Cylindrical porous electrode model impedance

The random structure of the porous electrode, illustrated in Figure 13.11(a), leads to a distribution of pore diameters and lengths. Nevertheless, the porous electrode is usually represented by the simplified single-pore model shown in Figure 13.11(b) in which pores are assumed to have a cylindrical shape with a length i and a radius r. The impedance of the pore can be represented by the transmission... 

The frequency dispersion of porous electrodes can be described based on the finding that a transmission line equivalent circuit can simulate the frequency response in a pore. The assumptions of de Levi s model (transmission line model) include cylindrical pore shape, equal radius and length for all pores, electrolyte conductivity, and interfacial impedance, which are not the function of the location in a pore, and no curvature of the equipotential surface in a pore is considered to exist. The latter assumption is not applicable to a rough surface with shallow pores. It has been shown that the impedance of a porous electrode in the absence of faradaic reactions follows the linear line with the phase angle of 45° at high frequency and then... 

The cylindrical pore model is an idealization of a real porous electrode. Other pore geometries were also studied. De Levie [413] obtained an analytical solution for the impedance of V-grooved pores. Such pores might be obtained, for example, by scratching the electrode surface. A cross section of such a groove is displayed in Fig. 9.8. Its impedance per unit of groove length is... 

Several important technological applications, such as battery devices and electrocatalysis, need a very large effective surface of contact between the electrode and the electrolyte. This expanded surface can be developed on porous electrode surfaces. The complexity of the random structure of the porous electrode and various experimental situations related to mass-transport impedance in the pores, coupled with interfacial kinetics inside the pores, led investigators initially to investigate simple single-pore models. Of the possible shapes modeled, the cylindrical pore with a length I and a radius r has been... 

As the first approximation, impedance of a porous electrode can always be considered as a series combination of two processes—a mass-transport resistance inside the pores and impedance of electrochemical reactions inside the pores. De Levie was the first to develop a transmission line model to describe the frequency dispersion in porous electrodes in the absence of internal diffusion limitations [66]. De Levie s model is based on the assumption that the pores are cylindrical, of uniform diameter 2r and semi-infinite length /, not intercoimected, and homogeneously filled with electrolyte. The electrode material is assumed to have no resistance. Under these conditions, a pore behaves like a imiform RC transmission line. If a sinusoidal excitation is applied, the transmission line behavior causes the amplitude of the signal to decrease with the distance from the opening of the pore, and concentration and potential gradients may develop inside the pore. These assumptions imply that only a fraction of the pore is effectively taking part in the double-layer charging process. The RpQi i- [ohm] resistance to current in a porous electrode structure with number of pores n, filled with solution with resistivity p, is ... 

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