Processes with coupled chemical reactions

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

Convolution methods simplify to some extent the treatment of data for electrode processes with coupled chemical reactions (20) and may be useful in analytical applications (22). 

We have been mainly discussing the redox properties of compounds which commonly undergo single-electron reversible or quasKeversible oxidations. Hovrever, for some types of complexes, irreversible redox processes with coupled chemical reactions have been detected and examples are considered below. 

The aim of this chapter has been to show how SECM, operating as an ultra-thin-layer cell, can be used to quantitatively study electrode processes involving coupled chemical reactions. The advantages of SECM are that a wide range of calculable mass transport rates can be achieved with high reproducibility simply by changing the interelectrode separation and the tip... 

When CV is conducted at stationary microelectrodes with slow V, in both forward and backward scans sigmoidal current-voltage curves are found which are usually coincident, except for processes involving coupled chemical reactions that display more or less marked hystereses. This sigmoidal shape (steady-state current) can be accounted for by considering the radial diffusion to the edges of ultramicroelectrode surfaces that is very important at slow v, so as to make the diffusion rate of analyte molecules to the electrode surface comparable with the charge transfer rate. 

The situation is very different when the redox reaction is slow or coupled with a chemical reaction, hideed, it is these nonideal processes that are usually of greatest chemical interest and for which the diagnostic power of cyclic voltammetry is most useful. Such information is usually obtained by comparing the experimental... 

Many anodic oxidations involve an ECE pathway. For example, the neurotransmitter epinephrine can be oxidized to its quinone, which proceeds via cyclization to leukoadrenochrome. The latter can rapidly undergo electron transfer to form adrenochrome (5). The electrochemical oxidation of aniline is another classical example of an ECE pathway (6). The cation radical thus formed rapidly undergoes a dimerization reaction to yield an easily oxidized p-aminodiphenylamine product. Another example (of industrial relevance) is the reductive coupling of activated olefins to yield a radical anion, which reacts with the parent olefin to give a reducible dimer (7). If the chemical step is very fast (in comparison to the electron-transfer process), the system will behave as an EE mechanism (of two successive charge-transfer steps). Table 2-1 summarizes common electrochemical mechanisms involving coupled chemical reactions. Powerful cyclic voltammetric computational simulators, exploring the behavior of virtually any user-specific mechanism, have... 

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. 

A more interesting situation is found when the homogeneous redox reaction is combined with a chemical reaction between the electrocatalyst and the substrate. In this case, the catalytic process is called chemical catalysis. 3 This mechanism is depicted in Scheme 2 for reduction. The coupling of the electron transfer and the chemical reaction takes place via an inner-sphere mechanism and involves the formation of a catalyst-substrate [MC-S] complex. Here the selectivity of the mechanism is determined by the chemical step. Metal complexes are ideal candidates... 

Figure 3,55 Cyclic vollammograms of Re(Bipy)(CO)3CI in CH3CN/0.l M letrabutylammonium hexafluorophosphate as supporting electrolyte at a button Pt electrode, and with a sweep rate of 200 mV s (a) The switching potential characteristics of the coupled chemical reactions in the ahsence of C02. The lettered redox processes are discussed in the text. (b> The effect of saturating the solution with C02. From Sullivan et al. (1985).

Diagnostic criteria for two-electron transfers with different extents of reversibility. The voltammetric responses of EE processes can be qualitatively confused with processes complicated by coupled chemical reactions. The only distinctive criterium to define these processes is the constancy of the parameter ip/v112 relative to each step with the scan rate. 

It now remains to calculate the diffusion currents, zrequired times. An apparently simple way would be to use a substance fairly similar to Ox (or having a similar diffusion coefficient) capable of being reduced simply by a diffusion process (or, without coupled chemical reactions) through a process involving n + 2 electrons. A solution of this substance could therefore be prepared with the same molarity as that containing Ox, such that one can measure the potentiostatic current at the required times. In practice, however, this method is quite laborious. 

