Slow redox couple.

Slow redox couples can be shown to be systems where the relationship between current and potential is controlled by the electron transfer phenomena in a potential range around the standard potential. The concentration profiles near the interface are not marked and the interfacial concentrations can be considered as equal to the concentrations in the bulk of the electrolyte. 

Therefore, in a chronamperometry experiment, the interface concentrations are fixed, though this rule does not apply for a slow redox couple. 

Fast redox couple — 1 slow redox couple — [Pg.323]

If the initial concentration of Cu + is 1.00 X 10 M, for example, then the cathode s potential must be more negative than -1-0.105 V versus the SHE (-0.139 V versus the SCE) to achieve a quantitative reduction of Cu + to Cu. Note that at this potential H3O+ is not reduced to H2, maintaining a 100% current efficiency. Many of the published procedures for the controlled-potential coulometric analysis of Cu + call for potentials that are more negative than that shown for the reduction of H3O+ in Figure 11.21. Such potentials can be used, however, because the slow kinetics for reducing H3O+ results in a significant overpotential that shifts the potential of the H3O+/H2 redox couple to more negative potentials. 

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... 

The latter reaction must involve a large number of molecular steps and may be a much slower process. The mechanisms of a few inorganic electron transfer processes have been summarized by Taube (1968). The presence of very slow reactions when several redox couples are possible means that the Eh value measured with an instrument may not be related in a simple way to the concentrations of species present, and different redox couples may not be in equilibrium with one another. Lindberg and Runnells (1984) have presented data on the extent of disequilibrium... 

These measurements indicate that it is not possible to identify a single value of pe surrounding the O2/H2S interface in the environment. Redox couples do not respond to the pe of the environment with the same lability as hydrogen ion donors and acceptors. There is no clear electron buffer capacity other than the most general states of "oxygen containing" or "H2S containing." The reason for the vast differences in pec in the oxic waters is the slow oxidation kinetics of the reduced forms of the redox couples. The reduced species for which the kinetics of oxidation by O2 has been most widely studied is Mn. This oxidation reaction... 

Hence the picture of the cathodic and anodic waves obtainable for a completely reversible redox couple by means of the RDE corresponds fully with that in Fig. 3.9 the value of i, i.e., the height of the sigmoidal waves, is linearly proportional to to1/2 and to C (see eqn. 3.89 and the Levich constant). If for a well chosen combination of C and E a plot of i against co1/2 deviates from a straight line passing through the origin, then in the kinetics of the electrode reaction we have to deal only with a rapid electron transfer (cf., Fig. 3.10) or even with a slow electron transfer (cf., Fig. 3.11), in which latter instance the transfer coefficient a plays an appreciable role (cf., eqns. 3.17 and 3.18). 

In contrast to a mixture of redox couples that rapidly reach thermodynamic equilibrium because of fast reaction kinetics, e.g., a mixture of Fe2+/Fe3+ and Ce3+/ Ce4+, due to the slow kinetics of the electroless reaction, the two (sometimes more) couples in a standard electroless solution are not in equilibrium. Nonequilibrium systems of the latter kind were known in the past as polyelectrode systems [18, 19]. Electroless solutions are by their nature thermodyamically prone to reaction between the metal ions and reductant, which is facilitated by a heterogeneous catalyst. In properly formulated electroless solutions, metal ions are complexed, a buffer maintains solution pH, and solution stabilizers, which are normally catalytic poisons, are often employed. The latter adsorb on extraneous catalytically active sites, whether particles in solution, or sites on mechanical components of the deposition system/ container, to inhibit deposition reactions. With proper maintenance, electroless solutions may operate for periods of months at elevated temperatures, and exhibit minimal extraneous metal deposition. 

The evolution of a new set of electrochemical waves (as opposed to the gradual shifting of the redox couple) on addition of guest species may be due to a number of factors. If the complex formed has a particularly high stability constant and has a redox potential which is markedly different from that of the free ligand, a new set of waves may be observed. However, if the decomplexation kinetics of the complex formed is particularly slow on the electrochemical time scale then, as the potential is scanned between the vertex points during a cyclic voltammetric experiment, the solution complexed species will be stable over this time period and the two sets of waves will correspond to free ligand and complex. Therefore care should be taken to determine the cause of the evolution of a new set of electrochemical waves and... 

It is often useful to carry out voltammetric measurements at low temperatures in order to evaluate both the stability of an electrogenerated species (the decrease in temperature will slow down the kinetics of any decomposition processes of the species formed in the electrode process) and the variation in formal electrode potential of a redox couple as a function of temperature. The latter point regards thermodynamic considerations of the redox processes, which will be discussed in Chapter 13, Section 3. 

Most of the reactions that involve significant fractionation of Se and Cr isotopes appear to be far from chemical or isotopic equihbrium at earth-surface temperatures. Redox disequilibrium is common among dissolved Se species. Dissolved Se(IV) and solid Se(0) are often observed in oxic waters despite their chemical instability (Tokunaga et al. 1991 Zhang and Moore 1996 Zawislanski and McGrath 1998). In one study of shallow groundwater, Se species were found to be out of equilibrium with other redox couples such as Fe(III)/Fe(II) (White and Dubrovsky 1994). The kinetics of abiotic Se(VI) reduction, like those of sulfate, are quite slow. In the laboratory, conversion of Se(VI) to Se(IV) requires one hour of heating to ca. 100°C in a 4 M HCl medium. 

