Ideal oxygen transport

Care should be taken when using this relation in the limiting case of ideal oxygen transport. In this case Z) —> oo, while cq —> 1 so that the product D 1 — Co) is finite. 

In dimension variables this equation has the form (2.29), obtained above for an ideal catalyst layer. As seen, Eq. (2.29) holds when oxygen transport is ideal, 1 and jo > 2. The notion of ideal oxygen transport will be rationalized in Section 2.5. 

A sufEcient condition for the approximation of ideal oxygen transport is infinity of oxygen diffusivity D oo. A numerical study of the full system (2.10)-(2.12) (Section 2.5) enables us to formulate a more accurate criterion. The contribution of oxygen transport to the total voltage loss can... 

Equation (2.76) coincides with Eq. (2.49) derived in the case of ideal oxygen transport at small current. Small C is equivalent to small fjo or a large diffusion coefficient in both cases oxygen transport does not contribute to... 

One of the variables fj or j can be eliminated from the system of Equations 4.53 through 4.55. Usually, it is convenient to eliminate overpotential (the section Ideal Oxygen Transport ). The resulting system of equations for j and c should be supplemented by the following boundary conditions ... 

It is seen that b disappears and Equation 4.80 coineides with Equation 4.129, derived below, for the case of ideal oxygen transport at the small current. Small fo means small fjo or large diffusion coefficient. In both these cases, the oxygen transport does not eontribute to the potential loss. The respective polarization plots cover linear and Tafel regions (Figure 4.15, lower solid curves). 

This is the general polarization curve of the CCL with ideal oxygen transport for the case of large Equation 4.128 describes normal Tafel kinetics at small currents, double Tafel kinetics at large currents and the transition region between these two regimes. Moreover, this equation reduces to a correct limit at jo -> 0. 

FIGURE 4.18 The exact numerical (open circles) and the analytical (sohd hue, Equation 4.128) polarization curves of the CCL with the ideal oxygen transport. Dashed lines the low- and high-current curves. Equations 4.129 and 4.133, respectively. The exact numerical points are calculated with y heing the exact solution to Equation 4.122, while the analytical curve (4.128) is calculated with the approximate y given hy Equation 4.127. The current density is normalized to j = Opb/lci- Parameter ci = 1 and e = 100 (PEEC cathode. Table 5.7). Note the transition from normal to double Tafel slope at the current densities around io = 2. 

In this section, the assumption is made that the rate of oxygen transport through the CCL is large and, in addition, the square of the cell current density is much larger than(Equation 4.116). In that case, the electrochemical conversion typically occurs in one of the two regimes discussed in the section Ideal Oxygen Transport. ... 

Substituting Equations 5.69 and 5.70 into the first term in Equation 5.68, results in the cell polarization curve under ideal oxygen transport in the GDL ... 

In the general case, a full analytical solution to the system (5.91) and (5.92) can hardly be obtained. Part of the problem is that the general analytical steady-state solutions if and c have not been found yet. However, in the limiting case of ideal oxygen transport, an explicit steady-state function rf(jc) has been derived in the section The Case of -C 1 and 1. This allows analyzing the system (5.91) and (5.92),... 

FIG U RE 5.14 The impedance spectra of the CCL with an ideal oxygen transport in (a) normal Tafel, (b) and (c) double Tafel regimes for the indicated values of the dimensionless cell current densityy o, with (c) the high-frequency domain (linear branch) of the spectra in (b). Parameters for the calculations are listed in the second (PEFC) column of Table 5.6. 

Numerical calculations show that in the regime with ideal oxygen transport, the impedance spectra are independent of e. To understand the parametric dependencies, it is insightful to analytically solve a low-current version of Equation 5.111. 

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