Anodic diffusion control

Expressions for the cathodic and anodic diffusion-controlled limiting currents, Tjj1 6 and can be easily obtained from Eq. (2.27) by making e. 1 0 and e > oo... 

Fig. 4.9 Influence of relative positions and shapes of anodic and cathodic polarization curves on the corrosion current, lcorr. (a) Anodic diffusion control, (b) Cathodic diffusion control, (c) Anodic and cathodic diffusion control. Ecorr and lcorr refer to corrosion under diffusion control. (Ecorr) and (lcorr) refer to corrosion without diffusion control.

Fig. 3.13 Influence of diffusion-controlled polarization curves on the mixed potential of corroding systems (a) cathodic diffusion control and (b) anodic diffusion control.

In tlie polarization curve of figure C2.8.4 (solid line), tlie two regimes, activation control and diffusion control, are schematically shown. The anodic and catliodic plateau regions at high anodic and catliodic voltages, respectively, indicate diffusion control tlie current is independent of tlie applied voltage and7 is reached. 

Figure C2.8.4. The solid line shows a typical semilogaritlimic polarization curve (logy against U) for an active electrode. Different stages of reaction control are shown in tlie anodic and catliodic regimes tlie linear slope according to an exponential law indicates activation control at high anodic and catliodic potentials tlie current becomes independent of applied voltage, indicating diffusion control.

Under diffusion-controlled dissolution conditions (in the anodic direction) the crystal orientation has no influence on the reaction rate as only the mass transport conditions in the solution detennine the process. In other words, the material is removed unifonnly and electropolishing of the surface takes place. 

It also follows that if the solution is stirred the rate of arrival of oxygen at the cathode will be increased. This will result in a corresponding increase in the rate of bimetallic corrosion as is shown in Fig. 1.63 for the aluminium-mild steel couple in stirred 1 - On NaCl solution . The increase in galvanic corrosion rate will be in the inverse relation to the slope of the anodic polarisation curve of the more negative metal, provided that the cathodic reaction is not totally diffusion controlled. 

Fig. 3. Evans-diagram for the cementation of Cu2+ and Pb2 with zinc amalgam of different zinc content. If the zinc concentration in the mercury employed for this special extraction technique is low, the anodic zinc-dissolution current density may be diffusion controlled and below the limiting cathodic current density for the copper reduction. The resulting mixed potential will lie near the halfwave potential for the reaction Cu2+ + 2e j Cu°(Hg) and only Cu2 ions are cemented into the mercury.

After polarization to more anodic potentials than E the subsequent polymeric oxidation is not yet controlled by the conformational relaxa-tion-nucleation, and a uniform and flat oxidation front, under diffusion control, advances from the polymer/solution interface to the polymer/metal interface by polarization at potentials more anodic than o-A polarization to any more cathodic potential than Es promotes a closing and compaction of the polymeric structure in such a magnitude that extra energy is now required to open the structure (AHe is the energy needed to relax 1 mol of segments), before the oxidation can be completed by penetration of counter-ions from the solution the electrochemical reaction starts under conformational relaxation control. So AHC is the energy required to compact 1 mol of the polymeric structure by cathodic polarization. Taking... 

When a polymer relaxes at a constant anodic potential, the relaxation and partial opening of the polymeric structure involve a partial oxidation of the polymer. Once relaxed, the oxidation and swelling of the relaxed polymer goes on until total oxidation is reached this is controlled by the diffusion of the counter-ions through the film from the solution. This hypothesis seems to be confirmed by the current decay after the chronoam-perometric maximum is reached. We will focus now on the diffusion control. 

Equations (37) and (38), along with Eqs. (29) and (30), define the electrochemical oxidation process of a conducting polymer film controlled by conformational relaxation and diffusion processes in the polymeric structure. It must be remarked that if the initial potential is more anodic than Es, then the term depending on the cathodic overpotential vanishes and the oxidation process becomes only diffusion controlled. So the most usual oxidation processes studied in conducting polymers, which are controlled by diffusion of counter-ions in the polymer, can be considered as a particular case of a more general model of oxidation under conformational relaxation control. The addition of relaxation and diffusion components provides a complete description of the shapes of chronocoulograms and chronoamperograms in any experimental condition ... 

The charge consumed by oxidation swelling under diffusion control, once the structure is relaxed, depends on the anodic potentials applied at each moment. The process can be quantified by Fick s law ... 

