TECHNIQUES BASED ON CONCEPTS OF IMPEDANCE

In deriving the theory below, we will rely frequently on analogies between the electrochemical 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 chemical 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. 

This operation determines the values of R and C that, in series, behave as the cell does at the measurement frequency. The impedance is measured as a function of the frequency of the ac source. The technique where the cell or electrode impedance is plotted V5. frequency is called electrochemical impedance spectroscopy (EIS). In modem practice, the impedance is usually measured with lock-in amplifiers or frequency-response analyzers, which are faster and more convenient than impedance bridges. Such approaches are introduced in Section 10.8. The job of theory is to interpret the equivalent resistance and capacitance values in terms of interfacial phenomena. The mean potential of the working electrode (the dc potential ) is simply the equilibrium potential determined by the ratio of oxidized and reduced forms of the couple. Measurements can be made at other potentials by preparing additional solutions with different concentration ratios. The faradaic impedance method, including EIS, is capable of high precision and is frequently used for the evaluation of heterogeneous charge-transfer parameters and for studies of double-layer structure. 

The relationship between two phasors at the same frequency remains constant as they rotate hence the phase angle is constant. Consequently, we can usually drop the references to rotation in the phasor diagrams and study the relationships between phasors simply by plotting them as vectors having a common origin and separated by the appropriate angles. 

Let us apply these concepts to the analysis of some simple circuits. Consider first a pure resistance, R, across which a sinusoidal voltage, e = E sin cot, is applied. Since Ohm s law always holds, the current is E R)sin co t or, in phasor notation. 

Relationship between the voltage across a resistor and current through the resistor. 

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Chapter 10. Techniques Based on Concepts of Impedance where... 

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