Electrode reaction rate

Electrode reaction rate constant k (varies) = Ij nFAY[c ... 

A conditional electrode reaction rate constant ) which is defined as the common value of the anodic and cathodic rate constants at the conditional electrode potential is given according to... 

Electrode reactions are heterogeneous since they occur at interfaces between dissimilar phases. During current flow the surface concentrations Cg j of the substances involved in the reaction change relative to the initial (bulk) concentrations Cy p Hence, the value of the equilibrium potential is defined by the Nemst equation changes, and a special type of polarization arises where the shift of electrode potential is due to a change in equilibrium potential of the electrode. The surface concentrations that are established are determined by the balance between electrode reaction rates and the supply or elimination of each substance by diffusion [Eq. (4.9)]. Hence, this type of polarization, is called diffusional concentration polarization or simply concentration polarization. (Here we must take into account that another type of concentration polarization exists which is not tied to diffusion processes see Section 13.5.)... 

The surface concentrations that are attained as a result of balance between the electrode reaction rates and the rates of supply or escape of components by diffusion and migration are given by Eqs. (4.11) and (4.12). Hence, the overall expression for concentration polarization becomes... 

Table 5.1 Conditional electrode reaction rate constants k° and charge transfer coefficients a. (From R. Tamamushi)... 

The determination of the activation energies of electrode reactions is especially important for the theory of electrode reactions and for study of the relationship between the structure of the reacting substances and the electrode reaction rates. 

Several descriptions of electrode reaction rates discussed on the preceding pages and the difficulty to standardize electrode potential scales with respect to different temperatures imply several definitions of activation energies of electrode reactions. The easiest way to determine this quantity, for example, for an irreversible cathodic process, employs Eqs (5.2.9), (5.2.10) and (5.2.12) at a constant electrode potential,... 

For the sake of a practical analysis of the polarization curve the exponential dependence of the electrode reaction rate constant need not be assumed. Then the more general form of Eq. (5.4.22) can be written as... 

Each sort of complex including the free ions has a characteristic electrode reaction rate constant (for example, kc MX., / = 0, 1,.. ., n). 

We assume that neither the preexponential factor of the conditional electrode reaction rate constant nor the charge transfer coefficient changes markedly in a series of substituted derivatives and that the diffusion coefficients are approximately equal. In view of (5.2.52) and (5.2.53),... 

Strictly speaking, electrocatalysis applies to the dependence of the electrode reaction rate on the nature of the electrode material [152]. In the following, this term will be used in a broader sense and will be admitted to include the possibility that the catalyst be homogeneously dissolved in the electrolyte solution as well as the case where the catalyst is attached to the electrode surface. A short chapter on the electrocatalysis of inorganic chemicals by chemically modified electrodes can also be found in Vol. 10 of this Encyclopedia [9]. 

Derivation of the Butler-Volmer equation in terms of electrode reaction rate constants is given in most electrochemical texts.1,3 7 15... 

Now, there is a second group of factors called geometric that influence an electrode reaction rate, i.e., electrocalalysis. These factors will remind the reader of some of the structural matters covered in discussions of chemical catalysis. They refer to the structure and often to the heterogeneity of the catalyst s surface. Active sites on the surface can be identified. Examples of such factors are ... 

Here kel is the electrode reaction rate constant, Q is the volume per one semiconductor particle (atom or molecule), which leaves the solid and penetrates into the solution, p is the concentration of holes at the interface, p = p X(y,z, t), y, z), and v is the number of holes per one particle dissolved. In the quasistationary case (i.e., when the condition v Lpfrp is satisfied) the distribution of holes is described by the equation similar to Eq. (29) ... 

For ja > jc and vice versa, the electrode reaction rate coefficients can be obtained from the measured current, j, by... 

Since the current density depends on electrode potential, so does kobs. The dependence of the electrode reaction rate coefficients on potential is given by the empirical transfer coefficient a [8, 9]... 

The simplest effect of pure electrostatic ionic adsorption on electrode reaction rates of ions is the Frumkin double layer effect already been discussed in Sect. 3.5. 

The simplest treatment of this problem considers that, for a given potential, the electrode reaction rate coefficient is a linear function of the coverage by adsorbate. The overall electrode reaction rate coefficient is thus expressed as a weighted linear combination of the rate coefficients at the covered sites, fex, and at the adsorbate free surface, kQ... 

