Charge-Transfer Polarization from Experiment

Interpretation of Charge-Transfer Polarization from Experiment 

In the previous section, emphasis is placed on the fact that the externally measured current relates only to the difference of the currents of the oxidation and reduction components of the reaction, neither of which are known initially at a given potential. It is useful to visualize Iex, and iex = Iex/A at any small area over which the imbalance of oxida- 

The theoretical Tafel expression for polarization of the oxidation reaction was given as Eq 3.47, into which iox M from Eq 3.54 is now substituted to give  

If this analysis is carried through for negative overpotentials, the following equation results  

The Em versus log (-iex.red) or log iex red (remember that iex red is a negative quantity) behavior is shown as the lower solid curve in Fig. 3.11. In the initial part of the curve, -i red is small relative to iG M, and iox M is close in magnitude to i0 M. In the limit, when iex red = 0, iox M = i M and therefore, EM = E M. Consequently, this experimental curve also asymptotically approaches the equilibrium half-cell potential as iex red — 0. In the limit of large i ed values (i.e., large negative values of iex,red, red i0x,M 311(1 from Eq 3.56), -iex red = ired M- Therefore, the last term of Eq 3.60, which is the overpotential term, becomes  

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The first term on the right, y, is the electronic contribution of 7° to the polarization at 2o) and the second term the contribution from pz. Note that pz cannot be determined from this experiment without a knowledge of the dipole moment. In compounds exhibiting significant charge transfer resonance pzPz y and the contribution of y is often ignored. 

Potentiometric measurements are done under the condition of zero current. Therefore, the domain of this group of sensors lies at the zero-current axis (see Fig. 5.1). From the viewpoint of charge transfer, there are two types of electrochemical interfaces ideally polarized (purely capacitive) and nonpolarized. As the name implies, the ideally polarized interface is only hypothetical. Although possible in principle, there are no chemical sensors based on a polarized interface at present and we consider only the nonpolarized interface at which at least one charged species partitions between the two phases. The Thought Experiments constructed in Chapter 5, around Fig. 5.1, involved a redox couple, for the sake of simplicity. Thus, an electron was the charged species that communicated between the two phases. In this section and in the area of potentiometric sensors, we consider any charged species electrons, ions, or both. 

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