Zone diagram

Rigorous quantitative treatments lead to kinetic zone diagrams that distinguish between different extreme and borderline cases depending on which parameters controll the overall reaction (Fig. 2). A realistic picture is obtained from cross... 

Fig. 2a-c. Kinetic zone diagram for the catalysis at redox modified electrodes a. The kinetic zones are characterized by capital letters R control by rate of mediation reaction, S control by rate of subtrate diffusion, E control by electron diffusion rate, combinations are mixed and borderline cases b. The kinetic parameters on the axes are given in the form of characteristic currents i, current due to exchange reaction, ig current due to electron diffusion, iji current due to substrate diffusion c. The signpost on the left indicates how a position in the diagram will move on changing experimental parameters c% bulk concentration of substrate c, Cq catalyst concentration in the film Dj, Dg diffusion coefficients of substrate and electrons k, rate constant of exchange reaction k distribution coefficient of substrate between film and solution d> film thickness (from ref. 

A kinetic zone diagram representing the various regimes of competition between diffusion and the follow-up reaction is shown in Figure 2.1.2 As expected, significant influence of the reaction requires the equilibrium... 

FIGURE 2.1. EC reaction scheme in cyclic voltammetry. Kinetic zone diagram showing the competition between diffusion and follow-up reaction as a function of the equilibrium constant, K, and the dimensionless kinetic parameter, X. The boundaries between the zones are based on an uncertainty of 3 mV at 25°C on the peak potential. The dimensionless equations of the cyclic voltammetric responses in each zone are given in Table 6.4. 

FIGURE 2.3. EC reaction scheme in cyclic voltammetry. Variation of the peak potential and of reversibility upon crossing the kinetic zone diagram (Figure 2.1) for K= 103. 

FIGURE 2.1 7. Homogeneous catalysis electrochemical reactions. Kinetic zone diagram in the case where the homogeneous electron transfer step is rate limiting. 

A completely opposite situation is reached when Xe is large, but the excess factor is small, so that the substrate is consumed to a large extent. Its concentration at the electrode surface is then much smaller that in the bulk, implying that diffusion of the substrate toward the electrode surface may become the slow step of the catalytic process. Under these conditions (left-hand part of the zone diagram in Figure 2.17), the cyclic voltammetric responses are governed by the parameter... 

The results obtained with several aryl halides in 90 10 mixtures of water and dimethylsulfoxide or acetonitrile39 are displayed in Figure 2.37 under the form of a zone diagram based on two dimensionless parameters ... 

The plateau currents are thus a function of two dimensionless parameters, Jis/ik and 4/4(1 — k/i )- On this basis, a kinetic zone diagram may be established (Figure 4.19) as well as the expressions of the plateau currents pertaining to each kinetic zone (Table 4.1).17 Derivation of these expressions is described in Section 6.4.4. There are in most cases two successive waves, and the expressions of both limiting currents are given in Table 4.1. The general case corresponds to a situation where none of the rate-limiting factors... 

FIGURE 4.19. Kinetic zone diagram characterizing the RDEV plateau currents for the reaction scheme in Figure 4.10. Solid lines substrate concentration profile. Dashed lines concentration profile of the reduced form of the catalyst. Adapted from Figure 5.5 of reference 17d, with permission from John Wiley Sons. 

Another case of interest is the transition between no catalysis and the pure kinetic conditions leading to plateau-shaped responses. In the kinetic zone diagram of Figure 2.17, it corresponds to the extreme right-hand side of the diagram, where the cyclic voltammogram passes from the Nernstian reversible wave of the cosubstrate to the plateau-shaped wave, under conditions where the consumption of the substrate is negligible. The peak... 

FIGURE 5.17. Dynamics of molecular recognition. Binding of the target molecule to the receptor. Kinetic zone diagram and characteristic equations. Adapted from Figure 1 of reference 22, with permission from the American Chemical Society. 

Manipulation of these equations or of those pertaining to the q formulation for various limiting values of the two dimensionless parameters defining the zone diagram allows derivation of the expressions of the plateau currents given in Table 4.1. With the two-step reaction scheme discussed in Section 4.3.6, a similar procedure may be used to obtain the various expressions of the plateau currents given in Table 4.2. 

Immobilizing the catalyst on the electrode surface is useful for both synthetic and sensors applications. Monomolecular coatings do not allow redox catalysis, but multilayered coatings do. The catalytic responses are then functions of three main factors in addition to transport of the reactant from the bulk of the solution to the film surface transport of electrons through the film, transport of the reactant in the reverse direction, and catalytic reaction. The interplay of these factors is described with the help of characteristic currents and kinetic zone diagrams. In several systems the mediator plays the role of an electron shuttle and of a catalyst. More interesting are the systems in which the two roles are assigned to two different molecules chosen to fulfill these two different functions, as illustrated by a typical experimental example. 

J. Chem. Ed. 1996, 73, 165 A. Rojas-Hernandez, M. T. Ramirez, I. Gonzalez, and J. G. Ibanez, Predominance-Zone Diagrams in Solution Chemistry, ... 

Fig. 4. The zone diagram for the eC mechanism. Zone designations are explained in the text. Reprinted with permission from ref. 29.

Fig. 6.10 Zone diagram corresponding to a CE mechanism in Cyclic Voltammetry. Reproduced with permission from [25]...

With the results from (i) and (ii) we now draw the predominance-zone diagram for the Al(III)... 

As discussed above, soil pH may play a major role in its interactions with pollutants. Species distribution diagrams (see Chapter 2) set the framework to know which species are predominant at a given pH. For example, phosphates have the predominance-zone diagram shown in Figure 8.5. 

Figure 5. Zone diagram for an ErCj mechanism based on DPSC measurements of the...

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