Electrode kinetics rate-determining step

The treatment may be made more detailed by supposing that the rate-determining step is actually from species O in the OHP (at potential relative to the solution) to species R similarly located. The effect is to make fi dependent on the value of 2 and hence on any changes in the electrical double layer. This type of analysis has permitted some detailed interpretations to be made of kinetic schemes for electrode reactions and also connects that subject to the general one of this chapter. 

At mercury and graphite electrodes the kinetics of reactions (15.21) and (15.22) can be studied separately (in different regions of potential). It follows from the experimental data (Fig. 15.6) that in acidic solutions the slope b 0.12 V. The reaction rate is proportional to the oxygen partial pressure (its solution concentration). At a given current density the electrode potential is independent of solution pH because of the shift of equilibrium potential, the electrode s polarization decreases by 0.06 V when the pH is raised by a unit. These data indicate that the rate-determining step is addition of the first electron to the oxygen molecule ... 

When, as it is assumed here, the B —> C reaction is the rate-determining step, the dimensionless rate parameter, 2, is the same as in the ECE case. As 2 increases, the wave loses its reversibility while the electron stoichiometry passes from 1 to 2, as in the ECE case. Unlike the latter, there is no trace crossing upon scan reversible. This is related to the fact that now only the reduction of A contributes to the current. C has indeed disappeared by means of its reaction with B before being able to reach back to the electrode surface. The characteristic equations, their dimensionless expression, and their resolution are detailed in Section 6.2.1. The dimensionless peak current, tjj, thus varies with the kinetic parameter, 2, from 0.446, the value characterizing the reversible uptake of one electron, to 2 x 0.496 = 0.992, the value characterizing the irreversible exchange of two electrons (Figure 2.11a). 

The kinetics of MeOH oxidation of a 1 1 PfRu in an MEA has been well established by Vidakovic, Christov, and Sundmacher. At low overpotentials, the MeOH oxidation reaction was found to be zero order in MeOH concentration, indicating that CO oxidation is the rate-determining step. A Tafel slope of 50-60 mV dec was found at 60°C. At higher overpotentials, positive reaction orders were found, suggesting that MeOH adsorption becomes rate determining. An activation energy of 55 kj moP was found this agrees well with the values found for similar bulk PtRu electrodes. 

Equations 2.26 and 2.27 carmot be solved analytically except for a series of limiting cases considered by Bartlett and Pratt [147,192]. Since fine control of film thickness and organization can be achieved with LbL self-assembled enzyme polyelectrolyte multilayers, these different cases of the kinetic case-diagram for amperometric enzyme electrodes could be tested [147]. For the enzyme multilayer with entrapped mediator in the mediator-limited kinetics (enzyme-mediator reaction rate-determining step), two kinetic cases deserve consideration in this system in both cases I and II, there is no substrate dependence since the kinetics are mediator limited and the current is potential dependent, since the mediator concentration is potential dependent. Since diffusion is fast as compared to enzyme kinetics, mediator and substrate are both approximately at their bulk concentrations throughout the film in case I. The current is first order in both mediator and enzyme concentration and k, the enzyme reoxidation rate. It increases linearly with film thickness since there is no... 

Hendrikx et al. [36] investigated the reaction kinetics and mechanism of zinc and amalgamated zinc electrode in KOH solutions in the concentration range 1.5-10 M using galvanostatic methods. On the basis of Tafel slopes and reaction orders for OH , the following rate determining step (rds) in anodic and cathodic processes was postulated ... 

In voltammetric experiments, electroactive species in solution are transported to the surface of the electrodes where they undergo charge transfer processes. In the most simple of cases, electron-transfer processes behave reversibly, and diffusion in solution acts as a rate-determining step. However, in most cases, the voltammetric pattern becomes more complicated. The main reasons for causing deviations from reversible behavior include (i) a slow kinetics of interfacial electron transfer, (ii) the presence of parallel chemical reactions in the solution phase, (iii) and the occurrence of surface effects such as gas evolution and/or adsorption/desorption and/or formation/dissolution of solid deposits. Further, voltammetric curves can be distorted by uncompensated ohmic drops and capacitive effects in the cell [81-83]. 

Charge density of electrode, determination, 858 Charge of double layer, 1217 Charge transfer, 1213 mechanism, 1294 overpotential and, 1172 rate determining step and, 1179 steady state and. 1213 transport in electrolyte, 1211 Charge transfer, equilibrium at interface kinetic treatment. 1058 Nemst s equilibrium treatment, 1058 polarography, 1240 thermodynamics, 1057... 

It should be stressed at this point that in electrochemical kinetics the relative heights of the activation barriers for the individual elementary steps may not be influenced by the electrode potential in the same way. The mechanism, and thus the rate-determining step, may not be the same at different electrode potentials as ilustrated in Fig. 8. 

