Electrode thickness

Utilization in theory derived from Eq. (29) utilization in practice mainly depends on electrode thickness (cf. Ref. f 121). 

Curves showing the cnrrent densities as functions of x are presented for two val-nes of electrode thickness in Fig. 18.5. The parameter L has the dimensions of length it is called the characteristic length of the ohmic process. It corresponds approximately to the depth x at which the local current density has fallen by a factor of e (approximately 2.72). Therefore, this parameter can be nsed as a convenient characteristic of attenuation of the process inside the electrode. 

The net cnrrent density can be computed by integrating the volume current density over electrode thickness ... 

FIGURE 18.5 Current density distribution inside a porous electrode [according to Eq. (18.18)] for two values of electrode thickness dj = 0.33L , jj and dj =... 

Ukraine s Y. Maletin et al. presented a comprehensive overview describing state of the art as well as future development trends in supercapacitors, as the fifth paper in this chapter. The authors establish key performance bars for supecapacitors upon meeting those, supercapacitors may start to compete with batteries. Also, this paper highlights so-called hybrid applications where supercapacitors complement operation of batteries and/or fuel cells. Optimization of supercapacitor performance through varying electrode thickness is contemplated in length. 

In order to see how the electrode thickness might be optimized in order to provide the lowest electrode resistivity, we have developed a theoretical model to describe the charge/discharge processes in porous carbon electrodes. As a first approximation, let us consider an electrode having two sets of cylindrical pores, namely, nanopores (NP) of less than 3 nm in diameter and transport channels (TC) of more than 20 nm in diameter, with each nanopore having an exit to only one TC. ... 

Now let us consider a model for a SC device that comprises two electrodes (anode and cathode), each of them being electrically connected to a current collector fabricated of A1 foil. Let two of such collectors have a certain thickness of SAi- As an electrode material, an activated carbon powder is considered below. Anode and cathode are interposed with a separator of thickness Ss. The electrodes and separator are impregnated with electrolyte. In this paper we mostly focus on the optimization of SC performance by varying the electrode thickness, while some other effects will briefly be considered in the next section. 

From the practical point of view, this is the discharge of a SC device under constant power conditions that is normally of the most interest. That is why the present work is aimed at determining the optimum electrode thickness that enables one to obtain the maximum energy, E, output (referred to as unit of volume or mass) if the discharge with a fixed power takes place. For the sake of simplicity we will speak about the energy density (E) and power density (p), but all the expressions derived below can easily be transformed to obtain the specific energy or power, if the volume is substituted by mass. 

In contrast to battery technology, ultra thin electrodes cannot provide an increase in SC power density. Our theoretical model shows an optimum electrode thickness to exist in the range of 50-150 pm, the exact value depending on the porosity and nature of the electrode material. 

In addition to bilayered electrodes with a functional layer and a support layer, electrodes have also been produced with multilayered or graded structures in which the composition, microstructure, or both are varied either continuously or in a series of steps across the electrode thickness to improve the cell performance compared to that of a single- or bilayered electrode. For example, triple-layer electrodes commonly utilize a functional layer with high surface area and small particle size, a second functional layer (e.g., reference [26]) or diffusion layer with high porosity and coarse structure, and a current collector layer with coarse porosity and only the electronically conductive phase (e.g., reference [27]) to improve the contact with the interconnect. 

The increase of electrode thickness is an effective remedy to leaking gas, but is expensive and demonstrates some problems in the industrial production of the electrodes. The variation of the microstructure is also effective in principle, but is rather... 

More recent studies of dense LSM films appear to confirm these original conclusions as well as fill in some of the details.In particular, loroi and co-workers ° were able to produce very high quality films with clean, well-resolved impedances at 800—1000 °C in air, as shown in Figure 36. Consistent with bulk transport limitations, the impedance of these films was Warburg-like in shape and scaled properly with electrode area and electrode thickness, assuming an entirely bulk path. By extrapolating their results to zero film thickness, the authors also... 

Figure 47. Measured area-specific admittance (reciprocal of the polarization resistance Rp) as a function of electrode thickness for Pt/ESB and LSM/YSZ composite electrodes. Performance of the same electrode materials without an ionic subphase are also shown for comparison. Lines indicate fits to the model shown in Figure 48, as discussed in the text. (Reprinted with permission from refs 300 and 301. Copyright 1991 and 1992 The Electrochemical Society, Inc. and Elsevier, respectively.)...

Ceria, particularly when doped with Gd203 or SmzOs," has received some attention for direct hydrocarbon conversion in SOFC. Dating back to Steele and co-workers,interesting properties have been demonstrated for ceria-based anodes in direct utilization of methane. Later work suggested that the performance of ceria-based anodes in hydrocarbons could be improved by the addition of precious-metal catalysts, at dopant levels,but the performance of these cells was still too low for practical considerations. The problem with doped ceria is likely that its electronic conductivity is not sufficient. In general, the electrode material should have a conductivity greater than 1 S/cm in order to be practical since a conductivity of 1 S/cm would lead to a cell resistance of 0.1 Q cm for an electrode thickness of 1 mm, even... 

Figure 12. Effect of electrode thickness on performance of an oxygen-reducing laccase electrode (a) optimum current density, imax, at 0.5 V vs SHE and (b) optimum support porosity (e) and relative gas-phase porosity (eg/e) for carbon fiber supported electrodes optimized for (—) gas...

Figure 6. Charge storage utilization versus current density at —20°C for various initial water contents and electrode thickness, (reproduced with permission from Thompson et al.10)...

The analysis starts from the main assumption that diffusion within the electrodes occurs primarily along the electrode thickness and that the electrochemical reaction takes place at the electrode/electrolyte interface. The analysis is here conducted at steady-state. Under these assumptions, Equation (3.2), combined with Equation (3.47), after some calculation, becomes [82] ... 

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