One final issue remains to be resolved Of the portion of the AEpi that is due to resistance, what part is caused by solution resistance and what part is caused by film resistance To explore this issue we examined the electrochemistry of a reversible redox couple (ferrocene/ferricinium) at a polished glassy carbon electrode in the electrolyte used for the TiS 2 electrochemistry. At a peak current density essentially identical to the peak current density for the thin film electrode in Fig. 27 (0.5 mV see ), this reversible redox couple showed a AEpi of 0.32 V (without application of positive feedback). Since this is a reversible couple (no contribution to the peak separation due to slow kinetics) and since there is no film on the electrode (no contribution to the peak separation due to film resistance), the largest portion of this 0.32 V is due to solution resistance. However, the reversible peak separation for a diffusional one-electron redox process is —0.06 V. This analysis indicates that we can anticipate a contribution of 0.32 V -0.06 V = 0.26 V from solution resistance in the 0.5 mV sec control TiS2 voltammogram in Fig. 27. 

The electrochemical and chemical behavior of rotaxane 7 + was analyzed by CV and controlled potential electrolysis experiments.34,35 From the CV measurements at different scan rates (from 0.005 to 2 V/s) both on the copper(I) and on the copper(II) species, it could be inferred that the chemical steps (motions of the ring from the phenanthroline to the terpyridine and vice versa) are slow on the timescale of the experiments. As the two redox couples involved in these systems are separated by 0.7 V, the concentrations of the species in each environment (tetra- or pentacoor-dination) are directly deduced from the peak intensities of the redox signals. In Fig. 14.13 are displayed some voltammograms (curves a-e) obtained on different oxidation states of the rotaxane 7 and at different times. 

In general, the modest efficiencies of Cu(I)/(II) redox couples compared to the iodide/triiodide can be explained by a slow dye reduction, which could be reasonably anticipated, given the slow kinetics that are associated to the Cu(I)/(H) redox chemistry. On the other hand, using a suitably built photoanode equipped with a compact Ti02 underlayer and an appropriate heteroleptic dye like Z907, the detrimental electronic... 

Despite the lack of theoretical models for interfacial recombination processes in excitonic solar cells, it is obvious empirically that those cells which function efficiently must have a very slow rate of recombination. In DSSCs, this can be explained simply by the slow electron self-exchange rate of the I /I2 redox couple and the absence of field-driven recombination. However, in the case of solid-state, high-surface-area OPV cells, such as the conducting polymer/C60-derivative cells [36,39], the slow rate of interfacial recombination is an important problem that is not yet understood. 

Upon reoxidation of the Os(II) complexes, hydration of the ligands bound to Os(III) is much slower than the dehydration of the ligands bound to Os(II). Thus, reversible redox couples are found for the oxidation of the Os(II) dehydration products. Though the S02 and nitrile ligand will hydrate in the Os(III) oxidation state, the latter forms amides and is quite slow. In the case of the CO complex, the Os(III) complex is too labile for any appreciable CO hydration to occur within the lifetime of the complex. 

A more accurate way to use potentiometric data is to prepare a Gran plot6-7 as we did for acid-base titrations in Section 11-5. The Gran plot uses data from well before the equivalence poinl (Ve) to locate Ve. Potentiometric data taken close to Ve are the least accurate because electrodes are slow to equilibrate with species in solution when one member of a redox couple is nearly used up. 

A screening of possible redox couples has led to the choice of Fe3+/Fe2+ as a very suitable catholyte, while Cr2+/Cr3+ and Ti3+/Ti02+ have been suggested for the anolyte. The latter shows problems connected with hydrolysis effects unless very low pH is maintained, and in addition has a low exchange current density. Cr /Cr3+ is also kinetically slow, especially in the charging direction. In cells tested so far, voltages and current densities have been low and considerable improvements are needed in... 

So the product, R, of the electrochemical reduction reacts in the solution with an electroinactive oxidizer, Ox, to regenerate O, etc. If Ox is present in large excess, the chemical reaction is pseudo-first-order in R and O. For thermodynamic reasons, Rc can only proceed if the standard potential of the redox couple Ox/Red is more positive than that of O/R. Then, for Ox to be electroinactive, it is required that its electroreduction proceeds irreversibly, in a potential range far negative to the faradaic region of the 0/R reaction. Thus, Ox being stable for reasons of the slow kinetics of its direct reduction, it can be said that, in the presence of O, it is being catalytically reduced. 

Redox equilibrium is not achieved in natural waters, and no single pe can usually be derived from an analytical data set including several redox couples. The direct measurement of p thus is usually not meaningful because only certain electrochemically reversible redox couples can establish the potential at an electrode (4, 35). However, p is a useful concept that indicates the direction of redox reactions and defines the predominant redox conditions. Defining pe on the basis of the more abundant redox species like Mn(II) and Fe(II) gives the possibility of predicting the equilibrium redox state of other trace elements. The presence of suitable reductants (or oxidants) that enable an expedient electron transfer is, however, essential in establishing redox equilibria between trace elements and major redox couples. Slow reaction rates will in many cases lead to nonequilibrium situations with respect to the redox state of trace elements. 

Since in fact No and organic matter, at least, persist in waters containing dissolved oxygen, no total redox equilibrium is found in natural water systems, even in the surface films. At best there are partial equilibria, treatable as approximations to equilibrium either because of slowness of interaction with other redox couples or because of isolation from the total environment as a result of slowness of diffusional or mixing processes. 

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