Electrode reaction, representation

Fig. 12. Schematic representation of the effect of adsorption of intermediates on the activation barrier for an electrode reaction. Both initial and final states are taken at the same free energy.

Fig. 1. (a) Network representation of the current pathways in the electrochemical halfcell. (b) The processes possibly involved in an electrode reaction O + n e = R. 

Fig. 6.9. (a) Schematic representation of the path followed by an electrode reaction. The effect of the electrode s electric field begins at the outside of the double layer, but for there to be reaction the species has to reach xu from the electrode (b) Variation of 0 with distance, showing that the potential difference to cause electrode reaction is (0M — 0 ). 

Figure 4.22 Simultaneous idealized representation of ETSM processes. Curve a (solid line) represents the current flow in the cell for a redox cycle, while curve b (dotted line) represents the concurrent frequency shift associated with the adsorption (fwward arrow) and desorption (reverse arrow) of mass at the electrode surface during the redox electrode reaction. The reference electrode is a saturated calomel electrode (SCE).

It has to be mentioned that such equivalent circuits as circuits (Cl) or (C2) above, which can represent the kinetic behavior of electrode reactions in terms of the electrical response to a modulation or discontinuity of potential or current, do not necessarily uniquely represent this behavior that is other equivalent circuits with different arrangements and different values of the components can also represent the frequency-response behavior, especially for the cases of more complex multistep reactions, for example, as represented above in circuit (C2). In such cases, it is preferable to make a mathematical or numerical analysis of the frequency response, based on a supposed mechanism of the reaction and its kinetic equations. This was the basis of the important paper of Armstrong and Henderson (108) and later developments by Bai and Conway (113), and by McDonald (114) and MacDonald (115). In these cases, the real (Z ) and imaginary (Z") components of the overall impedance vector (Z) can be evaluated as a function of frequency and are often plotted against one another in a so-called complex-plane or Argand diagram (110). The procedures follow closely those developed earlier for the representation of dielectric relaxation and dielectric loss in dielectric materials and solutions [e.g., the Cole and Cole plots (116) ]. 

Fig. 8 Schematic representation of the double layer for the electrode reaction given in Eq. (3). The thickness of the double layer is of the order of nanometers.

Figure 8.5. Representation of a conductivity cell when the applied potential exceeds the potential for reaction. Re - ohmic resistance, Cj - double layer capacitance, Z, - impedance due to the electrode reaction.

Figure 8.6. Complete representation of a conductivity cell. Re - ohmic resistance, Cs - double layer capacitance, Rw - Warburg s resistance, Cw - Warburg s capacitance, - resistive component due to the finite rate of electrode reaction, Cq — stray capacitance.

The empirical representation of electrode process rates according to a relation such as Eq. (1) or its exponential form, Eq. (4), takes into account that, for many electrode processes. In i is linear in 7) over an appreciable range (> 0.2 V say) of potentials. More will be said about this later with regard to specific examples however, it must be stated here that for some processes such as rapid redox reactions (high Iq values) and some organic electrode reactions, a quadratic term in ry may also arguably appear in Eq. 

For symmetrical processes, each of these ways of representing the significance of gives the latter quantity a value of 0.5. However, the unsymmetrical processes, the different representations do not lead to identical values of for a given reaction note that atom transfer processes are normally highly unsymmetrical, so how p is considered from the theoretical point of view is especially important for such types of electrode reaction. 

The previous conclusion means that existing conventional representations of the activation process according to an electrochemical Arrhenius type of equation involving the Boltzmann factor l/fc7 are seriously inadequate and fail to represent the real kinetic behavior of most electrode reactions from the important point of view of temperature effect—a central aspect of most evaluations of kinetics of chemical processes. 

From the above, it seems clear that a Fermi-type distribution for the electronic energy levels in the metal should certainly be employed in the representation of electrode reaction rates as a function of potential and hence enters into how the Tafel slope or transfer coefficient is expressed, including its relation to T. 

Electrochemical (electrode) reactions are inherently heterogeneous. The electron transfer reaction occurs at a metal (or other electrically conducting substrate)-solution interface. However, prior to and following the electron transfer reaction, transport of chemical species between the bulk of the solution and the interface also takes place. Figure 6 is a representation of these processes which constitute the totality of the electrochemical reaction. 

Figure 6. Representation of transport and kinetic processes in electrode reactions...

Since a and b are constants, plotting the anode and cathode overpotential curves of a simple electrode reaction in semilogarithmic representation results in straight lines when the overpotential is plotted on the linear axis and the current density I o on the logarithmic axis. 

Fig. 7 Schematic representation of the variation of the individual rate coefficients (c (broken lines) and the overall rate coefficient (solid line) for a two-electron electrode reaction as a function of the electrode potential.

