Kinetic zones

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. 

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. 

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. 

The kinetic zone most suitable for heterogeneous charge transfer studies is the QR zone (Fig. 4). Studies are also possible in the IR zone, but these are less productive since there is no reverse peak during CV and it is necessary to know Eiev, which is usually not available for irreversible processes, in order to apply LSV studies. Theoretical relationships for CV and LSV will be presented in the following sections and some practical examples are presented later. 

The rate laws and hence the mechanisms of chemical reactions coupled to charge transfer can be deduced from LSV measurements. The measurements are most applicable under conditions where the charge transfer can be considered to be Nernstian and the homogeneous reactions are sufficiently rapid that dEv/d log v is a linear function, i.e. the process falls into the KP or purely kinetic zone. In the 1960s and 1970s, extensive... 

Meanwhile, the majority of chemical and biochemical processes proceeds in the kinetic zone. Therefore, the synchronization of two chemical reactions or more is of special importance. 

As shown below, the observed intermodulation of synchronized chemical reaction yields is clearly displayed in the kinetic zone and represents a valid tool for voluntary manipulation of their rates. 

On the other hand, the kinetic zone of chemical reaction proceeding is characterized by a much lower rate of chemical transformations than the rate of reagent transport to the... 

Figure 4. Kinetic zone diagram and corresponding compass card for a competition between three hypothetical mechanisms, as discussed in the text.

Figure 5. Kinetic zone diagram for an ECDim/ECE/DISP competitive sequence [see text, Eqs. (48) through (53), and Table 2 for definitions of p], P2, and P3 note that for the example discussed in the text kj = kdif]. The hatched zone in b corresponds to the region without experimental validity.

This allows the construction of the kinetic zone diagram in Fig. 7a according to the previously explained procedure. The location of the experimental systems considered in Fig. 6 indicates that the benzonitrile or naphthalene derivatives undergo an ECE/ECC competition without interference from the DISP route. Thus, as indicated by the compass card in Fig. 7a or by the formulation of Pi in Eq. (62), or 0 = 8 /D has no effect on the... 

Figure 7. (a) Kinetic zone diagram for the ECC/ECE/DISP competitive sequence in the ArD versus ArH formation under the experimental conditions of Fig. 6 [see text and Eqs. (48) through (51) and (58) through (61) note that for the example discussed = k if]. (b) Theoretical variations in the yield of ArD as a function of the concentration of ArX (numbers on the curves) and of the rate constants ratio ki/kn- (Experimental data from Ref. 25.)... 

FIG. 6 Kinetic zone diagram illustrating the regions of finite irreversible kinetics, diffusion-controlled feedback, and insulating substrate behavior. (From Ref. 14. Copyright 1992 American Chemical Society.)... 

A plot of Et/4 vs. log (kt) is shown in Figure 12.2.1. Note that the limiting diffusion and kinetic zones are described by the solid lines, and the dashed curve represents the exact equation, (12.2.24). Of course, the boundaries of these zones depend on the approximation employed, and the applicability of the limiting equations depends on the accuracy of the electrochemical measurements. For example, if potential measurements are made to the nearest 1 mV, the pure kinetic zone will be reached (for n = I and 25°C) when 25.7 In [erf(A /) ] < 1 mV or when > 1.5. 

Under these conditions (12.2.32) becomes identical to the equation for unperturbed reversal chronopotentiometry and T2 = /i/3 (see equation 8.4.9). When kt is large (kinetic zone), T2 approaches 0. The variation of T2lt with kt is shown in Figure 12.2.2 (20-22). Note that kinetic information can be obtained from reversal measurements only in the intermediate zone (0.1 kt 5). The actual value of k is obtained by determining T2//1 for different values of t and fitting the data to the working curve shown in Figure 12.2.2 (23). Kinetic information can also be obtained in the kinetic zone from the shift of potential with t however, fP must be known for the electron-transfer step before an actual value of k can be determined. 

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