Figure 26 shows the redox potential of 40 monolayers of cytochrome P450scc on ITO glass plate in 0.1 KCl containing 10 mM phosphate buffer. It can be seen that when the cholesterol dissolved in X-triton 100 was added 50 pi at a time, the redox peaks were well distinguishable, and the cathodic peak at -90 mV was developed in addition to the anodic peak at 16 mV. When the potential was scanned from 400 to 400 mV, there could have been reaction of cholesterol. It is possible that the electrochemical process donated electrons to the cytochrome P450scc that reacted with the cholesterol. The kinetics of adsorption and the reduction process could have been the ion-diffusion-controlled process. 

In such systems the researcher can electrochemically clean and precondition the metal electrode before each run to provide an identical surface for the anodic and the cathodic half-reactions as well as for the catalytic reaction between them. Use of a rotating disk electrode/ckatalyst also allows surface- and diffusion-controlled processes to be easily distin-guished. ... 

The first cathodic wave was studied by cycling the potential across it at various scan rates and the peak potentials were found to increase as indicative of a reversible, diffusion-controlled system, with ° = — 1.43 V vs. SCE. However, at sweep rates 20mV/s the peak anodic current is much smaller than expected which was interpreted by the authors as indicating that the reduced species undergoes a subsequent chemical reaction, i.e. an EC process. 

In a detailed rotating-disk electrode study of the characteristic currents were found to be under mixed control, showing kinetic as well as diffusional limitations [Ha3]. While for low HF concentrations (<1 M) kinetic limitations dominate, the regime of high HF concentrations (> 1 M) the currents become mainly diffusion controlled. However, none of the relevant currents (J1 to J4) obeys the Levich equation for any values of cF and pH studied [Etl, Ha3]. According to the Levich equation the electrochemical current at a rotating disk electrode is proportional to the square root of the rotation speed [Le6], Only for HF concentrations below 1 mol 1 1 and a fixed anodic potential of 2.2 V versus SCE the traditional Levich behavior has been reported [Cal 3]. 

At this point, depending on whether or not the experimental data (i.e. the ratio between the anodic currents at the times t and the cathodic currents at the times t—x) follow the diagram reported in Figure 49, valid for Ox/Red couples that undergo diffusion-controlled processes, one can... 

When the cathodic reaction is the reduction of oi n molecules for which the equilibrium potential is relatively high (much more anodic than the corrosion potential), the corrosion current is frequently controlled by the diffusion of hydrated o Q en molecules towards the corroding metal electrode thus, the corrosion ciurent equals the diffusion current of o en molecules as shown in Fig. 11-8. For this mode of diffusion-controlled corrosion of metals the cathodic Tafel constant is... 

Figure 6.13 Schematic cyclic voltammogram for the reduction reaction at a solid electrode. As in Figure 6.12, the solution was under diffusion control, which was achieved by adding inert electrolyte and maintaining a still solution during potential ramping. The initial solution contained only the oxidized form of the analyte couple, so the upper (cathodic) peak represents the reaction, O + e - R, while the lower (anodic) peak represents the electrode reaction, RO + ne". Note also that the jc-axis represents overpotential, so the peaks are centred about .

Figure 6.2-12 Cyclic voltammogram of 0.1 - 1 mmol dm Geb on gold in dry [BMIMj PFg , starting at-500 mV towards cathodic (a) and anodic (b) regime. Two quasireversible (E, and E2) and two apparently irreversible (E4 and E5) diffusion-controlled processes are observed. E3 is correlated with the growth of two-dimensional islands on the surface, E4 and E5 with the electrodeposition of germanium, Ej with gold step oxidation, and E, probably with the iodine/iodide couple. Surface area 0.5 cm (picture from [59] - with permission of the Peep owner societes).

This system can be taken as an example of so-called reversible, diffusion-controlled electrochemical processes. In short, during the initial anodic scan, an electron-transfer process between the ferrocyanide (or hexacyanoferrate(II)) ions, [Fe(CN)6] ", and the working electrode occurs. This can be represented by means of the equation (here, aq denotes species in aqueous solution) ... 

The theory for cyclic voltammetry was developed by Nicholson and Shain [80]. The mid-peak potential of the anodic and cathodic peak potentials obtained under our experimental conditions defines an electrolyte-dependent formal electrode potential for the [Fe(CN)g] /[Fe(CN)g]" couple E°, whose meaning is close to the genuine thermodynamic, electrolyte-independent, electrode potential E° [79, 80]. For electrochemically reversible systems, the value of7i° (= ( pc- - pa)/2) remains constant upon varying the potential scan rate, while the peak potential separation provides information on the number of electrons involved in the electrochemical process (Epa - pc) = 59/n mV at 298 K [79, 80]. Another interesting relationship is provided by the variation of peak current on the potential scan rate for diffusion-controlled processes, tp becomes proportional to the square root of the potential scan rate, while in the case of reactants confined to the electrode surface, ip is proportional to V [79]. 

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