The large amplitude potential step method

The linear rate equation, eqn. (18), was assumed to hold throughout Sect. 2 because it is the most simple case from a mathematical point of view. Evidently, it is valid in the case of the linear mechanism (Sect. 4.2.1) as it is also in some special cases of a non-linear mechanism (see Table 6 and ref. 6). The kinetic information is contained in the quantity l, to be determined either from the chronoamperogram [eqn. (38), Sect. 2.2.3] or from the chronocoulogram [eqn. (36), Sects. 2.2.2 and 2.2.4], A numerical analysis procedure is generally preferable. The meaning of l is defined in eqn. (34), from which ks is obtained after substituting appropriate values for Dq2 and for (Dq/Dr)1/2 exp ( ) = exp (Z) [so, the potential in this exponential should be referred to the actual standard potential, see Sect. 4.2.3(a)]. 

A plot of In kf vs. potential (in fact, this is a Tafel plot) will be curved in the case of a linear mechanism with more than one rate-determining step. It is of the utmost importance to cover a large potential range. However, in the potential step method, l values exceeding ca. 200 s 1/2 cannot be determined and the accessible potential range is correspondingly limited. 

If the electrode reaction proceeds via a non-linear mechanism, a rate equation of the type of eqn. (123) or (124) serves as a boundary condition in the mathematics of the diffusion problem. Then, a rigorous analytical derivation of the eventual current—potential characteristic is not feasible because the Laplace transfrom method fails if terms like Co and c are present. The most rigorous numerical approach will be 

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