Charge transfer resistance Potential dependence

Charge-transfer resistance is the resistance that occurs when electrons transfer at the electrode/electrolyte interface. The charge-transfer resistance is dependent on the reaction, the electrode surface, and the electrode potential. In general, an increase in overpotential leads to a decrease in charge-transfer resistance. 

A calculated transient current response to a 10 mV step in potential, introduced at time to, is presented in Figure 7.1 for the electrical circuit inserted in the figure. The time constants for the circuit tmder the conditions of tiie simulation were Ti = 0.0021 s (76 Hz) and T2 = 0.02 s (8 Hz). The potentiail dependence of parameter l i is consistent with the behavior of the charge-transfer resistance described in Chapter 10. 

Figure 7.1 The current response of an electrochemical system to a 10 mV step change in applied potential from 0.09 V to 0.1 V for the inserted electrical circuit with parameters l o == 1 R = 10 - /0060 n, Cl = 10 F, 1 2 = 10 n, and C2 = 20 if. The potential dependence of parameter Ki is consistent with the behavior of the charge-transfer resistance described in Chapter 10.

The potential dependence of the charge-transfer resistance can be expressed in terms of the Tafel slope as... 

It seems to be questionable whether these two distinct sequences can be described by the model discussed earlier. At this point, the reader should be reminded that although the mechanisms discussed are believed to represent essential features of the individual systems, all of them are simplified caricatures of the true system. The validity of the simplifications, of course, changes with the operating parameters, and thus the potential of a certain model to predict experimental observations depends on the experimental conditions. In the case of the last example, it was proposed that a second negative differential charge-transfer resistance, owing to the formation of higher oxides, plays a role in the second MMO sequence. Obviously, such a mechanism is not captured in the model (and also has not yet been experimentally verified). 

The oxidation of chloride and bromide ions is an example of an electroca-taly tic reaction and the mechanism has been the subject of much speculation [23, 24]. The oxidation of chloride ions is also the major industrial route to chlorine gas [25, 26]. Reactions of this family are termed electrocatalytic because the rate of the reaction, as measured by the current or the charge transfer resistance at a given potential, depends on the electrode material. This is a major reaction type in electrode kinetics. 

PDEIS is a new technique based on fast measurements of the interfacial impedance with the virtual instruments [3] that benefits from the efficient synchronization of direct hardware control and data processing in the real-time data acquisition and control [4], The built-in EEC fitting engine of the virtual spectrometer divided the total electrochemical response into its constituents those result from different processes. Thus, just in the electrochemical experiment, we come from the mountains of raw data to the characteristics of the constituent processes - the potential dependencies of the electric double layer capacitance, charge transfer resistance, impedance of diffusion, adsorption, etc. The power of this approach results from different frequency and potential dependencies of the constituent responses. Because of the uniqueness of each UPD system and complex electrochemical response dependence on the frequency and electrode potential, the transition from the PDEIS spectrum (Nyquist or Bode plot expanded to the 3D plot... 

Linear polarization measurements are executed rapidly. The currents in linear polarization measurements are measured in the potential range between 10 and 20 mV from the equilibrium potential. The E-I dependence in this potential range follows a linear relationship. The slope of the plot, dE/ di, represents the polarization resistance. The corrosion current is calculated using the Stem-Geary equation for known values of the anodic and cathodic Tafel slopes. The ratio of the overpotential to the current represents the resistance in Ohm s law and is often termed the charge transfer resistance or the polarization resistance, Rp. 

The following problem arises in the interpretation of such semicircles in the complex plane impedance plots every parallel combination of a constant resistance and constant capacity leads to a semicircle in the Nyquist plot of the impedance. To verify a charge transfer, for instance, the potential dependence of the charge-transfer resistance should be investigated to demonstrate the Butler-Volmer potential dependence of the exchange current. 

Fig. 9 Concentration dependence of a the charge transfer resistance (Ret) and b the double layer capacitance (Cdi) of [FelCNig] " in 2 wt% agarose (squares), 2 wt% /c-carrageenan (triangles) and aqueous solution (diamonds) containing 0.5 M KCl at the rest potential (reprinted with permission from Elsevier [48])...

It is evident that the shape of the impedance spectra varies with the potential since the values of the charge transfer resistance (Ret), the low frequency (redox) capacitance (Cl) and the Warburg coefficient change with the potential more exactly, they depend on the redox state of the polymer. In many cases D is also potential-dependent. The double-layer capacitance (Cdi) usually shows only slight changes with potential. The ohmic resistance (Rq) is the sum of the solution resistance and the film resistance, and the latter may also be a function of potential due to the potential-dependent electron conductivity, the sorption of ions, and the swelling of the film. In Fig. 3.9 three spectra are displayed, which were constructed using the data obtained for a PTCNQ electrode at three different potentials near its equilibrium potential [23]. 

The dependence of the kinetic parameter and mass transfer coefficient a on the potential is shown in Fig. 4.4. The logarithm of the mass transfer coefficient is symmetrical around and has a minimum exactly at E1/2, and the slopes are dE/ dlnff = RTInF. The minimum of the charge transfer resistance is at the potential described by Eq. (4.52). If the process is not symmetrical, then the slopes of the cathodic and anodic branches of log re different dE/dIn/Jc =-RTIanF and dE/ dln/ ct = RT/(l-a)nF. 

To obtain the total impedance, the faradaic impedance, Eq. (5.19), must be inserted into the total impedance (Fig. 4.1b). The complex plane and Bode plots of the total impedance are as in Fig. 2.35. The circuit parameters R i and Cp depend on the potential, as illustrated in Fig. 5.1. The charge transfer resistance displays a minimum at Ep and its logarithm is linear with the potential further from the minimum, while the pseudocapacitance displays a maximum. These values at the potential Ep are... 

Fig. 7.3 Dependence of charge transfer resistance (per real surface area) on potential for HUPD reaction at polycrystalline Pt in 0.1 MH2SO4 (From Ref. [242], copyright (2012), with permission from Elsevier)...

Note that both the charge transfer resistance Rot and the Warburg coefficient aw depend on potential because they contain terms in ft We note from Eqn. 360 that... 

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