Regimes of Electrode Operation

This equation is the simplest polarization curve of the CCL, demonstrating a typical exponential dependence of the converted current density on the cathode overpotential. Solving Equation 1.75 for t]q results in 

Note that/ is the exchange current density per surface area of the porous electrode. It is related to the intrinsic exchange current density / of the catalyst as f = where pt is the specific catalyst surface in the electrode per cm of electrode area. 

At small current densities, jo and t]o/b are small, the reverse reaction cannot be neglected, the exponent in Equation 1.75 should be replaced by 2sinh( o/ ), and Equation 1.76 transforms to 

Finally, at small cell current densities, expansion of the arcsinh function simplifies Equation 1.77 to 

The variation of proton current density along x is due to the proton consumption in the ORR at a rate given by the right-hand side. 

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