Normal region

FIGURE 34.4 Dependence of electrochemical rate constant on the electrode potential for outer-sphere electron transfer. An exponential increase in the normal region changes for the plateau in the activationless region. 

Equation (34.32) is remarkable in the relation that it shows that (1) the observable symmetry factor is determined by occupation of the electron energy level in the metal, giving the major contribution to the current, and (2) that the observable symmetry factor does not leave the interval of values between 0 and 1. The latter means that one cannot observe the inverted region in a traditional electrochemical experiment. Equation (34.32) shows that in the normal region (where a bs is close to ) the energy levels near the Fermi level provide the main contribution to the current, whereas in the activationless (a bs 0) and barrierless (a bs 1) regions, the energy levels below and above the Fermi level, respectively, play the major role. 

As shown, the data patterns 1 and 2 are classified as Normal with high certainty, as they lie within the boundaries of the normal class. However, 3 and 4 are classified as normal with medium certainty, as they lie outside the normal region, but their similarities are closest to the normal cluster. Similarly, the data pattern represented by 5 is classified as fault2 with medium certainty and the data patterns represented by 6, 7, and 8 are classified as fault2, and so on. If the data are collected every 20 seconds as in the case study, the dynamic interpretation is tabulated as shown in Table V, with the labels in italics representing the correct class and appropriate certainty. An x means there was not an interpretation with this certainty. 

WBDs) and the second group wore swimming suits to give maximum skin exposure. The cotton WBDs were chosen to normalize regional differences in surface contact and to increase the sample size relative to cotton-patch dosimeters (Durham and Wolfe, 1962). 

Two situations may be distinguished according to whether the electron transfer step of the stepwise mechanism lies in the normal region or in the inverted... 

Most photoinduced CS processes take place within the Marcus normal region. However, chaige recombination processes take place within the inverted region. Thus, the small reorganization eneigy of CHI will slow down CR processes. 

Chen, J., Bandoni, A., and Romagnoli, J. A. (1996). Robust PCA and normal region in multivariable statistical process monitoring. AIChE J. 42, 3563-3566. 

In the normal region, thermodynamic driving forces are small. The electron-transfer process is thermally activated, with its rate increasing as the driving force increases. 

The PET process in the dyad is located in the normal region of the Marcus curve, while the back-electron transfer from Q0 to ZnPor+ is in the Marcus inverted region (Figure 6.27). 

Because of the quadratic dependence, the variation of ln(fcET) versus AG° is expected to be a parabol whose maximum corresponds to AG° = 0 (Figure 4.5). Beyond the maximum (AG° > 0), fcET decreases when AG° increases (normal region), whereas below the maximum (AG° < 0), the inverse behavior is expected (Marcus inverse region). 

Figure 4. Schematic diagram to show the reorganization energy X for nonisotopic reactions for harmonic free energy profiles. This figure shows a normal region activation barrier when-AG° < an activationless situation when -AC =. l.and an inverted region activation barrier when-AG° > A for the harmonic potential inii andGfin represent the initial (reactant) and the final (product) system free energy, respectively.

Driving-force studies, using mixed-ligand coordination to alter formal potentials, show only normal-region behavior (Fig. 11), not the inverted Marcus curve seen for electrostatically bound compounds. Similar behavior has been reported for phosphonate-bound dyes on 2 in water [67]. Other studies on 2 in nonaqueous environments have yielded Marcus inverted rate behavior or else no sensitivity to driving force, suggesting that water may induce mechanistically distinct behavior [14,37,68]. 

Variable-temperature studies show that the back reaction is thermally activated. The dependence of AH on driving force (variations in dye formal potential) is illustrated in Fig. 13 and is consistent with normal-region reactivity [67]. If AS can be neglected, application of Eq. (1) yields values of approximately... 

Figure 11 Dependence on driving force of first-order rate constant for back electron transfer from colloidal Sn02 films to covalently attached complexes. The variations indicate that the reactions occur in the Marcus normal region. The identities of the molecular redox couples, listed from highest driving force to lowest, are, Rulll/n (5-Cl-phen)2 (phos-...

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