The Coulostatic Charge-Injection Method

Consider the application of a very short current pulse to the interface. The charge g = j X tp injected during the pulse changes the potential across the double-layer 

We shall treat here the simplest case, in which the pulse duration is very short compared to the time constant for charging the double-layer capacitance, (tp/Xc l) and diffusion limitation can be ignored. Under such conditions, no Faradaic reaction takes place during the charging pulse. Once on open circuit, the capacitor will be discharged through the Faradaic resistor, It is easy to derive the form of the decay transient. On the one hand, the current is given by  

On the other hand, since we are dealing with small perturbations, it is also given by jonFr] T] 

Remember that the current density in Eq. (14.15) is an internal current, since the decay of overpotential is followed at open circuit. It is also interesting to note here that during the charging pulse, Cji and Rp are effectively connected in parallel, while during open-circuit decay the same two circuit elements must be considered to be connected in series, and the same (internal) current is flowing through both. 

The relaxation time for charge transfer, can be obtained from the slope of a plot of 

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