Ionic Conductivity Complex Impedance Technique

Usually, the ionic conductivity is much smaller than that of the electrons. To determine it, the convenient tool is the complex impedance technique, because it requires very small current (prevents heating) and very small ionic motion. The a.c. method is called electrochemical impedance spectroscopy (EIS) because the impedance spectrum measured in a wide frequency range evaluates the performance of batteries and characterizes the various elements such as electrode, electrolyte and electrolyte/electrode interface. First, let us consider the ionic conductivity in a solid electrolyte. The complex impedance due to the Li-motion is  

Therefore, the determination of R and t is reduced to the measurement of a resistance and a capacitance. The way to do it is to make a Cole-Cole plot. For that purpose, we write Eq. (13.68) under the more symmetric form  

This is the equation of a circle in the Re(Z), lm(Z) plane, centered at R/2, of radius R/2 Note RC (or t) are positive, so that only half of the circle has a physical meaning. Measurements of Z as a function of the frequency scan this semi-circle when plotting -lm(Z) as a function of Re(Z) This is the Cole-Cole plot (Fig. 13.21). 

This is, however, the ideal case. In practice, situations more difficult to analyze may happen. For instance, in some cases, we observe an impedance of the form  

A quasi linear behavior can be observed in the low frequency limit 

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The ionic conductivity of a solvent is of critical importance in its selection for an electrochemical application. There are a variety of DC and AC methods available for the measurement of ionic conductivity. In the case of ionic liquids, however, the vast majority of data in the literature have been collected by one of two AC techniques the impedance bridge method or the complex impedance method [40]. Both of these methods employ simple two-electrode cells to measure the impedance of the ionic liquid (Z). This impedance arises from resistive (R) and capacitive contributions (C), and can be described by Equation (3.6-1) ... 

These examples and the general subjects mentioned above illustrate that ion conduction and the electrochemical properties of solids are particularly relevant in solid state ionics. Hence, the scope of this area considerably overlaps with the field of solid state electrochemistry, and the themes treated, for example, in textbooks on solid state electrochemistry [27-31] and books or journals on solid state ionics [1, 32] are very similar indeed. Regrettably, for many years solid state electrochemistry/solid state ionics on the one hand, and liquid electrochemistry on the other, developed separately. Although developments in the area of polymer electrolytes or the use of experimental techniques such as impedance spectroscopy have provided links between the two fields, researchers in both solid and liquid electrochemistry are frequently not acquainted with the research activities of the sister discipline. Similarities and differences between (inorganic) solid state electrochemistry and liquid electrochemistry are therefore emphasized in this review. In Sec. 2, for example, several aspects (non-stoichiometry, mixed ionic and electronic conduction, internal interfaces) are discussed that lead to an extraordinary complexity of electrolytes in solid state electrochemistry. 

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