Potential homogeneous chemical reaction

Double potential steps are usefiil to investigate the kinetics of homogeneous chemical reactions following electron transfer. In this case, after the first step—raising to a potential where the reduction of O to occurs under diffrision control—the potential is stepped back after a period i, to a value where tlie reduction of O is mass-transport controlled. The two transients can then be compared and tlie kinetic infomiation obtained by lookmg at the ratio of... 

Chemical reactions can be involved in the overall electrode process. They can be homogeneous reactions in the solution and heterogeneous reactions at the surface. The rate constant of chemical reactions is independent of potential. However, chemical reactions can be hindered, and thus the reaction overpotential rj can hinder the current flow. 

SEV is an effective means of probing homogeneous chemical reactions that are coupled to electrode reactions, especially when it is extended to cyclic voltammetry as described in the next section. Considerable information can be obtained from the dependence of ip and Ep on the rate of potential scan. Figure 3.20 illustrates the behavior of ip and Ep with variation in scan rate for a reversible heterogeneous electron transfer reaction that is coupled to various types of homogeneous chemical reactions. The current function j/p is proportional to ip according to the equation... 

Chlorobenzonitrile and adrenaline, our second example, both give electrode products that are unstable with respect to subsequent chemical reaction. Because the products of these homogeneous chemical reactions are also electroactive in the potential range of interest, the overall electrode reaction is referred to as an ECE process that is, a chemical reaction is interposed between electron transfer reactions. Adrenaline differs from/ -chlorobenzonitrile in that (1) the product of the chemical reactions, leucoadrenochrome, is more readily oxidized than the parent species, and (2) the overall rate of the chemical reactions is sufficiently slow so as to permit kinetic studies by electrochemical methods. As a final note before the experimental results are presented, the enzymic oxidation of adrenaline was known to give adrenochrome. Accordingly, the emphasis in the work described by Adams and co-workers [2] was on the preparation and study of the intermediates. 

Here (3 is the cathodic symmetry factor of the rate-determining step and v is a positive integral number indicating how many times the RDS is occurring in the global electron-transfer reaction (mostly v=l). The parameter r takes into account a homogeneous chemical reaction, the rate of which is not dependent on the potential, as RDS when the RDS is a charge-transfer step, r=l applies, and for a chemical RDS, r=0. 

Sometimes the oxidized species can exist in two forms in chemical equilibrium, with one of them electro-inactive in the potential range where the electrochemical process occurs. This type of reaction pathway is known as a CE mechanism because a homogeneous chemical reaction (C) precedes the heterogeneous electrochemical process (E). If the chemical step is of first or pseudo-first order, the process can be expressed by the reaction scheme ... 

The position of the voltammogram is also affected by the homogeneous chemical reaction. Thus, the reductive RPV curve shifts toward more positive potentials as species B is consumed faster by the chemical process. This shift can be easily monitored by means of the mid-wave potential ( d,Rpv) which helps to characterize the chemical reaction as well as to determine the formal potential of the electrode reaction, Ct°. ... 

For an electrode process followed up by an irreversible homogeneous chemical reaction (K = 0, Fig. 4.31b), the peak currents are independent of the chemical kinetics whereas the peak potential takes more positive values as xi increases because the chemical reaction facilitates the reduction process by removal of species B. In all cases plotted in this figure, the value of the crossing potential can be evaluated with good accuracy from Eq. (4.255) (error smaller than 3 mV for X2 > 102). With respect to the E mechanism of species A, in the EC response both peak currents are smaller, and this effect is especially noticeable in the minimum which is more affected by the follow-up reaction. 

In Sect. 6.3, the application of SCV and CV techniques is discussed with respect to reversible charge transfer reactions complicated with homogeneous chemical reactions. It is highlighted that, except in the case of a first-order catalytic mechanism, relatively simple analytical general expressions for the current potential response of CE, EC, or ECE mechanisms have not been found. Numerical procedures have been applied to analyze the influence of kinetic parameters of the homogeneous reactions on these curves. 

If the product of the tip or substrate ET reaction [Eqs. (1) and (3)] participates in a homogeneous reaction within the tip-substrate gap, the feedback response is altered. In this case, the shape of the iT versus d curve depends on the rate of the homogeneous chemical reaction [84]. If the tip and the substrate are biased at extreme potentials, so that reactions (1) and (3) are rapid, the shape of the SECM current-distance curve for a relatively simple mechanism is a function of a single kinetic parameter, K = const x kc/D, where kc is the rate constant of the irreversible homogeneous reaction. 

Nernstian boundary conditions, or those for quasireversible or irreversible systems. All of these cases have been analytically solved. As well, there are two systems involving homogeneous chemical reactions, from flash photolysis experiments, for which there exist solutions to the potential step experiment, and these are also given they are valuable tests of any simulation method, especially the second-order kinetics case. 

Another case of interest with LSV is the catalytic system, described above in the section on potential steps. The equations are the same except that the potential here is not constant and very negative, following (2.29) in its dimensionless form. For small and intermediate rates of the homogeneous chemical reaction (dimensionless constant K), the same procedure as mentioned above, that is, convergence simulations, must be used. For large K, however, the LSV curves become sigmoid, with a plateau equal to the current for the potential step, G = y/K. This can be used to test methods. Figure 2.7 shows LSV curves for some A -values, where this effect is seen. 

The rate of electron transfer and its potential dependence can be described by the Butler-Volmer equation (20) (see Section 2). An electron transfer often initiates a cascade of homogeneous chemical reactions by producing a reactive radical anion/cation. The mechanism can be described mathematically by a rate equation for each species these form part of the electrochemical model. The rate law of the overall sequence is probed by the voltammetric experiment. 

Proton-coupled electron transfer is a prominent theme in biological redox systems. There are three basic mechanisms for these processes (Figure 18). In the first mechanism (path A), electron transfer occurs prior to proton transfer. This mechanism is commonly observed for the electrochemical reduction and oxidation of quinones and flavins in protic media [52], In this interfacial environment, proton transfer is manifested as an ECE (E represents an electron transfer at the electrode surface and C represents a homogeneous chemical reaction) two-electron reduction of these systems to their fully reduced states (Figure 19). As electron transfer occurs prior to the proton transfer event, proton transfer does not affect either the redox potential or the electron transfer rate to or from the cofactor. 

A homogeneous chemical reaction occurring in the gap between the tip and substrate electrodes causes a change in iT, therefore its rate can be determined from SECM measurements. If both heterogeneous processes at the tip and substrate electrodes are rapid (at extreme potentials of both working electrodes) and the chemical reaction (rate constant, kc) is irreversible, the SECM response is a function of a single kinetic parameter K = const X kc/D, and its value can be extracted from IT vs. L dependencies. 

It is convenient to classify the different possible reaction schemes by using letters to signify the nature of the steps. E represents an electron transfer at the electrode surface, and C represents a homogeneous chemical reaction (10). Thus a reaction mechanism in which the sequence involves a chemical reaction of the product after the electron transfer would be designated an EC reaction. In the equations that follow, substances designated X, Y, and Z are assumed to be not electroactive in the potential range of interest. It is also convenient to subdivide the different types of reactions into (1) those that involve only a single electron-transfer reaction at the electrode and (2) those that involve two or more E-steps. 

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