Anodic limiting current

Limiting currents are usually associated with cathodic reactions (e.g., in metal deposition), although anodic reactions are by no means excluded. Whenever the supply of a dissolved species from the solution to the electrode surface becomes the rate-limiting factor, limiting-current phenomena may be observed. Anodic limiting currents can be obtained, for example, in the oxidation of ferrous to ferric ion, or ferro- to ferricyanide ion (El). Diffusion of H20 limits 02 evolution in fused NaOH (A2). In these examples the limiting current is caused by depletion of the reactant species at the anode. 

Here, we distinguish cathodic and anodic limiting currents as qc and qa, respectively. The cathodic current being positive and the anodic current... 

We consider a transfer reaction of redox electrons in which the interfacial transfer of electrons is in quasi-equilibrium ( Hh =0) and the diffusion of redox particles determines the overall reaction rate. The anodic diffusion current, and the anodic limiting current of diffusion, inm, in the stationary state of the electrode reaction are given, respectively, in Eqns. 8-33 and 8-34 ... 

The working electrode is silver metal. At 0% titration, the anodic limiting current is controlled by the mass transport of Cl to the electrode for the oxidation of Ag to form AgCl. As the titration proceeds, the decrease in this limiting current reflects the decrease in Cl" concentration due to addition of Ag+ titrant until the current becomes zero at the equivalence point (100% titration). 

In Fig. 2.12, the analytical current-time curves under anodic and cathodic limiting current conditions calculated from Eq. (2.137) (Fig. 2.12a and b, respectively) when species R is soluble in the electrolytic solution (solid curves) and when species R is amalgamated in the electrode (dotted lines) are plotted. In Fig. 2.12a, the amalgamation effect on the anodic limiting current has been analyzed. As expected, when species R is soluble in the electrolytic solution, the absolute value of the current density increases when the electrode radius decreases because of the enhancement of... 

Expressions for the cathodic and anodic limiting currents can also be easily obtained for spherical electrodes by making e —> 0 and e 1 > oo in Eq. (2.142),... 

From Eqs. (2.183) and (2.184), it is possible to rewrite the expression of the surface concentrations in terms of the current, and the cathodic and anodic limiting currents are as follows ... 

In order to establish the most appropriate conditions for the determination of the diffusion coefficients of both electroactive species by using Eqs. (4.38) and (4.39), it has been reported that when the reaction product is absent (i.e., cR = 0) neither planar electrodes nor ultramicroelectrodes can be used in DPC for determining diffusion coefficients (see Eqs. (4.48) and (4.50)) because in these situations the anodic limiting current is either independent of DR or null, respectively. 

In Fig. 4.5 it can be seen the influence of t2 on the normalized RPV curves calculated from planar, spherical, and disc electrodes from Eqs. (4.67) and (4.36). From these curves, it can be observed that the decrease of t2 causes an increase of the anodic limiting current (with this increase being more noticeable in the case of planar electrodes), whereas it has no effect on the half-wave potential of the responses (marked as a vertical dotted line). 

The effect of the electrode radius and of I)R on the RPV curves can be seen in Fig. 4.6. It is observed that an increase of DR gives rise to a shift of the RPV curve toward more positive potentials regardless of the electrode size. Nevertheless, the influence of DR on the anodic limiting current depends on the electrode size. Thus,... 

From Eqs. (4.221) and (4.222), it is clear that both limiting currents increase when the electrode radius decreases and, when the chemical reaction is irreversible (K = 0). the anodic limiting current / pvu s independent of the electrode size. 

Due to the role of surface states, the dark limiting current of silicon electrode is extremely sensitive to surface defects and thus surface preparation. Any scratch even barely visible on the mirror like surface can result in a significant increase of the anodic limiting current. According to Chazalviel, defects associated with surface treatment are primarily responsible for the large limiting current values reported in the literature. The effect caused by surface states may, however, be reduced by the formation of a... 

FIGURE 5.27. Variations of anodic limiting current as a function of [F"] for solutions of pH 2 for Si (111) and (100). (Reprinted from Allongue et 1995, with permission from Elsevier Science.)... 

The anodic limiting current in lithium salt solutions is determined by the diffusion of the solvated electrons to the electrode. This was quantitatively established by the measurements taken on rotating disc electrodes and also by galvanostatic measurements In fact, as seen from Fig. 8, the limiting current density is proportional to the square root of the disc electrode rotation rate. This, in accordance with the rotat-... 

When both members of the redox couple exist in the bulk, we must distinguish between a cathodic limiting current, // c, when Cq x = 0) 0, and an anodic limiting current, // a, when Cr(x = 0) 0. We still have Cq( = 0) given by (1.4.11), but with // now specified as // c- The limiting anodic current naturally reflects the maximum rate at which R can be brought to the electrode surface for conversion to O. It is obtained from (1.4.7) ... 

Fig. 1.9 Methanol concentration profile at zero cell current (solid line), and close to the anode limiting current (dashed line) (Adapted from Ref. [35])...

Given the sign conventions used, once again one finds that the anodic limiting current is positive, while the cathodic one is negative. 

This algebraic equation must involve the anodic limiting current for the reductant and the cathodic limiting current for the oxidant. 

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