The exchange current Iq is a measure of the rate of exchange of charge between oxidized and reduced species at any equilibrium potential without net overall change. The rate constant k, however, has been defined for a particular potential, the formal standard potential of the system. It is not in itself sufficient to characterize the system unless the transfer coefficient is also known. However, Eq. (2.21) can be used in the elucidation of the electrode reaction mechanism. The value of the transfer coefficient can be determined by measuring the exchange current density as a function of the concentration of the reduction or oxidation species at a constant concentration of the oxidation of reduction species, respectively. A schematic representation of the forward and backward currents as a function of overvoltage, 7] = E - E, is shown in Fig. 2.6, where the net current is the sum of the two components. 

Fig. 1 The electrode/electrolyte interface, iUustiatmg Faradaic chaige transfer (top) and capacitive redistribution of chaige (bottom) as the electrode is driven negative, (a) Physical representation (b) Two-element electrical circuit model for mechanisms of charge transfer at the interface. The capacitive process involves reversible redistribution of chaige. The Faradtiic process involves transfer of electrons from the metal electrode, reducing hydrated cations in solution (symbolically 0 + e R, where the cation O is the oxidized form of the redox couple O/R). An example reaction is the reduction of silver ions in solution to form a silver plating on the electrode, reaction (8a). Faradaic charge injection may or may not be reversible...

Fig. 5. Generalized reaction path for an organic electrode reaction. This representation is generally similar to that proposed by Hush. ...

Over the years the original Evans diagrams have been modified by various workers who have replaced the linear E-I curves by curves that provide a more fundamental representation of the electrode kinetics of the anodic and cathodic processes constituting a corrosion reaction (see Fig. 1.26). This has been possible partly by the application of electrochemical theory and partly by the development of newer experimental techniques. Thus the cathodic curve is plotted so that it shows whether activation-controlled charge transfer (equation 1.70) or mass transfer (equation 1.74) is rate determining. In addition, the potentiostat (see Section 20.2) has provided... 

Fig. 19.39 Schematic representation of reactions during (a) controlled potential and (b) conventional corrosion tests in acidic chloride solutions. In (a) charge balance must be maintained by migration of Cl" ions, since the cathodic reaction occurs elsewhere at the counter-electrode. In (b) the anodic and cathodic sites are in close proximity, and charge balance is maintained without migration of Cl" ions from the bulk solution (after France and Greene )...

Because of the variety of ionic species present in the melt, the reactions that take place at the electrodes are considerably more complex than the simple representations given here. Nevertheless, the net reaction is the one given by these simplified reactions 4 e I f) + 6 0 m slt) + 3 (. ) -> 3 C02(g) + 4 Al(/)... 

Fig. 5.6 (Left) Comparison of band energy levels for different II-VI compounds. Note the high-energy levels of ZnSe. Representation is made here for electrodes in contact with 1 M HQO4. The reference is a saturated mercury-mercurous sulfate electrode, denoted as esm (0 V/esm = +0.65 V vs. SHE). (Right) Anodic and cathodic decomposition reactions for ZnSe at their respective potentials (fidp, Fdn) and water redox levels in the electrolytic medium of pH 0. (Adapted from [121])...

Figure 9.23 Schematic representation of the various electrochemical and chemical reactions occurring in a membrane electrode assembly and the concentration gradients of O2, H2, and Pt ions. The location where the local O2 molar flux equals one-half of the local H2 molar flux is marked by 5pt. (Reproduced with permission from Zhang J et al. [2007a].)...

Figure 15.2 Schematic representation of different electrochemical cell types used in studies of electrocatalytic reactions (a) proton exchange membrane single cell, comprising a membrane electrode assembly (b) electrochemical cell with a gas diffusion electrode (c) electrochemical cell with a thin-layer working electrode (d) electrochemical cell with a model nonporous electrode. CE, counter-electrode RE, reference electrode WE, working electrode.

The cell reaction is the sum of the electrochemical reactions taking place at both electrodes. The cell reaction may be written in two ways which are dependent on the sequence of phases in the graphical scheme of the cell. The representation of the cell reaction should correspond to the flow of positive charge through the cell (in a graphical scheme) from left to right ... 

Figure 9. Schematic representation of the acrylic chambers used for treatment of P815 cells with DC. Chambers are connected in series by filter-paper bridges, and fitted with platinum electrodes in their extremities. In this system, cell suspensions can be exposed directly to the anodic reactions (AC) or cathodic reactions (CC) or to electric current without contact with the electrodes, in the intermediary chamber (IC). Internal volume 3 cm3. After Veiga et al.62...

The reduction half-reaction does not include a solid conductor of electrons, so an inert platinum electrode is used in this half-cell. The platinum electrode is chemically unchanged, so it does not appear in the chemical equation or half-reactions. However, it is included in the shorthand representation of the cell. 

---