Redox ladder

The qualitative application is illustrated by the approximate location of E°w for the azobenzene/aniline couple on redox ladders constructed by Schwarzenbach et al. (e.g., Figure K.3 in Reference 120). The estimate, around -0.1 V vs. NEIE, comes from electrochemical studies that report non-Nemstian dependence of E1/2 on pEI and additional evidence for the non-reversibility of this reaction (8,121). 

THE REDOX BEHAVIOR OF NATURAL SYSTEMS 11.2.1 Redox Reaction Sequences and Redox Ladders... 

Figure 1. Redox ladder at pH 5 and pH 7 for major redox couples ([Ox]/[Red] = 1).

Some elements have many oxidation states. You can construct redox ladders like the one shown below for sulfur ... 

Chlorine can have different oxidation states. Using the following species, construct a redox ladder for chlorine ... 

Look back at the redox ladder for sulfur In Exercise 7D ... 

Ladder diagrams can also be used to evaluate equilibrium reactions in redox systems. Figure 6.9 shows a typical ladder diagram for two half-reactions in which the scale is the electrochemical potential, E. Areas of predominance are defined by the Nernst equation. Using the Fe +/Fe + half-reaction as an example, we write... 

The ladder diagram for this system is shown in Figure 11.24a. Initially the potential of the working electrode remains nearly constant at a level near the standard-state potential for the Fe UFe redox couple. As the concentration of Fe + decreases, however, the potential of the working electrode shifts toward more positive values until another oxidation reaction can provide the necessary current. Thus, in this case the potential eventually increases to a level at which the oxidation of H2O occurs. 

For more complex mechanisms, picturesque names such as square, ladder, fence [18] or cubic schemes [20] have been selected. In redox polymer films, additional transport of counterions, solvation, and polymer reconfiguration are important and four-dimensional hyper-cubes are needed to describe the reactions [21]. 

We now turn our attention to molecular hysteresis which has two essential factors. One is that a system can be expressed a double square scheme diagram (or ladder scheme diagram ) [5], as shown in Fig. 17a. A, A, A", B, B, and B" are chemical species or states. These series of A and B vary reversibly with one another under an external perturbation such as potential, pH, ion concentration, light, etc. With A and B more stable than B" and A", respectively, A" and B" can be rapidly converted to B and A. Hence we will obtain a scheme as shown in Fig. 17b. The other important thing is that the conversion is slow between A and B. The slow rate produces a bistability, A and B, which depends on the direction of an external perturbation. This is molecular hysteresis. Some binuclear or multinuclear metal complexes with the double square scheme diagram have been reported [31]. However, because they were not designed to exhibit molecular hysteresis, their hysteresis behaviors in redox are insufficient. 

Polymetallorotaxanes 7.24 (M = Zn" or Cu ) have been prepared by electropolymerization, which involved anodic oxidation of the pre-assembled metallorotaxane precursors (Scheme 7.2) [48]. Importantly, studies of these materials have allowed an evaluation of the individual contributions of the organic backbone and the metal-centered redox process to the overall conductivity measured on interdigitated microelectrodes. The Zn and Cu polymers behave quite differently. The Zn polymer behaves in a similar fashion to the metal-free material 7.25, whereas the matching of the polymer and Cu-centered redox potentials in 7.24 (M=Cu ) leads to enhancement of the communication between these two units resistance drops by a factor of 10 for the Cu polymer 7.24 relative to metal-free 7.25. In a further development in this general area, two-step electropolymerizations have been used to generate three-stranded conducting ladder polymetallorotaxanes 49]. 

The so-called ladder equivalent circuit shown in Figure 27.13 is characteristic of many ACs. It represents a set of several R-C parallel circuits and also Warburg diffusion impedance. Herewith, apart from the proper distributed line related to a porous structure of the studied object, one or several circuits in the ladder characterize parallel faradaic redox reactions of surface groups on the electrode. It was shown theoretically that phase angle (p = 45° independent of frequency co is observed... 

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