The search for new electrode materials is expected to be guided by the fundamental understanding of the factors governing the activity. In electrochemistry, this branch of the discipline is known by the name of electrocatalysis . Strictly speaking, electrocatalysis is the science devoted to the relationship between the properties of materials and the electrode reaction rate. The scope of electrocatalysis as a science is to establish a predictive basis for the design and the optimization of electrocatalysts. 

The exchange current density is the electrode reaction rate at the equilibrium potential (identical forward and reverse reaction rates) and depends on the electrode properties and operation. The typical expression for determining the exchange current density is the Arrhenius law (3.23), where the constant A depends on the gas concentration. Costamagna et al. [40] provide the following expressions for the anodic and cathodic exchange current density, respectively ... 

The electrochemical reduction of nitrobenzene to produce p-aminophenol has attracted industrial interest for several decades. However, some limitations may be met in this process regarding overall reaction rate, selectivity and current efficiency using a two-dimensional electrode reactor. These restrictions are due to the organic electrode reaction rate being slow and to the low solubility of nitrobenzene in an aqueous solution. In this example, a packed bed electrode reactor (PBER), which has a large surface area and good mass transfer properties, was used in order to achieve a high selectivity and a reasonable reaction rate for the production of p-aminophenol. The reaction mechanism in an acid solution can be simplified as... 

A detailed examination of the mass transport effects of the HMRDE has been made. At low rotation speeds and for small amplitude modulations (as defined in Section 10.3.6.2) the response of the current is found to agree exactly with that predicted by the steady-state Levich theory (equations (10.15)-(10.17)) [27, 36, 37]. Theoretical and experimental application of the HMRDE, under these conditions, to cases where the electrode reaction rate constant was comparable to the mass-transfer coefficient has also been made [36]. At higher rotation speeds and/or larger amplitude modulations, the observed current response deviated from the expected Levich behaviour. 

High temperature membranes, that can operate at temperatures above 100 °C, are desirable to promote heat rejection, speed up electrode reaction rates, and to improve tolerance to impurities. This is an active area of materials research. Unfortunately, space constraints preclude a detailed description of fuel cell technologies and the underlying issues. Instead, the reader is referred to excellent reviews and books that exist on this topic.45 47... 

Such an approach could explain, though in a semiquantitative way, the behavior of the systems studied earlier, when a minimum was observed on the kf versus solvent composition dependence. Analysis of the change in the rate of reaction, expressed as a product of the electrode reaction rate constant and the reactant concentration in the surface phase, c, in mixtures of water with acetone reveals a deep minimum, which corresponds to the greatest difference in composition of the surface and bulk phases. 

An important factor to analyze the performance of a battery is to characterize the electrode kinetics reaction rate, because the chemical energy is transformed into electrical energy through the electrode kinetics. The rates of the electrode reactions depend on the nature of the electrode surface, the composition of the electrolyte solution adjacent to the electrode (outside the double layer), and the electrode potential [15]. Before we analyze the typical expressions for electrode reaction rates, we need to discuss some important concepts such as double layer, and surface overpotential. 

Expressions used for the reaction rates of the electrodes relate the current density with the surface overpotential and the concentration outside the double layer. One of the simplest relations used to express electrode reaction rates is the... 

Limiting current, q Current plateau reached in voltammetry when the electrode reaction rate is limited by the rate of mass transfer. 

The temperature effect often disturbs precise measurements if isothermal conditions cannot be maintained and if it leads to damage of the sample. Equation 1.12 shows that at constant power density the temperature effect decreases with decreasing pulse times. Therefore, the application of short pulses may be of advantage to avoid damages. If, however, the modification of the surface requires a large amount of total energy, it should be delivered with low power density. On the other hand, there are numerous applications of the thermal heating. It can be used to evaporate or to dissociate the substrate (LAMMA) [64], to enhance reaction rates at the surface or the convection of the electrolyte [65-67]. Finally, it can be employed to study electrode reaction rate constants and the dynamics of the double layer [68]. 

Before proceeding to direct attention to the real temperature dependence of Tafel slopes as found experimentally for a number of systems, it will be necessary to review the conventional behavior usually assumed and describe its theoretical and historical origins. The remarkable contrast of the behavior actually observed, to be described in Section III, to that conventionally assumed will then be apparent and thus the present major gap in our understanding of the fundamental aspect of potential dependence of electrode reaction rates will be better perceived. 

---