Steps in an Electrode Process

In its simplest form, an electrode process may proceed through all or some of the following steps  

The electroactive particle is transferred to the electrode surface from the bulk solution. 

The reacted particle suffers desorption and chemical reaction, in either order, then is transported back into the bulk solution. Or, the reacted particle becomes an adatom, then is incorporated into the electrode surface. 

Take for example the discharge of hydrogen ions. One possible scheme is shown in Table 3.1. 

For the discharge of a metal such as zinc we might expect the pattern in Table 3.2. 

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The measurement of a from the experimental slope of the Tafel equation may help to decide between rate-determining steps in an electrode process. Thus in the reduction water to evolve H2 gas, if the slow step is the reaction of with the metal M to form surface hydrogen atoms, M—H, a is expected to be about If, on the other hand, the slow step is the surface combination of two hydrogen atoms to form H2, a second-order process, then a should be 2 (see Ref. 150). 

Thus, an equation in agreement with the experimental data for the hydroquinone-silver ion reaction can be derived either on the basis of the assumption that adsorption of silver ions by the silver is a prelude to the reaction, or on the basis of the assumption that the rate-controlling step in an electrode process is the rate of transfer of electrons to the silver electrode. The first mechanism carries with it the assumption that a silver ion adsorbed by silver is more easily reduced than an ion in solu-... 

Particularly, temperatures above ambient are used because of the beneficial effect on the kinetics of all steps in an electrode process. The diffusion coefficient, the exchange current density and the rate of chemical reactions are all increased. 

Some complications can arise when rate constants for reverse directions of a step are mnch smaller than that for the forward direction of the given process. This of course then leads to a large qnasi-equilibrium constant, 1, for the step concerned. For steps in an electrode reaction... 

Knowledge of whether an electrode process is reversible or irreversible is crucial in interpreting polarograms. The reversibility of the electrode reaction depends upon the rate of reaction of the following stages in an electrode process (1) the charge transfer step, (2) the chemical reaction, (3) diffusion of analyte to the electrode, and (4) adsorption processes. 

In spite of these limitations, there has been an increasing tendency to apply the qualitative aspects of the theory, such as the energy diagrams, to more complex electrode processes, but it seems unlikely that extensions of the model will lead to a correct understanding, even at the intu we level, of the activation step in such electrode processes. 

Although the effect of temperature on each of the steps in an overall electrode process is readily predictable, it is surprising to find in the literature very few systematic studies of this variable or attempts to use it to change the rate, products or selectivity of an organic electrosynthetic process. A recent paper has, however, discussed equipment and suitable solvents for low-temperature electrochemistry (Van Dyne and Reilley, 1972a). 

A simulation (Volume 3, Chapter 3.1) is the reproduction of an electroanalytical experiment in the form of a set of mathematical equations and their solutions, usually on a digital computer [7]. The equations express a physical model of the real experiment. Thus, the main steps of the electrode process (see Section 1.2.1) are included. 

Since not only the electron-transfer step but also adsorption and some of the chemical steps involved in an electrode reaction take place in the layer, the whole process should be strongly influenced by polar factors. The orientation of polar-adsorbed species, such as ion-radicals in particular, is electrostatically influenced, and consequently, the stereochemistry of their reactions is also controlled by such kind of electrostatic factor. All these phenomena have been summarized in several monographs. The collective volume edited by Baizer and Lund (1983) is devoted to organic electrochemistry. This issue is closer to the scope of our consideration than its latest version edited by Lund and Hammerich (2001) (these editors have changed the invited authors and, consequently, the chapters included). 

The first step in the deposition process is that in which an ion crosses the electrified interface, i.e., the charge-transfer reaction. Picture the situation (Fig. 7.122). A hydrated ion (e.g., a silver ion) is waiting at the OHP. In the direction of the silver metal electrode, there is the three-dimensional network, or lattice, consisting of silver ions cemented together by an electron gas. The silver ions in the lattice each lay claim to an electron of the electron gas in this sense, they can be said to be neutral and... 

