Porous electrode effects

H. Deng, M. Zhou and B. Abeles, Transport in solid oxide porous electrodes Effect of gas diffusion. Solid State Ionics, 80 (1995) 213-222. 

As with porous carbon double-layer capacitor devices, all the above pseudocapacitance systems are subject to the same RC time-scale restrictions on charging rates arising from the de Levie porous electrode effects which give rise to dispersion of capacitances with increase of charging rate or with respect to AV modulation rate (to) in studies of their impedance spectroscopy. 

It is to be noted (cf. Pajkossy [1994], Brug et al. [1984]) that the roughness-factor effect is really a Umiting case of the de Levie porous electrode effect The impedance spectrum for such systems can have a part that can be approximately modeled by a CPE having the 9 parameter equal to 0.5. 

Deng, H., Zhou, M., and Abeles, B., Transport in solid oxide porous electrodes effect of gas diSusion, Solid State Ionics, 1995, 80, 213-22. 

Fig. 8. Representation of the current distribution in porous electrodes showing the effect of conductivities of the electrolyte and electrodes where for (a)...

The effectiveness of a porous electrode over a plane surface electrode is given by the product of the active surface area S in cm /mL and the penetration depth Tp of the reaction process into the porous electrode. 

An effectiveness value greater than one indicates that the porous electrode is more effective than an electrode of the same geometric surface area, and that the reaction extends into the porous electrode stmcture. 

As in the case with PAFC s, voltage obtained from an AFC is affected by ohmic, activation, and concentration losses. Figure 4-7 presents data obtained in the 1960 s (18) which summarizes these effects, excluding ohmic losses, for a catalyzed reaction (0.5-2.0 mg noble metal/cm ) with carbon-based porous electrodes for H2 oxidation and O2 reduction in 9 N KOH at 55-60 C. The electrode technology was similar to that employed in the fabrication of PAFC electrodes. Performance of AFC s with carbon-based electrodes has not changed dramatically since these early results were obtained. 

Although the matrix may have a well-defined planar surface, there is a complex reaction surface extending throughout the volume of the porous electrode, and the effective active surface may be many times the geometric surface area. Ideally, when a battery produces current, the sites of current production extend uniformly throughout the electrode structure. A nonuniform current distribution introduces an inefficiency and lowers the expected performance from a battery system. In some cases the negative electrode is a metallic element, such as zinc or lithium metal, of sufficient conductivity to require only minimal supporting conductive structures. 

Recently, other CFD models have been published. The model of Siegel et al. ° used an agglomerate approach instead of the porous-electrode approach of the other CFD models. They showed that the agglomerate approach enables good comparisons to experimental data and showed the effects of agglomerate radius and membrane loading on perfor-... 

As noted in the Introduction, one of the defining characteristics of any fuel-cell model is how it treats transport. Thus, these equations vary depending on the model and are discussed in the appropriate subsections below. Similarly, the auxiliary equations and equilibrium relationships depend on the modeling approach and equations and are introduced and discussed where appropriate. The reactions for a fuel cell are well-known and were introduced in section 3.2.2. Of course, models modify the reaction expressions by including such effects as mass transfer and porous electrodes, as discussed later. Finally, unlike the other equations, the conservation equations are uniformly valid for all models. These equations are summarized below and not really discussed further. 

The other approach is more complicated and requires a deeper knowledge of the agglomerate structure or yields more fitting parameters. In this approach, the porous-electrode equations are used, but now the effectiveness factor and the agglomerate model equations are incorporated. Hence, eq 64 is used to get the transfer current in each volume element. The gas composition and the overpotential... 

However, there is another kind of influence on current distribution that may even the score. This is called secondary current distribution and describes the resistances set up at the interface of the working electrodes in a cell in which the interface tends to be polarizable. For example, it was shown [Eq. (7.36)] that when f) < RT/F, the interfacial resistance per unit area is RT/igF. If i0 is very small (e.g., 10-10 A cm-2, hence, an interfacial resistance cm-2 of 2.6 x 10 ohms), it is this interfacial resistance and not the ohmic resistance in the bulk solution that detennines the current distribution. Thus, in an extreme case of high solution concentration (low solution resistance) and low i q, a substantial fraction of the length of the pores in a porous electrode remains active.34 Considerations such as these, together with resistance effects at edges, all count in cell design. 

The most effective method of porous electrode preparation has been the deposition of aqueous dispersions of colloidal graphites and carbons on fibrous backing materials. 

The above equations for the diffusion coefficients do not take into account the volume fraction of porosity and the tortuous nature of the path through porous bodies. When the transport occurs through a porous body, as in fuel cell electrodes, effective diffusion coefficients accounting for the interaction of gaseous species with the porous matrix must be employed. Different theoretical approaches for the determination of the effective diffusion have been proposed in the literature. The Bruggemann correction allows the evaluation of these coefficients, through the following expression [47] ... 

In Figure 4.10, hydrogen and oxygen concentration at the electrode/electrolyte interface are shown. While a lower concentration of O2 is observed under the ribs, this is not the case forH2. This gas distribution can be explained considering that the diffusion in the porous electrodes is mainly affected by the following two effects ... 

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