Interfacial impedance Blocking

Fig. 10.13 Impedance plane diagrams for metal non-blocking electrodes with two mobile species in the electrolyte, (a) Interfacial impedance is only a Warburg impedance. (b) Interfacial impedance shows a charge transfer resistance semicircle.

Some electrochemical systems can be described as blocking electrodes for which no Faradaic reaction can occur. At steady state, the current density for such a system must be equal to zero. The transient response of a blocking electrode is due to the charging of the double layer. At short times or high frequency, the interfacial impedance tends toward zero, and the solution adjacent to Ihe electrode can then be considered to be an equipotential surface. The short-time or high-frequency current distribution, therefore, follows the primary distribution described in the... 

The representation of an Ohmic impedance as a complex number represents a departure from standard practice. As will be shown in subsequent sections, the local impedance has inductive features that are not seen in the local interfacial impedance. As the calculations assumed an ideally polarized blocking electrode, the result is not influenced by Faradaic reactions and can be attributed only to the Ohmic contribution of the electrolyte. 

Huang et al. ° ° demonstrated for blocking disk electrodes that, while the local interfacial impedance represents the behavior of the system unaffected by the current and potential distributions along the surface of the electrode, the local impedance shows significant time-constant dispersion. The local and global Ohmic impedances were shown to contain the influence of the current and potential distributions. 

In this case, the dispersive capacitance can be described by another interfacial element capable of dealing with such low-frequency dispersion. A blocking capacitive interface response that takes into account a frequency dependency can generally be modeled by an interfacial impedance element such as ... 

Figure 13.1 Schematic representation of an impedance distribution for a blocking disk electrode where Ze r) represents the local Ohmic impedance, Co(r) represents the interfacial capacitance, and Qo(r) and (r) represent local CPE parameters a) 2-dimensional distribution and b) combined 2-dimensional and 3-dimensional distribution.

The local Ohmic impedance Zg accounts for the difference between the loccil interfacial and the local impedances. The calculated local Ohmic impedance for Tafel kinetics with 7 = 1.0 is presented in Figure 13.9 in Nyquist format with normalized radial position as a pcirameter. The results obtained here for the local Ohmic impedance are very similar to those reported for the ideally polarized electrode and for the blocking electrode with local CPE behavior. ° ° At the periphery of the electrode, two time constants (inductive and capacitive loops) are seen, whereais at the electrode center only an inductive loop is evident. These loops are distributed around the asymptotic real value of 1/4. 

The main hypotheses for developing the EHD impedance theory are that the electrode interface is uniformly accessible and the electrode surface has uniform reactivity. However, in many cases, real interfaces deviate from this ideal picture due, for example, either to incomplete monolayer adsorption leading to the concept of partial blocking (2-D adsorption) or to the formation of layers of finite thickness (3-D phenomena). These effects do not involve the interfacial kinetics on bare portions of the metal, which, for simplification, will be assumed to be inherently fast. The changes will affect only the local mass transport toward the reaction sites. Before presenting an application of practical interest, the theoretical EHD impedance for partially blocked electrodes and for electrodes coated by a porous layer will be analyzed. 

Non-reacting surface-active solutes may tend to keep reactants, which are less surface-active, out of the interface and so slow down the reaction rate. They may also retard mass transfer and hence reactions, by impeding the surface renewal. But surface-active solutes, which enter into reactions, may speed up surface renewal and accelerate reactions by causing turbulence in the vital interfacial region. Examples of all the three effects have been discussed and their relative importance considered by Richardson (1982). It would appear that the interfacial blocking may retard rates up to one-hundred fold, whereas retardation or enhancement of surface renewal in stirred systems is only likely to decrease or increase rates by a factor of five or ten. Interfacial phenomena may also... 

If the electrodes are non-blocking, then the Cai is now shunted in parallel by a charge-transfer resistance, as shown in Fig. 1.4(b) and discussed in Section 1.4.2. Evaluation of the impedance expression for this equivalent circuit produces two semicircles. The high-frequency semicircle is related to the bulk electrolyte and the low-frequency semicircle, which is more distant from the origin, arises from interfacial prcx esses. The bulk resistance is the Z value at the high-frequency end of the interface semicircle. 

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