Local polarization curve

Figure 41. Comparison of localized polarization curves between experiments (a) and model predictions (b) for a 50 cm DMFC with an anode flow stoichiometry of 27 and a cathode air stoichiometry of 5 at 0.1 A/cm. ...

Equation (154) gives the local polarization curve of individual segment at a distance z from the channel inlet. The set of curves for different z is shown in Fig. 27. 

Fig. 27 Local polarization curves at the indicated distances from the inlet of the oxygen channel (0 is at the inlet, 1 is at the outlet). Shown is the local polarization voltage versus local current density. All values are dimensionless.

We see that this simple model well describes the characteristic S-shaped profiles of local polarization curves far from the channel inlet, detected in experiments [197, 200]. Physically, these maxima result from the effect of oxygen starvation . Qualitatively, Eq. (154) shows that local current is a product of two factors. The preexponential factor a describes the growth of local current with the increase in rj due to exponential dependence of the rate constant of ORR on rj (Tafel law). The second (exponential) term in Eq. (154) describes oxygen consumption upstream from the given point z. 

The respective local current density is jt/fl) = zexp(-l )//T Clearly, t) exists if z > ft. The point z = ft thus separates the domains of monotonic and nonmonotonic local polarization curves [201], Note that if for some reason the local current in the monotonic domain is limited, the cell voltage exhibits oscillations [201],... 

In Section 6.2.2, we have shown that the general expression for local polarization curve can be approximated by Eq. (6.35). By analogy with (6.35), we may write down the following generalization of Eq. (6.47), valid for all currents in the cell ... 

This S-shape effect shows up only in the case of constant inlet velocity. It is easy to show that in the case of constant A local polarization curves are monotone. 

Figure 4.8 (a), (b) Experimental voltage-current curves at different points along a single flow channel (1 mm x 1 mm cross-section) on the cathode side of a fuel cell, for an air flow rate of 20 seem (a), and 50 seem (b). Hydrogen flow rate on anode of 25 seem. Cell temperature of 30 °C. Dimensionless distances along the channel are listed below each curve. Dotted line, average cell performance, (c) Theoretical local polarization curves (4.60) for the indicated dimensionless distances from the channel inlet. Parameters for these curves are listed in Tables 3.1 and 4.1. 

Equation (5.149) is a local polarization curve of the cell it includes a yet undefined parameter E. To calculate this parameter we equate two... 

FIGURE 5.6 (a) A local polarization curve of the cathode side of a PEFC (5.46) for the indicated values of the oxygen diffusion coefficient in the cathode GDL (cm s ). Both the curves correspond to infinite oxygen stoichiometry k = oo. (h) A polarization curve with the account of finite oxygen stoichiometry (5.59) for the indicated k and E/y = 0.02 cm s. The other parameters are listed in Table 5.7. 

To rationalize the effect of oxygen stoichiometry X on the potential loss, consider first the case of a small cell current. In this case, the local polarization curve is given by Equation 5.43. To calculate the polarization curve as a function of mean cell current density rjo (/), it is advisable to divide the terms under the logarithms in Equation 5.43... 

What is the effect of finite A, at high currents In this section, the case will be considered for poor oxygen diffusivity and ideal proton conductivity of the CCL. In this case, the local polarization curve of the CCL is given by Equation 4.87. Substituting Equation 5.41 into Equation 4.87, one obtains the local polarization curve with the term describing oxygen transport in the GDL ... 

At low inlet fluxes, Equation 5.174 holds and the local polarization curves of remote segments exhibit negative slopes (Kulikovsky et ah, 2004). In this case, the local impedance spectra of remote segments turn into quadrant di(Z) < 0, that is, they exhibit negative resistivity. 

To rationalize the effect, suppose that the local polarization curve of an individual segment is given by Equation 5.43, which contains Tafel activation overpotential (the first term) and the potential loss resulting from the oxygen transport in the GDL (the second term). 

At z > the second logarithm in Equation 5.188 is real, which means that fjo exists. Closer to the inlet, this logarithm is imaginary, that is, the local polarization curve has no turning point. With the data in Figure 5.29, z = 0.5. 

FIGURE 5.29 Local polarization curves at the indicated normalized distances z from the channel inlet (Equation 5.187). Parameters e = 100, M x = I ijim critical overpo-... 

If local impedance spectra are available. Equation 5.191 can be used to evaluate7. If, in addition, local polarization curves are measured, the curve for any segment with z > Zcrit can be used to determine one of the parameters b or /, provided that the other parameter is known from independent measurements. Indeed, withand at hand. Equation 5.192 gives b or i. Note that no fitting is necessary. Also note that the model of this section does not take into account the local flooding or membrane drying effects thus, care should be taken to avoid these effects in using the equations above for the interpretation of measurements. 

Critical overpotential for negative slope of the local polarization curve (V), Equation 5.188... 

Polarization curves were first measured for the whole surface as a function of the ageing time in 0.1 M H2SO4+O.OI M KSCN solution. The SVET was then used to measure the local polarization curve on single grains for samples with maximum ageing time, in order to obtain the polarization curves of the ferrite phase and to identify local variation in the degree of chromium depletion in the iron-rich region. 

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