DC Reversible Case

Equations of the faradaic impedance can be simplified assuming that the surface concentrations follow the Nemst law that is they correspond to the electro-chemical equilibrium after staying at a constant potential for a certain time while the ac concentrations corresponding to higher frequencies or shorter times are out of equilibrium. Using the Nemst equation  

In the particular case where initially only Ox species are present in the solution with bulk concentration C q, the surface concentrations may be calculated as functions of the electrode potential [17]  

4 Impedance of the Faradaic Reactions in the Presence of Mass Transfer 

The Warburg impedance is a function of and cannot be represented as a simple function of R, C, and L parameters. It contains real and imaginary parts of the same value, with the real part positive and the imaginary negative. Its phase angle is = atan(Z /Z ) = atan( 1) = —jt/2 = —45°. It is inversely proportional to the bulk concentration and depends on the electrode potential, but it is independent of any kinetic parameters. It can be shown thatZ has a minimum at E = 1/2. 

Similarly, under the same conditions of initial concentrations, the charge transfer resistance can also be presented  

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