The pseudo-limiting-current

It is clear that rate Equations 4.38,4.40 and 4.47 do not appear to be able to explain the deviation of the experimental current-potential relation occurring with the more positive potentials in the prewave. However, these relations apply only under restrictive conditions (k 3 k4 and/or k 2 k 4 for Equation4.38, k 4 k5 for Equation4.40 and k 4 k5 for Equation 4.47), which have only been introduced to eliminate (1-0) terms from 

A possible explanation for the pseudo-limiting-current formation is as follows considering the global rate equations of stages 3 and 4 of mechanism 1 (without restrictions, only anodic terms)  

Since stage 4 is the RDS, the (1-0) term of 02 is equal to 1. However, this is not the case for the (1-0O ) term. What can be considered is that k 3 k4 so that formed O particles react only in a very restricted way back into the OH radical. In order to clarify the rate difference between stages 3 and 4, the rate relation can be examined, without the relation of the exponents being simplified  

It can be concluded that the combination of sub-mechanism 1 with stage 4 as RDS and sub-mechanism 2 with stage 5 as RDS qualifies for a possible global mechanism to explain the experimentally observed evidence. 

In section 4.6.5, stage 5 of mechanism 1 as a possible RDS with potentials more positive than ca. E = 0.2 V vs. SCE was not excluded. Based on the above-mentioned arguments, this stage as RDS can be excluded. Moreover, the relation of the rate equations of stages 4 and 5 of mechanism 1 cannot explain that stage 5 would become slower than stage 4  

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From the preliminary research described in the previous section, it appears that the small oxidation wave with half-value potential (EV2) of ca. 0.21V vs. SCE offers favourable perspectives for the amperometric determination of relatively high hydrogen peroxide concentrations. In contrast to the second oxidation wave with I2=0.76 V vs. SCE, the pseudo-limiting currents obtained in the prewave do not satisfy the relation of Levich (Chapter 1, Equationl.15). However, they are almost completely independent of the rotation rate of the electrode, revealing that these limiting currents are not controlled by transport of electroactive species but by (an) other process(es). This is illustrated in Fig.4.5. 

Apparently, the current in the ascending part of the wave and the pseudo-limiting current are mostly determined by transport-independent, kinetic factors. The limiting current of the second wave, obtained after correction for the IR voltage drop, satisfies the Levich relation (Chapter 1, Equation 1.15) and is hence determined by the transport rate of hydrogen peroxide to the electrode surface. This wave will not be further discussed since it is of no use for the aim of this investigation. 

In consideration of a sensor based on the prewave, the highest ascending part of this wave is not important from an analytical point of view. In a possible analytical application, the pseudo-limiting-current needs to be applied, because the current is higher and because it is less sensitive to variations in the potential of the reference electrode. 

As was done earlier for the pseudo-limiting-current area, unified relations can be derived for the potential area in the steeper ascending part of the prewave. Since this derivation is highly analogous to the above-mentioned treatment, it will not be repeated here. It appears that the conclusions are analogous, and that only the numerical values of factor G are different. With the knowledge of the mechanism and its rate equation, one can start with the development of an analytical method. This will be explained in detail in Chapter 5. 

This indicates that no synergist effects occur with regard to the pseudo-limiting-current of the prewave of hydrogen peroxide. To verify that the wrong conclusions had not been drawn because of slow setting in adsorption equilibria, the experiment was repeated, adding both additives in reverse direction. Flence, in a second experiment, of which the results are also presented in Fig.5.4, first Defindol E was added and subsequently... 

From this, it can be concluded that the adsorption equilibria occur quickly. However, the pseudo-limiting-current of the prewave of hydrogen peroxide is not further influenced by the addition of a second additive to a solution that already contains an additive, unless the most recently added additive mixture contains components with a stronger current-lowering effect than the first. 

Relationship between pseudo-limiting-current of the pre-wave at = 0.45 V vs. SCE and the hydrogen peroxide concentration for various pH values, recorded at a glassy carbon electrode rotating at 16.67 Hz. The numbered curves correspond to pH values of (1) 10, (2) 11, (3) 12, (4) 13 and (5) 14 other curves correspond to each increment of 0.2 pH units. 

