Diffusion to a planar electrode

Figure 18 (a) Model of the linear diffusion to a planar electrode for the faradaic process... 

Diffusion to a Planar Electrode. The basic approach in controlled-potential methods of electrochemistry is to control in some manner the potential of the working electrode while measuring the resultant current, usually as a function of time. When a potential sufficient to electrolyze the electroactive species completely is applied to the electrode at (t = 0), the concentration at the electrode surface is reduced to zero and an electrode process occurs, for example... 

Figure 3.1 Concentration-distance curves for different periods of linear diffusion to a planar-electrode surface. Diffusion times (1) 10 s (2) 100 s (3) 1000 s (4) 10,000 s. Data for a diffusion coefficient D of 1 x 10-5 cm2 s 1.

In practice two methods are used for stationary planar electrodes in quiescent solution chronoamperometry and chronopotentiometry. By use of an electroactive species whose concentration, diffusion coefficient, and n value are known, the electrode area can be calculated from the experimental data. In chronoamperometry, the potential is stepped from a value where no reaction takes place to a value that ensures that the concentration of reactant species will be maintained at essentially zero concentration at the electrode surface. Under conditions of linear diffusion to a planar electrode the current is given by the Cottrell equation [Chapter 3, Eq. (3.6)] ... 

The mercury-pool electrode. Mercury pools of sufficient diameter to approach a planar configuration obey the equations derived for linear diffusion to a planar electrode. This has certain theoretical advantages because of the large number of equations that have been derived for the planar electrode geometry, especially in terms of constant-current chronopotentiometry and linear-potential sweep chronoamperometry. 

The example to be given is semi-infinite linear diffusion to a planar electrode—concentration variation is only perpendicular to the electrode. Fick s second law is... 

Fig. 7.6 Concentration profile for diffusion to a planar electrode (xp corresponds to Ljjff in the text). (After ref. [2])...

Figure 4.4.5 Types of diffusion occurring at different electrodes. (a) Linear diffusion to a planar electrode, (b) Spherical diffusion to a hanging drop electrode.

As in the previous section, we have assumed semi-infinite linear diffusion to a planar electrode throughout the mathematical discussion here. With a reversible dc process, the effects of sphericity and drop growth at the DME are exactly as discussed in Section... 

We have seen already that under the conditions of a typical dc po-larography experiment the analyte approaches the spherical mercury drop under diffusion control. An equation is required which relates the current developed by this diffusion mechanism to the analyte concentration in the bulk solution. Such an equation has been avilable for diffusion to a planar electrode since 1902. It was derived by Cottrell and takes the form,... 

Fig. 2. Graph showing how voltammetric peak current is expected to diminish with increasing molecular weight in the case of redox-active spherical molecules diffusing to a planar electrode. PCMH = p-cresol-methylhydroxylase (see Sect 7.3)...

This is the quiet-solution experiment discussed in Section 1.2 with the current response shown in Fig. 2A. App is instantaneously switched from an initial value (open circuit or a value at which no electrolysis is occurring) to slightly past p, held constant for a fixed time, then normally switched off or back to E. If material diffuses to a planar electrode surface in only one direction (linear diffusion), then the exact description of the current-time curve is given by the Cottrell equation ... 

Third, an equally serious objection is that in the experiment discussed above the equations used are for semi-infinite linear diffusion to a planar electrode. This obviously is not the case for a disordered polymer. In fact, in the resits mentioned above [61] the current does not obey the Cottrell equation but instead has a dependence where 0 < a < I. This is, in fact, the behavior expected for irregular surfaces, and this makes the evaluation of the transport parameter more complicated. Thus the diffusion coefficients reported in the literature may be in considerable error. The behavior has been discussed by Pajkossy and Nyikos [64] in the context of diffusion to a fractal surface. The experimental support for this is discussed in the following paragraphs. 

Considering diffusion to a planar electrode with a surface area increasing with time for description of the transport to a growing mercury drop, Ilkovic derived for the mean limiting diffusion current (i(j) Equation 1, bearing his name ... 

On the other hand it should be noted that Equation (1.40) has been derived from a model which assumes linear diffusion to a planar electrode. In the laboratory we cannot use electrodes that are flat on a molecular level or of infinite... 

Figure 2.7 (a) Cyclic voltammograms simulated assuming two-dimensional semi-infinite diffusion to an inlaid disk electrode (—) (electrode A in Eigure 2.1) and one-dimensional diffusion to a planar electrode (--) (electrode B in Eigure 2.1) and the corresponding semiinte-... 

Figure 11.5 Cyclic voltammogram and corresponding O and R concentration profiles for diffusion to a planar electrode. Numbers on the concentration profiles correspond to the numbered points on the voltammogram.

Nonstationary Linear Diffusion to a Planar Electrode Under Electrostatic Conditions... 

Fig. 5.9 Relationship between the process rate and time for nonstationary diffusion to a planar electrode (potentiostatic electrolysis)...

The initial and boundary conditions have the same physical meaning as the ones previously used for nonstationary diffusion to a planar electrode. Initially (when f = 0), the concentration of oxidized form at any distance from the electrode equals its bulk value (initial condition) ... 

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