Impedance of Ideally Polarizable Porous Electrodes

Pore geometry influences the shape of impedance plots. In what follows, various pore geometries will be presented. First, the ohmic drop in solution only will be taken into account, and later the ohmic drop in solution and in the electrode material will be considered [407]. 

1 Cylindrical Pore with Ohmic Drop in Solution Only fide = 0,r = 0, r 0) 

The simplest model involves a cylindrical pore with length / and radius r filled with 

The ac current I enters the pore and flows to the walls. Because of the ohmic drop in the solution, inside the pore it decreases with the penetration depth and its amplitude decreases as it flows to the walls as j. An equation for the impedance of the cylindrical pore was developed by de Levie [408]. The following assumptions were made  

The specific impedance of the pore walls is Zei = /jeoCQ cm ), where 

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Fig. 9.14 Transmission representing impedance of ideally polarizable porous electrode in presence of solution and electrode resistance and are resistances of small sections of solution and electrode, respectively, and is the double-layer capacitance of such a section...

According to the theory of de Levie, the impedance complex plane plots of an ideally polarizable porous electrode take the form shown in Figure 27.1 la. 

In the industrial applications of electrochemistiy, the use of smooth surfaces is impractical and the electrodes must possess a large real surface area in order to increase the total current per unit of geometric surface area. For that reason porous electrodes are usually used, for example, in industrial electrolysis, fuel cells, batteries, and supercapacitors [400]. Porous siufaces are different from rough surfaces in the depth, /, and diameter, r, of pores for porous electrodes the ratio Hr is very important. Characterization of porous electrodes can supply information about their real surface area and electrochemical utilization. These factors are important in their design, and it makes no sense to design pores that are too long and that are impenetrable by a current. Impedance studies provide simple tools to characterize such materials. Initially, an electrode model was developed by several authors for dc response of porous electrodes [401-406]. Such solutions must be known first to be able to develop the ac response. In what follows, porous electrode response for ideally polarizable electrodes will be presented, followed by a response in the presence of redox processes. Finally, more elaborate models involving pore size distribution and continuous porous models will be presented. 

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