Complex-impedance method, ionic conductivity

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) ... 

So far, the ionic conductivity of most ILs has been measured by the complex impedance method [116], In this method, charge transfer between carrier ions and electrode is not necessary. Therefore platinum and stainless steel are frequently used as blocking electrodes. However, it is often difficult to distinguish the resistance and dielectric properties from Nyquist plots obtained by the impedance measurement. In order to clarify this, additional measurements using non-blocking electrodes or DC polarization measurement are needed. 

The Rb based on the sample cannot be calculated correctly, since the electric charge transfer resistance and the electric double layer in an electrode interface are also detected as a resistance, even if bias voltage is impressed to the measurement cell in order to measure the ionic conductivity. For the ionic conductivity measurement, a dc four-probe method, or the complex-impedance method, is used to separate sample bulk and electrode interface [4]. In particular, the complex-impedance method has the advantage that it can be performed with both nonblocking electrodes (the same element for carrier ion and metal M) and blocking electrodes (usually platinum and stainless steel were used where charge cannot be transferred between the electrode and carrier ions). The two-probe cell, where the sample is sandwiched between two pohshed and washed parallel flat electrodes, is used in the ionic conductivity measurement by complex-impedance method as shown in Figure 6.1. 

The AC method also has problems of its own. We have a new parameter, the measuring frequency, which must be chosen. But perhaps the largest problem is that impedance is a complex quantity related to a capacitor and a resistor coupled in series, and the inverse quantity admittance is related to a capacitor and resistor coupled in parallel. Resistance and conductance are inverse when using DC excitation, but with AC the resistance will not be the inverse of the conductance. In this case, it is obvious that resistance and conductance are no longer inverse, as discussed in Section 3.3, and conductance should be preferred to resistance since ionic conduction and polarization basically appear in parallel in biological tissue. 

Measurement of Ionic Conductivity. The synthesis of solvent-free metal salt complexes of polyethylene oxides prompted detailed electrical measurements with the thought that these materials might prove to be useful electrolytes, in a hydrous environment, for high energy density batteries (13-15). Many fundamental properties of these polymer electrolytes have been examined and a large literature on the subject is available (16-17). We prepared a disk of one of our polyether complexes and measured its conductivity by impedance methods. 

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 ... 

Most of the polymer electrolytes that have been studied are solid solutions of salts in polymers. There is a possibility that both the cation and anion are mobile in such electrolytes. The ionic transport number in polymer electrolytes is a very important parameter in terms of the conduction mechanism of ions in polymers and of their practical application. Cationic transport numbers have been measured in the polymer electrolytes, especially in those of PEO using various methods, including nuclear magnetic resonance (NMR) [49,50], complex impedance measurements [51,52], tracer diffusion... 

The conductivity of an ionic conductor can be assessed by direct current (dc) or alternating current (ac) methods. Direct current methods give the resistance R and the capacitance C. The corresponding physical quantity when ac is applied is the impedance, Z, which is the total opposition to the flow of the current. The unit of impedance is the ohm (fl). The impedance is a function of the frequency of the applied current and is sometimes written Z(to) to emphasize this point. Impedance is expressed as a complex quantity ... 

Impedance spectroscopy, meaning the measurement of complex resistivities with ac current methods, is an important tool to study diffusion and to correlate it with ionic transport behavior. The diffusion coefficient, D , obtained from conductivity measurements (vide infra) is related to the self-diffusion coefficient, D... 

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