Bard Faulkner EIS


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CHAPTER 10 TECHNIQUES BASED ON CONCEPTS OF IMPEDANCE 10.1 INTRODUCTION In previous chapters we have discussed ways of studying electrode reactions through large perturbations on the system. By imposing potential sweeps, potential steps, or cur- rent steps, we typically drive the electrode to a condition far from equilibrium, and we ob- serve the response, which is usually a transient signal. Another approach is to perturb the cell with an alternating signal of small magnitude and to observe the way in which the system follows the perturbation at steady state. Many advantages accrue to these tech- niques. Among the most important are (a) an experimental ability to make high-precision measurements because the response may be indefinitely steady and can therefore be aver- aged over a long term, (b) an ability to treat the response theoretically by linearized (or otherwise simplified) current-potential characteristics, and (c) measurement over a wide time (or frequency) range (10 4 to 10~ 6 s or 10~ 4 to 10 6 Hz). Since one usually works close to equilibrium, one often does not require detailed knowledge about the behavior of the i-E response curve over great ranges of overpotential. This advantage leads to impor- tant simplifications in treating kinetics and diffusion. In deriving the theory below, we will rely frequently on analogies between the elec- trochemical cell and networks of resistors and capacitors that are thought to behave like the cell. This feature may seem at times to disembody the interpretation from the chemi- cal system, so let us emphasize beforehand that the ideas and the mathematics used in the interpretation are basically simple. We will do our best to tie them to the chemistry at every possible point, and we hope readers will avoid letting the details of interpretation obscure their view of the great power and beauty of these methods. 10.1.1 Types of Techniques (1-12) The prototypical experiment is the faradaic impedance measurement, in which the cell contains a solution with both forms of a redox couple, so that the potential of the work- ing electrode is fixed. For example, one might use 1 mM Eu 2 + and 1 mM Eu 3 + in 1 M NaClO4. A mercury drop of fixed area might be employed as the working electrode, and it might be paired with a nonpolarizable reference such as an SCE, which would act also as the counter electrode. It is probably easiest to understand the measurement of impedance by considering the classical approach with an impedance bridge. The cell is inserted as the unknown impedance into one arm of an impedance bridge, and the bridge is balanced by adjusting R and С in the opposite arm of the bridge, as shown in Figure 10.1.1. 368
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ЮЛ Introduction 369 Potentiometer to null dc cell voltage Figure 10.1.1 A bridge circuit for measurements of electrochemical impedance.
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