Potential step homogeneous reactions

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... 

ESTABLISHING THE MECHANISM AND MEASURING THE RATE CONSTANTS FOR HOMOGENEOUS REACTIONS BY MEANS OF CYCLIC VOLTAMMETRY AND POTENTIAL STEP CHRONOAMPEROMETRY... 

The important concept in these dynamic electrochemical methods is diffusion-controlled oxidation or reduction. Consider a planar electrode that is immersed in a quiescent solution containing O as the only electroactive species. This situation is illustrated in Figure 3.1 A, where the vertical axis represents concentration and the horizontal axis represents distance from the electrodesolution interface. This interface or boundary between electrode and solution is indicated by the vertical line. The dashed line is the initial concentration of O, which is homogeneous in the solution the initial concentration of R is zero. The excitation function that is impressed across the electrode-solution interface consists of a potential step from an initial value E , at which there is no current due to a redox process, to a second potential Es, as shown in Figure 3.2. The value of this second potential is such that essentially all of O at the electrode surface is instantly reduced to R as in the generalized system of Reaction 3.1 ... 

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. 

Double-step chronocoulometry is a powerful tool in identifying adsorption phenomena, in obtaining information on the kinetics of coupled homogeneous reactions and for the determination of the capacitive contribution. The double potential step is executed in such a way that after the first step from E to E2, a next step is applied, i.e., the reversal of the potential to its initial value Ei from 2 (see Fig. 3). 

These four methods are complementary in that they all involve, in one way or another, a modulation of the kinetics and course of the reaction in time. The resulting response behavior is then analyzable in terms of (a) rate equations for various steps (104, 108) and (b) potential dependences of coverages by adsorbed intermediates in those steps. The methods have their analogs in temperature- and pressure-step methods (T-jump or P-jump techniques of Eigen) used in the study of the kinetics of fast homogeneous reactions. In fact a T-jump method has recently been developed for the study of electrochemical reactions by Feldberg (109). 

The overall reaction, Eq. (1), may take place in a number of steps or partial reactions. There are four possible partial reactions charge transfer, mass transport, chemical reaction, and crystallization. Charge-transfer reactions involve the transfer of charge carriers (ions or electrons) across the double layer. This is the basic deposition reaction. The charge-transfer reaction is the only partial reaction directly affected by the electrode potential. In mass transport processes, the substances consumed or formed during the electrode reaction are transported from the bulk solution to the interphase (double layer) and from the interphase to the bulk solution. This mass transport takes place by diffusion. Chemical reactions involved in the overall deposition process can be homogeneous reactions in the solution and heterogeneous reactions at the surface. The rate constants of chemical reactions are independent of the potential. In crystallization partial reactions, atoms are either incorporated into or removed from the crystal lattice. 

The current-potential curves discussed so far can be used to measure concentrations, mass-transfer coefficients, and standard potentials. Under conditions where the electron-transfer rate at the interface is rate-determining, they can be employed to measure heterogeneous kinetic parameters as well (see Chapters 3 and 9). Often, however, one is interested in using electrochemical methods to find equilibrium constants and rate constants of homogeneous reactions that are coupled to the electron-transfer step. This section provides a brief introduction to these applications. 

Note that equations need not be written for species Y, since its concentration does not affect the current or the potential. If reaction (12.2.2) were reversible, however, the concentration of species Y would appear in the equation for 5Cr(x, t) dt, and an equation for 5Cy(, t) dt and initial and boundary conditions for Y would have to be supplied (see entry 3 in Table 12.2.1). Generally, then, the equations for the theoretical treatment are deduced in a straightforward manner from the diffusion equation and the appropriate homogeneous reaction rate equations. In Table 12.2.1, equations for several different reaction schemes and the appropriate boundary conditions for potential-step, potential-sweep, and current-step techniques are given. 

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