Electron transfers consecutive

We consider the simple scheme first discussed by Ivanov and Levich [174], viz. 

When the second electron transfer step at the disc is rapid (k 2 kb,B i.e. B does not have time to diffuse away) then the ring current is zero and an (nt + n2 ) electron wave is seen at the disc. Conversely, when it is slow (k2 k DB ) we obtain the usual 

To calculate the general behaviour, we use the steady-state approximation and the fact that 

the slope of the plot of iD /iR vs. to 2 gives the value of k 2 and the intercept nx. In a similar fashion 

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The simplest type of complex electrochemical reactions consists of two steps, at least one of which must be a charge-transfer reaction. We now consider two consecutive electron-transfer reactions of the type ... 

Figure 11.1 Tafel plot for two consecutive electron-transfer reactions. Parameters i = 0.4, a-2 = 0.5 (a) jn,2 = 5j0,i (b) j0,2 = 103io,i-...

Consider the reaction with two consecutive electron-transfer steps described by Eq. (11.12). (a) Show that, if j0,2 j0,1, there is an intermediate range of negative overpotentials in which the apparent transfer coefficient is (2 — ai) and the apparent exchange current density 2j0,i (see Fig. 11.1). (b) Derive the form of the Tafel plot for jo,i > jo,2-... 

We consider the investigation of two consecutive electron-transfer reactions with a ring-disc electrode under stationary conditions. A species A reacts in two steps on the disk electrode first to an intermediate B which reacts further to the product C. The intermediate is transported to the ring, where the potential has been chosen such that it reants bank to A. The overall scheme is ... 

Two one-electron transfers with different extents of reversibility. In the case where not all the processes of a consecutive electron transfer sequence are reversible, the irreversibility of a particular step becomes evident by the absence of the reverse peak in its pertinent response. For all other aspects the preceding considerations remain valid. 

As outlined in Section 1.5, consecutive electron transfers possessing electrode potentials separated by less than 0.1 V afford in cyclic voltammetry more or less overlapping peak-systems which cannot be adequately resolved to obtain the precise standard electrode potential for each step. In these cases it is convenient to make use of pulsed techniques. 

As mentioned, DPV is particularly useful to determine accurately the formal electrode potentials of partially overlapping consecutive electron transfers. For instance, Figure 40 compares the cyclic voltammogram of a species which undergoes two closely spaced one-electron oxidations with the relative differential-pulse voltammogram. As seen in DPV the two processes are well separated. 

Figure 43 Cyclic voltammograms recorded at a platinum electrode in a solution of a species able to undergo consecutive electron transfers. Starting potentials (a) 0.0 V (b) -0.8 V...

Let us now pass to multiferrocene compounds. Many compounds containing two, three, four or more ferrocene groups have been prepared and characterized. For these derivatives one can confidently expect that the number of one-electron oxidations equal the number of ferrocene groups. However, one must still determine whether these processes occur at separate or at identical potential values (according to that discussed in Chapter 2, Section 1.5, for consecutive electron transfers). 

Using the dropping zinc amalgam microelectrode, detailed kinetic data were obtained [40], and the two consecutive electron transfers followed by a chemical reaction (EEC) mechanism of Zn(II) reduction could be revealed. 

Constant current chronopotentiometry has been utilized by Honeychurch [156] to study reduction of methylene blue adsorbed at HMDE. The obtained results were interpreted in terms of a two consecutive electron transfers (EE) mechanism and the interfacial potential distribution model. 

It should be noticed that, unlike consecutive electron transfer reactions whose kinetics are determined by the slowest process, mixed potentials are determined by the fastest of several possible occurring electrode reactions. 

