Inner surface impedance

After the oxidation a considerable part of the inner micropore surface contributes to the double layer. In order to estimate the "created inner surface area the capacitance of micropore per unit surface has to be known. According to Probstle et al. [5] this capacitance is 6 nFjcm. By disregarding pseudo capacitance, a specific inner micropore surface accessible for 5 04 -ions can be estimated now from the measured specific capacitance. The maximum specific capacitance of 12.-5 F/g yield from impedance spectroscopy at G.l Hz gives an inner surface of 208 m jg. 

All applications of aerogels make use of their high porosity, which is responsible for the low index of refraction, the small Young s modulus, the low acoustic impedance, the low thermal conductivity, and the excellent accessibility of the inner surface. In addition, in some applications the high optical transparency is of importance. 

The models that consider this approach are largely based on the assumption of effectively homogeneous local relaxation processes related to transport in each of the phases and electrical charge exchange between them. Thus, the complex problem of an uneven distribution of electrical current and potential inside the electrode can be described analytically, and impedances can be calculated. Furthermore the models may be conveniently pictured as a double-channel transmission line (Fig. 3.5). In several papers, the theory of the impedance of porous electrodes has been extended to cover those cases in which a complex frequency response arises in the transport processes [100] or at the inner surface [194,203]. 

In a modified version, a perovskite electrolyte (SrCeOs doped with 5 mol% Yb) in the form of a tube was coated with a layer of impermeable Au-Pd alloy to allow access to oxygen gas on the outer surface, while impeding H2O transfer. The inner surface coated with platinum is exposed to both H2O and oxygen (Kumar et al. 1996, Cobb et al. 1996, Fray et al. 1995, Kumar 1997). 

Bcu/h-ft ). While the surfaces, Sheetrock, and siding each impede heat flow, 80 percent of the resistance to heat flow in this wall comes from the insulation. If the insulation is removed, and the cavity is filled with air, the resistance of the gap will be 0.16 (W/m -°C)" (0.9 (Btu/h-ft -T)" ) and the total resistance of the wall will drop to 0.54 (W/m -°C)" (3.08 (Btti/h-ft -°F)" ) resulting in a heat flow of 38.89 W/m (12.99 Btu/h-fr). The actual heat flow would probably be somewhat different, because the R-value approach assumes that the specified conditions have persisted long enough that the heat flow is steady-state, so it is not changing as time goes on. In this example the surface resistance at the outer wall is less than half that at the inner wall, since the resistance value at the outer wall corresponds to a wall exposed to a wind velocity of about 3.6 m/s (8 mph), which substantially lowers the resistance of this surface to heat flow. 

The double-layer structure at the electro-chemically polished and chemically treated Cd(OOOl), Cd(lOlO), Cd(1120), Cd(lOh), and Cd(1121) surface electrodes was studied using cyclic voltammetry, impedance spectroscopy, and chronocoulometry [9, 10]. The limits of ideal polarizahility, Epzc, and capacity of the inner layer were established in the aqueous surface inactive solutions. The values of iipzc decrease, and the capacity of the inner layer increases, if the superficial density of atoms decreases. The capacity of metal was established using various theoretical approximations. The effective thickness of the thin metal layer increases in the sequence of planes Cd(1120) < Cd(lOiO) < Cd(OOOl). It was also found that the surface activity of C104 was higher than that of F anions [10]. 

Basically, the impedance behavior of a porous electrode cannot be described by using only one RC circuit, corresponding to a single time constant RC. In fact, a porous electrode can be described as a succession of series/parallel RC components, when starting from the outer interface in contact with the bulk electrolyte solution, toward the inner distribution of pore channels and pore surfaces [4], This series of RC components leads to different time constant RC that can be seen as the electrical response of the double layer charging in the depth of the electrode. Armed with this evidence, De Levie [27] proposed in 1963 a (simplified) schematic model of a porous electrode (Figure 1.24a) and its related equivalent circuit deduced from the model (Figure 1.24b). 

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