The faradaic current response to a single potential step

2 The faradaic current response to a single potential step 

As argued earlier (Sect. 1.2), the initial potential Et either equals the equilibrium potential determined by eqn. (10), if the initial concentrations Cq and c are finite, or, in the case where c = 0 or Cq — 0, Ei can be fixed to a given value by means of the potentiostat. In the latter case, Ei is chosen to be in the so-called non-faradaic region where the faradaic current equals zero. For example, if only O is initially present, we take E E°, so that the rate of reduction is negligibly small. Consequently, the boundary conditions formulated in eqn. (19c) are valid in both cases. 

After a stepwise change of the potential from Ei to a value E within the faradaic region, where kf and/or kb have a substantial value, a current with density jF will start to flow and the interfacial concentrations will change with time. In the simple case adopted for this section, eqn. (18) 

The error function, erf (z) and its complement, erfc (z) — 1 — erf (z) are frequently encountered in the solution of diffusion problems. They can be handled numerically using their tabulated values [42], or graphical representations, or preferably by means of computer algorithms as, for example, recently published by Oldham [43]. 

The function exp (Pt) erfc (ltin) has been plotted against lt1/2 in Fig. 10. It follows that the extrapolated value of jF at t - 0 is equal to — nFkf [cq cr exp (ip)], i.e. the current that flows in the absence of rate control by diffusion, see eqn. (18). At the current approaches 

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