Heterogeneous electrode

According to the Marcus theory [64] for outer-sphere reactions, there is good correlation between the heterogeneous (electrode) and homogeneous (solution) rate constants. This is the theoretical basis for the proposed use of hydrated-electron rate constants (ke) as a criterion for the reactivity of an electrolyte component towards lithium or any electrode at lithium potential. Table 1 shows rate-constant values for selected materials that are relevant to SE1 formation and to lithium batteries. Although many important materials are missing (such as PC, EC, diethyl carbonate (DEC), LiPF6, etc.), much can be learned from a careful study of this table (and its sources). 

Many other heterogeneous electrodes have been developed based on, e.g., calcium oxalate or stearate in paraffin, barium sulphate in paraffin or silicone-rubber, bismuth phosphate or iron(III) phosphate in silicone-rubber, caesium dodecamolybdophosphate in silicone-rubber and amminenickel nitrate in phenol-formaldehyde resin39 these permit the determination, respectively, of Ca and oxalate, Ba and sulphate, Bi or Fe(HI) and phosphate, Cs, Ni and nitrate, etc. 

The interface between the electrode and the electrolyte or electrochemical interface is the site where heterogeneous electrode reactions occur. The structure and electrical properties of this interfacial region are therefore relevant to electrode kinetics. 

As will be discussed in Sect. 5, linear free energy relations allow comparisons between the kinetics of heterogeneous (electrode) and homogeneous homomolecular charge transfer reactions. 

The original work of Libby [66] and Weiss [67] in homogeneous redox reactions prompted the development of electrostatic theories for homogeneous and heterogeneous (electrode) electron transfer. 

In the text that follows, we examine the methodology of electrochemistry as it may be usefully applied to a wide variety of chemical problems. In short, when a molecule can be coupled to an electrode reaction, that reaction may be used for analytical, mechanistic, or kinetic studies involving this substance. We make no pretense about the fact that this is not a book for physical electrochemists. Those who wish to direct their efforts toward unraveling the microsteps in heterogeneous electrode processes per se are best served by other monographs. Those focused on generation of electrical power from chemical reactions will also find little here of direct interest. 

The increased rate of mass transport associated with shrinking electrode size means that electrode processes which appear electrochemically reversible at large electrodes may show quasi- or irreversible electrode kinetics when examined using both steady-state and transient mode microelectrode methods. The latter represents a powerful approach for the determination of fast heterogeneous electrode kinetics. Rate constants in excess of lcms have been reported (Montenegro, 1994). 

If the electrode potential, , is 118 mV smaller than for the preparative reduction of O, then X is 99 % or, expressed dilferently, only 1 % of O has not been transformed at the end of the electrolysis. Equation 98 is valid not only for fast (nernstian) but also for slow heterogeneous electrode reactions, since an equilibrium situation is always attained at the end of the electrolysis where the current is essentially zero. For an irreversible electrode reduction, the rate of electrolysis as expressed by the electrolysis current is, however, very low if E — Eq is — 118 mV. The employment of much higher overpotentials or mediated electrolysis (see Section 2.7) may then be required for achieving a reasonable rate of transformation. 

A rugged type of heterogeneous electrode was suggested by Freiser and others in which a slightly soluble salt is deposited as a polymeric matrix simply painted onto a platinum wire, as, for example, a dispersion with an epoxy resin. 

Figure 6.15 Voitammetric behavior of a heterogeneous electrode with active and inert parts, illustrating cases 1, 2, 3, and 4 (see text) [42].

The importance of Marcus theoretical work on electron transfer reactions was recognized with a Nobel Prize in Chemistry in 1992, and its historical development is outlined in his Nobel Lecture.3 The aspects of his theoretical work most widely used by experimentalists concern outer-sphere electron transfer reactions. These are characterized by weak electronic interactions between electron donors and acceptors along the reaction coordinate and are distinct from inner-sphere electron transfer processes that proceed through the formation of chemical bonds between reacting species. Marcus theoretical work includes intermolecular (often bimolecular) reactions, intramolecular electron transfer, and heterogeneous (electrode) reactions. The background and models presented here are intended to serve as an introduction to bimolecular processes. 

An electrochemically heterogeneous electrode is one where the electrochemical activity varies over the surface of the electrode. This broad classification encompasses a variety of electrode types [1, 2] including microelectrode arrays, partially blocked electrodes, electrodes made of composite materials, porous electrodes and electrodes modified with distributions of micro- and nanoscale electroactive particles. In this chapter, we extend the mathematical models developed in the previous chapter, in order to accurately simulate microelectrode arrays. Fbrther, we explore the applications of a number of niche experimental systems, including partially blocked electrodes, highly ordered pyrolytic graphite, etc., and develop simulation models for them. 

RRB and APEE mechanisms represent extreme cases. The RRB mechanism is to be favoured in cases in which strong protein adsorption is not apparent. The APEE mechanism, on the other hand, is to be favoured wherever diffusion-controlled voltammetry is observed despite strong adsorption with saturative electrode surface coverage. For a heterogeneous electrode surface, it is quite likely that both mechanisms can operate simultaneously with RRB and APEE occurring, respectively, at coolspots and hotspots . 

The classical modification processes for solid homogeneous electrodes are (i) film and (ii) membrane covering, as well as (iii) adsorption, and (iv) covalent attachment immobilization of the modifier. These avenues are also open to modify carbon paste as the most popular representative of heterogeneous electrode materials. But, because of its composite character, it facilitates simpler ways of modification by direct addition of the modifier to the paste either during or after the preparation of the material. The term direct mixing was coined by Baldwin [106], though the history of modification of CPEs dates back to the mid-1960s, when Kuwana was the first who added electroactive components to the paste [107]. (In his case, however, there had been no intention to alter the CPE characteristics, and the purpose was to study the redox behavior of the adduct in a nonaqueous environment.)... 

In the last case, a homogeneous reaction step permits the combination of the intermediates formed by the heterogeneous electrode reactions. 

Heterogeneous electrode reactions can be compared with homogeneous kinetics in solution, with regard to mass transport. The second-order rate coefficient for a fast homogeneous reactions in solution, k(hom), which would be observed if diffusion were infinitely fast, can be related to the measured rate coefficient, kob3(hom) by application of Eick s first law in a spherical continuum diffusion field around the reacting molecule. At a collision distance Tab. this corresponds to the average... 

Besides Ri = and Cj = C, one often finds parallel Ri, Ci response associated with a heterogeneous electrode reaction. For such a case we would set R = Rg and Cl = Cr, where Rr is a reaction resistance and C is the diffuse double-layer capacitance of the polarization region near the electrode in simplest cases. The circuit of Figure 1.3.1Z combines the above possibilities when R2 = Rr and C2 = Cr. The results shown in Figure 1.3.le and/are appropriate for the well-separated time constants, It is also possible that a parallel RC combination can arise... 

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