Warburg impedance, ionic conductivity

To maintain linear conditions in electrolytic systems, the signal ampUtude must be reduced —>0 as f — 0 (see Section 8.4.1). Except in the bulk of an electrolyte (see Eq. 2.2), DC conditions are therefore virtual unobtainable in electrolytic systems (see also the Warburg impedance concept described in Section 7.9.3). This is well illustrated with the logarithmic frequency scale, where both infinitely high and infinitely low frequencies are equally off-scale and unattainable. With electronic (not ionic) conduction and ordinary resistors, perfect DC conditions represent no difficulty, and these can therefore only be idealized models of electrolytic systems. 

An overview on the topic of IS, with emphasis on its application for electrical evaluation of polymer electrolytes is presented. This chapter begins with the definition of impedance and followed by presenting the impedance data in the Bode and Nyquist plots. Impedance data is commonly analyzed by fitting it to an equivalent circuit model. An equivalent circuit model consists of elements such as resistors and capacitors. The circuit elements together with their corresponding Nyquist plots are discussed. The Nyquist plots of many real systems deviate from the ideal Debye response. The deviations are explained in terms of Warburg and CPEs. The ionic conductivity is a function of bulk resistance, sample... 

The electrode layers formed using die physical loading method are usually relatively thicker (more than 10 pm in thickness), and the composite layers are composed of nanoparticles of the electrode material and the ionic polymer. These layers are both electronically and ionically conductive. The impedance for such electrodes is assumed to be similar to diat of porous electrodes. Levie (1963, 1964) was the first to develop a transmission line circuit (TLC) model of the porous electrode consisting of the electrolyte resistance and the double-layer capacitance. Subsequently, a number of authors proposed modified TLC models for the impedance of porous electrodes on the basis of Levie s model. Bisquert (2000) reviewed the various impedance models for porous electrodes. The composite electrode layers prepared by the physical loading method could be successfully represented by the impedance model for porous electrodes, as shown in Fig. 6d this model is composed of the double-layer capacitance, Cj, the Warburg diffusion capacitance, W and the electrolyte resistance, 7 (Liu et al. 2012 Cha and Porfiri 2013). 

Figure 10.6 shows that the overall impedance of the system decreases after addition of plasticizer. The data are in agreement with the increase observed in ionic conductivity. From the parameters obtained by fitting the experimental data shown in Fig. 10.6, the apparent diffusion coefficient can be estimated using equation 10.7,where 4 is the thickness of the electrolyte film and 5 is a parameter related to the element O in the equivalent circuit proposed, which accounts for a finite-length Warburg diffusion (Zd), which represents a kind of resistance to mass transfer. 

Greszczuk et al. [252] employed the a.c. impedance measurements to study the ionic transport during PAn oxidation. Equivalent circuits of the conducting polymer-electrolyte interfaces are made of resistance R, capacitance C, and various distributed circuit elements. The latter consist of a constant phase element Q, a finite transmission line T, and a Warburg element W. The general expression for the admittance response of the CPE, Tcpr, is [253]... 

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