Cathodic diffusion control

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.

When a metal is under cathodic diffusion control, agitation of the electrolyte increases the current density and the rate of corrosion increases up to a certain point. At a particular velocity (critical velocity), the rate becomes activation controlled rather than diffusion controlled, and, hence, the rate of corrosion becomes independent of velocity (Fig. 3.34). Beyond a certain point agitation has no effect. As fcritkal is exceeded, the metal attains passivity and corrodes only very slowly. 

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. 

This represents a special case of high-level turbulence at a surface by the formation of steam and the possibility of the concentration of ions as water evaporates into the steam bubbles . For those metals and alloys in a particular environment that allow diffusion-controlled corrosion processes, rates will be very high except in the case where dissolved gases such as oxygen are the main cathodic reactant. Under these circumstances gases will be expelled into the steam and are not available for reaction. However, under conditions of sub-cooled forced circulation, when cool solution is continually approaching the hot metal surface, the dissolved oxygen... 

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... 

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 ... 

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. ... 

Mohamed [63] investigated the complexation behavior of amodiaquine and primaquine with Cu(II) by a polarographic method. The reduction process at dropping mercury electrode in aqueous medium is reversible and diffusion controlled, giving well-defined peaks. The cathodic shift in the peak potential (Ep) with increasing ligand concentrations and the trend of the plot of EVl versus log Cx indicate complex formation, probably more than one complex species. The composition and stability constants of the simple complexes formed were determined. The logarithmic stability constants are log Bi = 3.56 log B2 = 3.38, and log B3 = 3.32 [Cu(II)-primaquine at 25 °C]. 

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. 

As discussed earlier, it is generally observed that reductant oxidation occurs under kinetic control at least over the potential range of interest to electroless deposition. This indicates that the kinetics, or more specifically, the equivalent partial current densities for this reaction, should be the same for any catalytically active feature. On the other hand, it is well established that the O2 electroreduction reaction may proceed under conditions of diffusion control at a few hundred millivolts potential cathodic of the EIX value for this reaction even for relatively smooth electrocatalysts. This is particularly true for the classic Pd initiation catalyst used for electroless deposition, and is probably also likely for freshly-electrolessly-deposited catalysts such as Ni-P, Co-P and Cu. Thus, when O2 reduction becomes diffusion controlled at a large feature, i.e., one whose dimensions exceed the O2 diffusion layer thickness, the transport of O2 occurs under planar diffusion conditions (except for feature edges). 

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 .

In the case ofn-Ge(lll) substrates, surface states affect electrochemical deposition of Pb [319]. At high cathodic potentials, the deposition occurs by instantaneous nucleation and diffusion-controlled three-dimensional growth of lead clusters. Comparing H- and OH-terminated n-Ge(lll) surfaces, the nucleation is more inhibited at n-Ge(lll)-OH, which can be explained by the different densities of Ge surface free radicals, being nucleation sites. In this case, nucleation site density is about 1 order of magnitude lower than that for n-Ge(lll)-H. 

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).

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]. 

The cathodic pinacolisation of 2- and 4-acetylpyridine, which had been investigated by one of the present authors (231-233), offered the chance for a complete kinetic analysis as the respective current voltage curves are of reversible character. They allow for evaluation of the kinetics of consecutive reactions, and one can show that at low pH reaction, Eq. (45c) is only possible if strong surfactants are absent. Such surfactants, by occupying the electrode surface, displace ketyl radicals, RiR2(OH)C , from the electrode surface because the latter are relatively weakly adsorbed and cannot compete with strong surfactants in adsorption. Ketyl radicals dissolved in aqueous or organic solvents of low pH are protonated in a fast almost diffusion-controlled reaction. After protonation they are further immediately reduced to form the monomeric carbinol instead of the hydrodimer—the pinacol ... 

The reduction of benzotriazole (119) to 2-aminophenylhydrazine (212), followed by condensation with orthoesters175 to benzo-l,2,4-triazines was mentioned in Section III,C. The reduction of 1-hydroxybenzotriazoles344 (213) via 119 to 212 was suggested to involve electrochemically produced hydrogen rather than a direct electron transfer. This seems improbable inasmuch as it occurs at a mercury cathode with very little catalytic activity. Furthermore, 1-phenylbenzotriazole345 (214) gives a four-electron diffusion-controlled polarographic wave, and both 214 and 119175 take up 4 F/mol in preparative reductions. 

Cyclic voltammetry provides a very convenient method for determining the redox potentials of couples as the peak potentials for the cathodic, E, and anodic, pa, processes of a reversible couple are related, at 25 °C, to the redox potential by pa = E /2 = E° + 0.285/n volts and E. = pa/2 = E° — 0.285/n volts. pc/2 and EpJ2 are the potentials at a point half-way up the wave at these points the current is half the maximum value, i.e. ipc for the cathodic wave or ipa for the anodic wave. Again, this technique will yield redox potentials only if the couple is reversible in the electrochemical sense, but this is now very readily established through the above relationship that pa — -Epc = A p = 57/n mV and by the requirement that ipjip3 = 1. In addition it should be established that Ep is independent of the scan rate, v, and that the process is diffusion controlled by showing ip/v h to be constant. 

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