidation to CO2 from the measured faradaic current for formaldehyde oxidation yields an additional current, which corresponds to the partial oxidation of formaldehyde to formic acid. The characteristics of the different Ci oxidation reactions are presented in more detail in the following sections. 

The current efficiencies for the different reaction products CO2, formaldehyde, and formic acid obtained upon potential-step methanol oxidation are plotted in Fig. 13.7d. The CO2 current efficiency (solid line) is characterized by an initial spike of up to about 70% directly after the potential step, followed by a rapid decay to about 54%, where it remains for the rest of the measurement. The initial spike appearing in the calculated current efficiency for CO2 formation can be at least partly explained by a similar artifact as discussed for formaldehyde oxidation before, caused by the fact that oxidation of the pre-formed COacurrent efficiency. The current efficiency for formic acid oxidation steps to a value of about 10% at the initial period of the measurement, and then decreases gradually to about 5% at the end of the measurement. Finally, the current efficiency for formaldehyde formation, which was not measured directly, but calculated from the difference between total faradaic current and partial reaction currents for CO2 and formic acid formation, shows an apparently slower increase during the initial phase and then remains about constant (final value about 40%). The imitial increase is at least partly caused by the same artifact as discussed above for CO2 formation, only in the opposite sense. 

The problem with redox reactions of this type is that their rate constants are usually too large for regular steady-state techniques to be reliably applied, a or p then have to be determined through the reaction order or by some method such as Faradaic rectification. Usually, such methods require evaluation of the double-layer behavior in order to make double-layer corrections. This is often an unsatisfactory business, especially when corrections would be required over a range of temperatures. We conclude that for this important class of electrochemical reactions more data for examination of b T) or a T) are required. However, for certain ionic redox reactions that are sufficiently slow, Weaver has been able to evaluate a as /( T) from Tafel plots over a range of 0.3 ... 

The faradaic admittance of reactions (116) and (117) is described by Eq. (135). Analysis of the complex plane plots in such a case was presented by Cao. Bai and Conway presented three-dimensional plots for such a reaction. Two general cases should be considered, depending on the sign of the parameter B ... 

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