Here, AH(A-B) is the partial molar net adsorption enthalpy associated with the transformation of 1 mol of the pure metal A in its standard state into the state of zero coverage on the surface of the electrode material B, ASVjbr is the difference in the vibrational entropies in the above states, n is the number of electrons involved in the electrode process, F the Faraday constant, and Am the surface of 1 mol of A as a mono layer on the electrode metal B [70]. For the calculation of the thermodynamic functions in (12), a number of models were used in [70] and calculations were performed for Ni-, Cu-, Pd-, Ag-, Pt-, and Au-electrodes and the micro components Hg, Tl, Pb, Bi, and Po, confirming the decisive influence of the choice of the electrode material on the deposition potential. For Pd and Pt, particularly large, positive values of E5o% were calculated, larger than the standard electrode potentials tabulated for these elements. This makes these electrode materials the prime choice for practical applications. An application of the same model to the superheavy elements still needs to be done, but one can anticipate that the preference for Pd and Pt will persist. The latter are metals in which, due to the formation of the metallic bond, almost or completely filled d orbitals are broken up, such that these metals tend in an extreme way towards the formation of intermetallic compounds with sp-metals. The perspective is to make use of the Pd or Pt in form of a tape on which the tracer activities are electrodeposited and the deposition zone is subsequently stepped between pairs of Si detectors for a-spectroscopy and SF measurements. 

The second part of the book discusses ways in which information concerning electrode processes can be obtained experimentally, and the analysis of these results. Chapter 7 presents some of the important requirements in setting up electrochemical experiments. In Chapters 8—11, the theory and practice of different types of technique are presented hydrodynamic electrodes, using forced convection to increase mass transport and increase reproducibility linear sweep, step and pulse, and impedance methods respectively. Finally in Chapter 12, we give an idea of the vast range of surface analysis techniques that can be employed to aid in investigating electrode processes, some of which can be used in situ, together with photochemical effects on electrode reactions— photoelectrochemistry. 

When an electrode process involves several steps, sometimes a succession of semi-circles side by side is obtained, corresponding to RC parallel combinations in series and with different RC time constants, from which it is possible to deduce the corresponding parameters. 

Charge-transfer overpotential — The essential step of an - electrode reaction is the charge (- electron or - ion) transfer across the phase boundary (- interface). In order to overcome the activation barrier related to this process and thus enhance the desirable reaction, an - overpotential is needed. It is called charge-transfer (or transfer or electron transfer) overpotential (f/ct). This overpotential is identical with the - activation overpotential. Both expressions are used in the literature [i-iv]. Refs. [i] Bard A], Faulkner LR (2001) Electrochemical methods. Wiley, New York, pp 87-124 [ii] Erdey-Gruz T (1972) Kinetics of electrode processes. Akademiai Kiadd, Budapest, pp 19-56 [Hi] Inzelt G (2002) Kinetics of electrochemical reactions. In Scholz F (ed) Electroanalytical methods. Springer, Berlin, pp 29-33 [iv] Hamann CH, Hamnett A, Viel-stich W (1998) Electrochemistry. Wiley VCH, Weinheim, p 145... 

This mechanism is denoted as an EC mechanism (Testa and Reinmuth, 1961 Bott, 1997). Thus homogeneous kinetic terms may be combined with the expressions for diffusion and convection [i.e. a modified version of (18)] to give the temporal variation of the concentration of a species in an electrode reaction mechanism. In order to model the voltammetric response associated with this mechanism, a knowledge of , a, ko and k is required, or deduced from a theoretical-experimental comparison, and the set of concentrationtime equations for species A, B and C must be solved subject to the constraints of the Butler-Volmer equation and the experimental design. Considerable simplification of the theory is achieved if the kinetics for the forward and reverse processes associated with the E step are fast, which is a good approximation for many organic reactions. Section 7 describes the approaches used to solve the equations associated with electrode reaction mechanisms, thus enabling theoretical simulation of voltammetric responses to be achieved. 

The involvement of chemisorbed intermediates in electrocatalytic reactions is manifested in various and complementary ways which may be summarized as follows (i) in the value of the Tafel slope dK/d In i related to the mechanism of the reaction and the rate-determining step (ii) in the value of reaction order of the process (iii) in the pseudocapacitance behavior of the electrode interface (see below), for a given reaction (iv) in the frequency-response behavior in ac impedance spectroscopy (see below) (v) in the response of the reaction to pulse and linear perturbations or in its spontaneous relaxation after polarization (see below) (vi) in certain suitable cases, also to the optical reflectivity behavior, for example, in reflection IR spectroscopy or ellipso-metry (applicable only for processes or conditions where bubble formation is avoided). It should be emphasized that, for any full mechanistic understanding of an electrode process, a number of the above factors should be evaluated complementarily, especially (i), (ii), and (iii) with determination, from (iii), whether the steady-state coverage by the kinetically involved intermediate is small or large. Unfortunately, in many mechanistic works in the literature, the required complementary information has not usually been evaluated, especially (iii) with 6(V) information, so conclusions remained ambiguous. 

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