Rate constant, of electrode reaction

Tab. 8.9 Examples of the rate constants of electrode reactions and subsequent reactions determined by rapid-scan cyclic voltammetry [51 d, 66e]...

If vdielectric permittivity in vacuum will then be equal to 80. This is the so-called static permittivity. The permittivity of the vaccum is 0.855x 10 C m. The static dielectric permittivity near the ion or the surface of the charged electrodes, however, will exhibit smaller values. For instance, in the case of water at the electrode surface is assumed to approach 6. When applying the Marcus theory [8] both static and optical permittivities are used in calculations. These parameters therefore are listed in Table 1. In other calculations and correlations of the rate constants of electrode reactions and the dynamic relaxation properties of the solvents, the relaxation time of the solvents is used (Thble 1). 

In the following we shall deal with several of the transient methods which are commonly used for the determination of the rate constants of electrode reactions. A few other known methods will not be described here in detail... 

X 10- 2.96 X 10- fc/5-Rate constant of electrode reaction, at zero V vs NHB uncorrected for liquid junction potential 8... 

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. 

Electron movement across the electrode solution interface. The rate of electron transfer across the electrode solution interface is sometimes called k. This parameter can be thought of as a rate constant, although here it represents the rate of a heterogeneous reaction. Like a rate constant, its value is constant until variables are altered. The rate constants of chemical reactions, for example, increase exponentially with an increasing temperature T according to the Arrhenius equation. While the rate constant of electron transfer, ka, is also temperature-dependent, we usually perform the electrode reactions with the cell immersed in a thermostatted water bath. It is more important to appreciate that kei depends on the potential of the electrode, as follows ... 

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. 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

The experimental technique and electrode geometry should be selected to match the kinetic time-scale (the time domain over which a chemical process occurs, e.g. 1/k, where k is a first-order rate constant) of the reaction being studied. This is achieved by varying the rate of mass transport via convection, electrode size/shape or potential scan rate. 

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. 

Studies by cyclic voltammetry of anodic oxidation of organotin compounds at a platinum electrode in acetonitrile show that the primary irreversible process is the outer sphere oxidation of R4Sn to the radical cation, followed by rapid fragmentation into R3Sn+ and R which is then rapidly oxidised further to R+. The rate constants of the reactions correlate with those for the oxidation by Fe(III) complexes. Values for the oxidation potentials and the ionisation energies are given in Table 5-3. 

A complete electrode reaction may involve homogeneous chemistry, one step of which could be the RDS. Although the rate constants of homogeneous reactions are not depen-... 

The sign holds for anodic and cathodic overpotentials respectively. A plot of electrode potential versus the logarithm of current density is called the Tafel plot and the resulting straight line is the Tafel line" The linear part (5=2.3 RT/anF) is the Tafel slope that provides information about the mechanism of the reaction, and "a" provides information about the rate constant of the reaction. The intercept at r =0 gives the exchange current density... 

As the experiment stands, the measured value contains an ohmic component from the ir drop between R and B, a concentration component resulting from concentration changes in the vicinity of the electrode, and a component, denoted by rj, which is related to the rate constant of the reaction. Thus... 

The SEI is formed by parallel and competing reduction reactions and thus its composition depends on i , ti and the concentrations of all the electroactive materials. It has been shown that the rate constants of the reactions of solvated electrons with electrolyte and solvent components (and impurities) are a good measure of the stability of these substances towards lithium. It is suggested the rate constants (kj for these reactions be used as a tool for the selection of electrolyte components. Good correlation was found between k and SEI-formation voltage and composition. Close to the electrode side, the SEI consists... 

In above two equations, rrij is an integer constant which takes values of -1, +1, and 0 for species R(z-i) Os and inert electrolyte species respectively if the reduction current is considered positive p refers to the thickness of the compact EDL Fq refers to the radius of electrode y is the ratio between the standard rate constant of ET reaction and the mass transport coefficient of the electroactive species. It can be seen that the current density, which is given in a dimensionless form through normalization with the limiting diffusion current density (i, and the electrostatic potential distribution appear simultaneously in the two equations. Equation 2.2 could be approximated to the PB equation at low current density, while Equation 2.3 would reduce to Eq. 2.4, which is the diffusion-corrected Butler-Volmer equation and has been used to perform voltammetric analysis in conventional electrochemistry, as exp(-Zj/ rcp/F)=1, that is, electrostatic potentials in CDL are close to zero. These conditions are approximately satisfied in large electrode systems, suggesting that the voltammetric behaviour and the EDL structure can be treated separately at large electrode interface ... 

Another tacit assumption is that the surface of the electrode remains unchanged during the experiment. Changes in the catalytic activity of the surface (which would change the specific rate constant of the reaction) could occur during metal deposition or dissolution, particularly when alloy deposition is concerned, where... 

---