Large-amplitude potential step

A straightforward solution of the set of equations formulated above is only possible if all boundary conditions are of first order in cG (0, t) and cR (0, f), i.e. if the adsorption of O and R obey linear isotherms 

The reader is invited to derive for himself the resulting expression for -jF (s)/nF = v s) 

The inverse transformation of this function is performed analogously to that of eqn. (157) in Sect. 5.2.1. Note that the term in s3/2 in the denominator disappears if only one of the reactants is adsorbed, i.e. if ko or kR equals zero. 

Other explicit examples will not be treated here. Instead, it is preferred to indicate the route by which many cases may be elaborated, as proposed by Reinmuth [28] and more extensively by Guidelli [75], whose reasonings will be followed here. In fact, Guidelli s treatment has been set up more generally and is applicable in the case of linear diffusion, spherical diffusion, and diffusion towards the expanding planar electrode (i.e. the dropping mercury electrode). Here, we confine ourselves to linear diffusion. 

After dividing both members of eqns. (166a) and (166b) by s, the convolution theorem (see Sect. 2.5.1) is applied to find their counterpart in the time domain. 

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The unusual cyclic voltammograms and responses to large-amplitude potential steps of a variety of conducting polymer films have prompted a number of groups to develop nucleation models for their oxidation. The key features that they have sought to explain are the peaks observed in anodic chronoamperometry (see Fig. 14), and the dependence of the anodic peak position on scan rate207 and the time spent in the undoped state.20 ... 

A good understanding of this behaviour requires expressions for the potential dependency of R ct, a, and p = Rctla. For this purpose, we will suppose that the mean perturbation is a series of large-amplitude potential steps of the kind treated in Sect. 2.2.5. As we did in that section, two cases will be distinguished, namely d.c. reversible and non-d.c. reversible behaviour. 

Large-amplitude potential step rigorous approach... 

Large-amplitude potential step diffusion layer approximation... 

The conditions defined to this point apply for any situation in which the solution is uniform before the experiment begins and in which the electrolyte extends spatially beyond the limit of any diffusion layer. The final condition defines the experimental perturbation. In the present case, we are considering a large-amplitude potential step, which drives the surface concentration of O to zero at the electrode surface after t = Q. 

The current-time relationship for a UME disk spans three regimes, as shown in Figure 5.3.2. If the experiment remains on a short time scale (Figure 5.3.2a), so that the diffusion layer remains thin compared to tq, the radial diffusion does not manifest itself appreciably, and the diffusion has a semi-infinite linear character. The early current flowing in response to a large amplitude potential step is therefore the Cottrell current,... 

Although there are some important differences in the behavior of UMEs with different shapes, it is useful here to recollect some common features in the responses to a large-amplitude potential step ... 

The consecutive reduction of two substances O and O in a potential scan experiment is more complicated than in the potential step (or sampled-current voltammetric) experiment treated in Section 5.6 (15, 16). As before, we consider that the reactions O ne and O + n e R occur. If the diffusion of O and O takes place independently, the fluxes are additive and the i-E curve for the mixture is the sum of the individual i-E curves of O and O (Figure 6.6.1). Note, however, that the measurement of /p must be made using the decaying current of the first wave as the baseline. Usually this baseline is obtained by assuming that the current past the peak potential follows that for the large-amplitude potential step and decays as A better fit based on an equation with two adjustable parameters... 

If a large amplitude potential step is applied, we write... 

As outlined previously, if a large-amplitude potential step is applied, then we can replace the parameter Ac in eqn. 272 with c to obtain... 

Electrochemical impedance spectroscopy was also used by Randria-mahazaka, Chevrot, and colleagues to study the responses of PEDOT (elec-trodeposited from acetonitrile solution on platinum) in EMTBTI. The results indicated two coexisting zones (compact and more open) in the PEDOT film. Consistently, two parallel diffusion paths with two time constants—for a slow and a fast process—are observed in accordance with chronocoulomet-ric experiments. The results could be further confirmed by the same group, using detailed large amplitude potential step experiments. Relaxation kinetics revealed that the time constant of the slow process was virtually independent of the film thickness, whereas the fast process depended upon the PEDOT film thickness. The kinetics for the oxidation were found to be faster than that of reduction. 

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