Polycyclic aromatic hydrocarbons contain extended conjugated rc-electron systems and are electroactive within the cathodic potential window of many organic sol-vent/tetraalkylammonium electrolyte combinations. For many of them reduction potentials were measured and reported. It is important to note that the reduction of polycyclic aromatics involves consecutive electron-transfers and protonations. The nature of the product depends on the number of electrons and protons consumed and higher numbers result in more hydrogenated, less conjugated and thus less electroactive products. A simplified reduction scheme for polycyclic aromatics is shown below. The products are divided into three groups (A) are reduced within the potential window and (B) require drastic reduction conditions as those described for the substrates in Chapt. 3. 

One of the favourite generic arrangement is the molecular triad, consisting of a photoactive centre (PC), an electron donor (D) and an electron acceptor (A). In systems such as D-PC-A, the charge separated state D+-PC-A is obtained in two consecutive-electron transfer processes after excitation of PC. Of course, several variants exist, depending on the electron transfer properties of PC and its excited state, PC, as well as on the precise arrangement of the various components (PC-Ai-A2 or D2-Di-PC, in particular, if PC is an electron donor or an electron acceptor, respectively). 

More complex electrode processes than those described above involve consecutive electron transfer or coupled homogeneous reactions. The theory of these reactions is also more complicated, but they correspond to a class of real, important reactions, particularly involving organic and biological compounds. 

Consecutive electron transfer to the N2 molecule with simultaneous addition of protons reflects these thermodynamics peculiarities of dinitrogen (Figure 1). 

We now proceed to the main topic of this chapter and examine the situation for an electrochemical reaction that involves multiple consecutive electron-transfer steps of the kind referred to in a general way in the introduction. A hypothetical reaction sequence involving n consecutive electron-transfer reduction steps is given in Scheme 1. The A,s are stable species that can be reactants or products and the ks are reaction intermediates of lower stability. The ZjS indicate the number of electrons trans-... 

Consider a reaction mechanism similar to Scheme 1, but involving only three consecutive electron-transfer steps. If, as an example, we take... 

Figure 5. Simulated Tafel plots [from Eq. (40)] for a reaction involving three consecutive electron-transfer steps, showing the effect of variation of rate constants for (a) intermediate-consuming and (b) intermediate-creating nonrds steps, (a) Rate constants A, = -2 = 10 cm s (i.e., the rds) and k =...

The rate expression for the multistep consecutive electron-transfer reaction of Scheme 1 [i.e., Eq. (31)] is able to relate complex consecutive electron-transfer reaction mechanisms to experimental potential vs. logarithmic current-density relations. When p is assumed to be 1/2, the Tafel slopes (1/a/) predicted by this relation can only have values less than or equal to 118 mV dec i (at 25 °C) for electron-transfer limited reactions, since electrons transferred in non-rds steps will add integers (to P) in the expected a values and therefore decrease the Tafel slope below 118 mV dec 1. For instance, the usual cathodic Tafel slope of 118 mV dec-i for a one- electron transfer over a synunetric harrier is decreased to 39 mV dec for one preceding quasi-equilibrium electron transfer and to 24 mV dec for two, etc., and the anodic Tafel slopes are similarly decreased for one and two following (where the reaction steps are still written as reductions, as in Scheme 1) electron transfers, respectively. It should be noted that the Tafel slopes that are determined hy a values involving y-i- P differ substantially and discontinuously from the value for a = P = 1/2, and therefore should be easily distinguishable. 

In general, for a series of nr consecutive electron transfers in the form given by (5.51), the current response can be calculated from... 

Overlapping bands can become a problem when, for example, there are two consecutive electron-transfer reactions [137]. One solution is to look at the time-or potential-resolved spectra [138], Overlapping bands are often responsible for nonlinear Nemstian plots in OTTLE studies [139]. There are only a few examples of the use of differentiating the absorbance [134], least-squares analysis [140], of the latest chemometric techniques [141]. In the latter study, evolutionary factor analysis of the spectra arising from the reduction of E. coli reductase hemoprotein (SiR-HP ) in which three species are present and the reduction of the [Cl2FeS2MoS2FeCl2] (four species present). The most challenging part of the work was the determination of the transformation matrix. 

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