Electrode kinetics charge transfer overvoltage

In 1989, Ekdunge and Simonsson published a model for the porous lead electrode in order to explain the limited discharge capacity at high rates of discharge [60]. They showed that the relationship between current and charge transfer overvoltage could be described by the kinetic expression... 

The charge-transfer kinetics of an electrochemical electrode can be formally treated on the basis of the Butler-Volmer equation. The overvoltage t/ct is then given by... 

Here we shall consider two components of this voltage balance in detail, ( + Ec) and and merely mention overpotentials (for a reversible charge transfer step) and overvoltages (nonreversible step) resulting from the polarization of electrodes. Overvoltages (overpotentials) are a function of electrode kinetics and electrode material and are discussed in Chapter 3. 

We will consider only the influence of activation overpotential or overvoltage on secondary current distribution. It is useful to regard the slope of the polarization curve dE /di (if any effect of concentration overpotential can be ignored) as a polarization resistance R. This represents the slowness of charge transfer across the interface and is based on the electrode kinetics of the reaction. If acts in series with R, the resistance of the electrolyte, we can distinguish between two situations. If R R, then the kinetics of charge transfer and not electrolyte resistance determine the current distribution, i.e., secondary current distribution dominates. Conversely, if R R, primary current distribution dominates. Secondary current distributions tend to smooth out the severe nonlinear variations of current associated with primary distributions and they eliminate infinite currents associated with electrode edges. 

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