Potential step reversible system

The simplest and most useful case that one can study by single potential step chronoamperometry is that in which " /2> 0/i (z.e. AEor = E2 - E 5 180 mV). This means that the primarily electrogenerated species Red converts to a new species Ox, which is more easily reducible than the initial species Ox. As seen in Section 1.4.3, in cyclic voltammetry such a system exhibits a single reversible process in the forward scan. 

Coupling of two heterocycles by a N-N-bridge is simple to achieve and produces especially significant examples of two step redox systems with excellent reversibility. With the following compounds 33 39 an increase in Ksem of 10 —10 compared to the dimethine derivatives is observed, so that most Ksem s are 10 . Additionally all potentials become more positive by as much as 1 V. Besides with hardly any exception, all three oxidation levels of these systems can be isolated . ... 

Rhenium forms a number of mono-oxo, CTs-dioxo, and trans-dioxo complexes in oxidation states IV through VII. Reversible, proton-independent, one-electron potentials for several systems are represented in Table 1 [13-22, 35, 36]. As is the case forTc, a large change in E° for a given redox step can be produced by changing the ancillary ligands. 

To impose the diffusion-controlled conversion of O to R as described earlier, the potential E impressed across the electrode-solution interface must be a value such that the ratio Cr/Cq is large. Table 3.1 shows the potentials that must be applied to the electrode to achieve various ratios of C /Cq for the case in which Eq R = 0. For practical purposes, C /C = 1000 is equivalent to reducing the concentration of O to zero at the electrode surface. According to Table 3.1, an applied potential of -177 mV (vs. E° ) for n = 1 (or -88.5 mV for n = 2) will achieve this ratio. Similar arguments apply to the selection of the final potential. On the reverse step, a small C /Cq is desired to cause diffusion-controlled oxidation of R. Impressed potentials of +177 mV beyond the E° for n = 1 (and +88.5 mV for n = 2) correspond to Cr/Cq = 10"3. These calculations are valid only for reversible systems. Larger potential excursions from E° are necessary for irreversible systems. Also, the effects of iR drop in both the electrode and solution must be considered and compensated for as described in Chapter 6. 

For quantitative observations, cyclic voltammetric (CV) measurements were performed over the triad of oxidation states, that is, anion, radical, and cation, available to these systems. The half-wave potentials for reduction and oxidation are summarized in Table 1. For all DTA radicals, oxidation is essentially reversible. Electrochemical reduction of radicals 10 and 12 is, however, almost irreversible, as in the case of radicals 3, 7, 10, and 12. Only for dithiazoles 13 and 33 <2004JA8256> are both the oxidation and reduction steps reversible. 

The equations for potential and current steps in reversible systems, neglecting capacitive contributions were derived in Chapter 5. In the present chapter we show the possibilities of using these methods to elucidate electrode processes. We also consider successions of steps, that is pulses, especially with sampling of the response, which in the case of potential control has wide analytical application. 

In the Cottrell experiment, as described in the last section, we have a step to a very negative potential, so that the concentration at the electrode is kept at zero throughout. It is possible also to step to a less extreme potential. If the system is reversible, and we consider the two species A and B, reacting as in (2.18), then we have the Nernstian boundary condition as in (2.24). Using (2.29) and assigning the symbols CA and Cb, respectively, to the dimensionless concentrations of species A and B, we now have the new boundary conditions for the potential step,... 

When the potential step is small and the system is chemically reversible three cases of interest are analyzed. First, when the reaction is kinetically sluggish (electrochemi-cally -> irreversible or quasireversible) and the -> mass transport effects are negligible. 

FIG. 2 Principles of SECMID using H+ as a model adsorbate. Schematic of the transport processes in the tip/substrate domain for a reversible adsorption/desorption process at the substrate following the application of a potential step to the tip UME where the reduction of H+ is diffusion-controlled. The coordinate system and notation for the axisymmetric cylindrical geometry is also shown. Note that the diagram is not to scale as the tip/substrate separation is typically <0.01 rs. 

Zinc deposits in the mercury during the potential steps thus a question arises about how the initial conditions are restored after each cycle in a sampled-current voltammetric experiment. Because the system is reversible, one can rely on reversed electrolysis at the base potential imposed before each step to restore the initial conditions in each cycle. This point is discussed in Section 7.2.3. 

In this section, we will treat the one-step, one-electron reaction O + R using the general (quasireversible) i-E characteristic. In contrast with the reversible cases just examined, the interfacial electron-transfer kinetics in the systems considered here are not so fast as to be transparent. Thus kinetic parameters such as kf, and a influence the responses to potential steps and, as a consequence, can often be evaluated from those responses. The focus in this section is on ways to determine such kinetic information from step experiments, including sampled-current voltammetry. As in the treatment of reversible cases, the discussion will be developed first for early transients, then it will be redeveloped for the steady-state. 

Simpler forms of (5.5.24) are used for the reversible and totally irreversible limits. For example, consider (5.4.17), which we derived as a description of the current-time curve following an arbitrary step potential in a reversible system. That same relationship is available from (5.5.24) simply by recognizing that with reversible kinetics A is very large, so that F (A) is always unity. The totally irreversible limit will be considered separately in Section 5.5.1(e). 

So far, it has been most convenient to think of (5.2.24) as describing the current-time response following a potential step however it also describes the current-potential curve in sampled-current voltammetry, just as we understood (5.4.17) to do for reversible systems. At a fixed sampling time r, A becomes f 0), which is a function... 

This experiment, which is called cyclic voltammetry (CV), is a reversal technique and is the potential-scan equivalent of double potential step chronoamperometry (Section 5.7). Cyclic voltammetry has become a very popular technique for initial electrochemical studies of new systems and has proven very useful in obtaining information about fairly complicated electrode reactions. These will be discussed in more detail in Chapter 12. 

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