The effects of the catalytic reaction on the CV curve are related to the value of dimensionless parameter A in whose expressions appear variables related to the chemical reaction and also to the geometry of the diffusion field. For small values of A, the surface concentration of species C is scarcely affected by the catalysis for any value of the electrode radius, such that r)7,> —> c c and the current becomes identical to that corresponding to a pseudo-first-order catalytic mechanism (see Eq. (6.203)). In contrast, for high values of A and f —> 1 (cathodic limit), the rate-determining step of the process is the mass transport. In this case, the catalytic limiting current coincides with that obtained for a simple charge transfer process. 

Under conditions where the conversion of B to A in solution is pseudo-lst-order, approximate solutions, valid for either extremely large or small k, were obtained by Klatt and Blaedel [103]. A more complete treatment, valid for all values of k, was given by Matsuda and co-workers [104]. The analysis showed that the catalytic reaction caused the diffusion-limited current in the presence of the catalytic cycle, 7cat, to be increased over the current that would be observed in the absence of the cycle (k = 0), Jd, by an amount depending on the parameter... 

The ratio of the anodic to the cathodic limiting current (peak currents) in CV technique applied to this mechanism is always unity independent of X. In the pure kinetic zone, currents during the reverse scan tend to retrace the currents of the forward scan (see Fig. 16). In most experiments, it is assumed that the catalytic agent Z is present in excess, c c, so that its concentration remains unchanged during the electrolysis (pseudo-first order reaction). 

For the systems where the amount of protonated ligand forms is insignificant, the equation defining such pseudo-limiting current (prewave) can be obtained [2] ... 

The overall gain of the multiphase mixture model approach above is that the two-phase flow is still considered, but the simulations have only to solve pseudo-one-phase equations. Problems can arise if the equations are not averaged correctly. Also, the pseudo-one-phase treatment may not allow for pore-size distribution and mixed wettability effects to be considered. Furthermore, the multiphase mixture model predicts much lower saturations than those of Natarajan and Nguyen - and Weber and Newman even though the limiting current densities are comparable. However, without good experimental data on relative permeabilities and the like, one cannot say which approach is more valid. 

The single pulse voltammograms of a pseudo-first-order catalytic process are easily characterized by the increase of the limiting current with the time or the chemical kinetic constants, whereas its half-wave potential remains unchanged. 

For a pseudo-first-order CE mechanism, both the limiting current (which is always less than that corresponding to an E mechanism) and the half-wave potential are affected by the equilibrium and rate constants. 

Reaction (49b) was the rate-limiting step that could be treated as a pseudo-first-order process in the presence of excess PhOH (0.1-0.43 M). The tip electrode (a 7-pm C fiber) and the substrate (a 60-pm Au electrode) were placed at a fixed separation distance, which was evaluated from the positive feedback current of decamethylferrocene. A series of current-distance curves for a range of PhOH concentrations showed the decrease in feedback with increasing [PhOH], This is because the consumption of AC in the gap caused a diminution of positive feedback for AC/AC couple. Fitting of the approach curves confirmed a DISP1 mechanism for the reduction of anthracene. In the presence of phenol. The results yielded a psudo-first-order rate constant for reaction (49b), ku from which the second-order rate constant, fc2 = k / [PhOH] = 4.4 0.4 x 103M-1s-1 was obtained. 

A denotes the starting material that is oxidised (or reduced) at the electrode (e.g. Ru(bpy)3+ oxidation or MV2+ reduction on a Pt electrode) and it is subsequently reformed by a catalyst in a pseudo first order reaction that concomitantly forms a product P. P, in our case, is 02 (or H2). On a planer electrode, from the limiting current in the case of pure catalytic control (i.e. at remote enough a potential after the peak in a potential sweep experiment or at t - in an experiment where the potential is fixed sufficiently past the E° of the redox couple), kca, can be calculated using the expression,... 

Note that this equation is the same as (12.3.29). This limiting current holds only in the region of small (o. When A (= b C lcS) becomes small, the behavior approaches the mass-transfer-controlled limiting current. Results of a digital simulation of the catalytic case (83) are shown in Figure 12.4.3. Other treatments of the ErCj case at the RDE, as well as variations of this mechanism, have also appeared (84-86). The treatment of the Ej-CJ case for the RRDE by digital simulation techniques showed that the results (i.e., plots of Nk vs. XKT) are indistinguishable from those of the Ej-Ci case for first- or pseudo-first-order reactions (83). 

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