Regime Two Limiting Cases

The voltage response of the CCL in the intermediate regime is dictated by the double Tafel slope term, -qo 2b In jo. This regime leads to similar expressions for reaction penetration depth and differential CCL resistance in the limiting cases of (i) rapid proton conduction and poor oxygen diffusion (g 1) and (ii) rapid oxygen diffusion and poor proton conduction (g 1). 

In the first case (g 1), the reaction penetration depth and the differential resistance of the layer are given by 

It should be emphasized that the characteristic lengths Id and / are independent of IcL, as they should be. This becomes obvious when the scaling of the characteristic current densities is considered / a and f x let-Intrinsic lengths and differential 

The reaction penetration depths. Id or la, are highly insightful parameters to evaluate catalyst layer designs in view of transport limitations, uniformity of reaction rate distributions, and the corresponding effectiveness factor of Pt utilization, as discussed in the sections Catalyst Layer Designs in Chapter 1 and Nonuniform Reaction Rate Distributions Effectiveness Factor in Chapter 3. Albeit, these parameters are not measurable. The differential resistances, Rd or Ra, can be determined experimentally either as the slope of the polarization curve or from electrochemical impedance spectra (Nyquist plots) as the low-frequency intercept of the CCL semicircle with the real axis. The expressions in Equation 4.33 thus relate the reaction penetration depths to parameters that can be measured. 

---