The rate-determining step, rds, for a given mechanism may change with potential. However, there is no violation of the principle of microscopic reversibility inspection of Fig. 9 shows that, at any potential, the transition state is always the same for the forward and backward reactions in eqn. (112). Transition states at different electrode potentials, on the other hand, need not be the same (see Fig. 8). Furthermore, there is no reason why the potential E, determined by kinetic factors, at which the transition of rds occurs, should be the same as the thermodynamic equilibrium potential Ee. 

The quantity njv, often called the electron number, on the other hand, is not arbitrary and is characteristic of the electrode reaction kinetics. It indicates the number of electrons gained or lost by the electrode in the completion of the rate-determining step. 

In electrode kinetics, interface reactions have been extensively modeled by electrochemists [K.J. Vetter (1967)]. Adsorption, chemisorption, dissociation, electron transfer, and tunneling may all be rate determining steps. At crystal/crystal interfaces, one expects the kinetic parameters of these steps to depend on the energy levels of the electrons (Fig. 7-4) and the particular conformation of the interface, and thus on the crystal s relative orientation. It follows then that a polycrystalline, that is, a (structurally) inhomogeneous thin film, cannot be characterized by a single rate law. 

The real power of digital simulation techniques lies in their ability to predict current-potential-time relationships when the reactants or products of an electrode reaction participate in some intervening chemical reaction. These kinetic complications often result in a fairly difficult differential equation (when combined with the conditions for diffusion or convection encountered in electrochemical problems) that resists solution by ordinary means. Through simulation, however, the effect of any number of chemical steps may be predicted. In practice, it is best to limit these predictions to cases where the reactants and products participate in one or two rate-determining steps each independent step adds another dimensionless kinetics parameter that must be varied over the range of... 

When the rate determining step of the electrode reaction is the charge transfer process (kinetic control), the faradic impedance ZF in Figure 1.18 can be described as RCJ, the charge transfer resistance [7,8], The impedance plot in the Nyquist plane describes a semicircle, as shown in Figure 1.19. 

Fig. 4 shows a simple phase diagram for a metal (1) covered with a passivating oxide layer (2) contacting the electrolyte (3) with the reactions at the interfaces and the transfer processes across the film. This model is oversimplified. Most passive layers have a multilayer structure, but usually at least one of these partial layers has barrier character for the transfer of cations and anions. Three main reactions have to be distinguished. The corrosion in the passive state involves the transfer of cations from the metal to the oxide, across the oxide and to the electrolyte (reaction 1). It is a matter of a detailed kinetic investigation as to which part of this sequence of reactions is the rate-determining step. The transfer of O2 or OH- from the electrolyte to the film corresponds to film growth or film dissolution if it occurs in the opposite direction (reaction 2). These anions will combine with cations to new oxide at the metal/oxide and the oxide/electrolyte interface. Finally, one has to discuss electron transfer across the layer which is involved especially when cathodic redox processes have to occur to compensate the anodic metal dissolution and film formation (reaction 3). In addition, one has to discuss the formation of complexes of cations at the surface of the passive layer, which may increase their transfer into the electrolyte and thus the corrosion current density (reaction 4). The scheme of Fig. 4 explains the interaction of the partial electrode processes that are linked to each other by the elec-... 

Diffusion current — The rate of an - electrode process is always determined by one of its consecutive steps (i.e., by the most hindered or slowest one). The - charge transfer step is always accompanied by - diffusion because, as the reagent is consumed or the product is formed at the electrode, concentration gradients between the vicinity of the interface and the bulk solution arise, which induce diffusion. When the diffusion is the rate-determining step we speak of diffusion kinetics. The - current which flows under this condition is called diffusion current. 

Another mechanistic possibility is the attack of the thiophene cation radical (420) upon a neutral thiophene monomer (419) to form a cation-radical dimer (421) [247]. The oxidation and loss of two protons leads to formation of the neutral dimer (422). Once again, rapid oxidation of the dimer occurs upon its formation due to its close proximity to the electrode surface and its lower oxidation potential. The cation-radical dimer (423) which is formed then reacts with another monomer molecule in a similar series of steps to produce the trimer 425. A kinetic study of the electrochemical polymerization of thiophene and 3-alkylthiophenes led to the proposal of this mechanism (Fig. 61) [247]. The rate-determining step in this series of reactions is the oxidation of the thiophene monomer. The reaction is first order in monomer concentration. The addition of small amounts of 2,2 -bithiophene or 2,2 5, 2"-terthiophene to the reaction resulted in a significant increase in the rate of polymerization and in a lowering of the applied potential necessary for the polymerization reaction. In this case the reaction was 0.5 order in the concentration of the additive. 

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