It may occur that an electroactive species is present in the system in equilibrium with some electroinactive form. Then, in addition to diffusion, so-called coupled chemical reactions will occur delivering or consuming the electroactive component. If the rate of such a reaction is sufficiently fast, it will appear that all of the species concerned are diffusing simultaneously to take part in the heterogeneous process. If the reaction rate is much lower than that of the diffusion, only the free ... 

The possible effect of a coupled chemical reaction on the response to an electrochemical perturbation can be deduced by combination of the j F vs. surface concentration relation with the proper rate equation for the charge transfer process and subsequent elaboration applying to a particular method. Naturally, a complex rate equation will be unfavourable if it is... 

Reversible, quasi-reversible and irreversible electrode processes have been studied at the RDE [266] as have coupled homogeneous reactions without [267] and with the effect of electrode kinetics [268], The theoretical results are very similar to those of a.c. polarography, being very phase-angle sensitive to coupled chemical reactions in the rotation speed range where convection can be neglected, the polarographic results may be directly applied [269]. 

In these types of laboratory reactor, the flow of the liquid is very carefully controlled so that, although the mass transfer step is coupled with the chemical reaction, the mass transfer characteristics can be disentangled from the reaction kinetics. For some reaction systems, absorption of the gas concerned may be studied as a purely physical mass transfer process in circumstances such that no reaction occurs. Thus, the rate of absorption of C02 in water, or in non-reactive electrolyte solutions, can be measured in the same laboratory contactor as that used when the absorption is accompanied by the reaction between C02 and OH ions from an NaOH solution. The experiments with purely physical absorption enable the diffusivity of the gas in the liquid phase DL to be calculated from the average rate of absorption per unit area of gas-liquid interface NA and the contact time te. As shown in Volume 1, Chapter 10, for the case where the incoming liquid contains none of the dissolved gas, the relationship is ... 

The most popular electroanalytical technique used at solid electrodes is Cyclic Voltammetry (CV). In this technique, the applied potential is linearly cycled between two potentials, one below the standard potential of the species of interest and one above it (Fig. 7.12). In one half of the cycle the oxidized form of the species is reduced in the other half, it is reoxidized to its original form. The resulting current-voltage relationship (cyclic voltammogram) has a characteristic shape that depends on the kinetics of the electrochemical process, on the coupled chemical reactions, and on diffusion. The one shown in Fig. 7.12 corresponds to the reversible reduction of a soluble redox couple taking place at an electrode modified with a thick porous layer (Hurrell and Abruna, 1988). The peak current ip is directly proportional to the concentration of the electroactive species C (mM), to the volume V (pL) of the accumulation layer, and to the sweep rate v (mVs 1). 

In this section, the different behavior of processes with coupled noncatalytic homogeneous reactions (CE and EC mechanisms) is discussed in comparison with a catalytic process. We will consider that the chemical kinetics is fast enough and in the case of CE and EC mechanisms K (- c /cf) fulfills K 1 so that the kinetic steady-state and even diffusive-kinetic steady-state approximation can be applied. 

According to these results, the characterization of the subsequent coupled chemical reaction of the EC mechanism can be achieved with RPV by examining the oxidative limiting current. The half-wave potential is also interesting in order to determine the formal potential of the electrode process [79]. 

As discussed in Sects. 3.4 and 4.5, electrode processes coupled with homogeneous chemical reactions are very frequent and their study is of interest in many applied fields, such as organic electrosynthesis, ecotoxicity, biosciences, environmental studies, among others [15-17]. In this section, multipulse techniques (with a special focus on Cyclic Voltammetry) are applied to the study of the reaction kinetics and mechanisms of electrogenerated species. 

The greatly reduced double-layer capacitance of microelectrodes, associated with their small area, results in electrochemical cells with small RC time constants. For example, for a microdisk the RC time constant is proportional to the radius of the electrode. The small RC constants allow high-speed voltammetric experiments to be performed at the microsecond timescale (scan rates higher than 106V/s) and hence to probe the kinetics of very fast electron transfer and coupling chemical reactions (114) or the dynamic of processes such as exocytosis (e.g., Fig. 4.25). Such high-speed experiments are discussed further in Section 2.1. 

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