Warburg impedances, conductance/capacitance

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]... 

It is evident that the shape of the impedance spectra varies with the potential since the values of the charge transfer resistance (Ret), the low frequency (redox) capacitance (Cl) and the Warburg coefficient change with the potential more exactly, they depend on the redox state of the polymer. In many cases D is also potential-dependent. The double-layer capacitance (Cdi) usually shows only slight changes with potential. The ohmic resistance (Rq) is the sum of the solution resistance and the film resistance, and the latter may also be a function of potential due to the potential-dependent electron conductivity, the sorption of ions, and the swelling of the film. In Fig. 3.9 three spectra are displayed, which were constructed using the data obtained for a PTCNQ electrode at three different potentials near its equilibrium potential [23]. 

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). 

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