Homogeneous outer-sphere reaction

In the simplest cases, it is possible to compare rates for homogeneous and heterogeneous electron-transfer reactions. According to the Marcus theory for homogeneous outer-sphere reactions [10],... 

According to the Marcus theory [64] for outer-sphere reactions, there is good correlation between the heterogeneous (electrode) and homogeneous (solution) rate constants. This is the theoretical basis for the proposed use of hydrated-electron rate constants (ke) as a criterion for the reactivity of an electrolyte component towards lithium or any electrode at lithium potential. Table 1 shows rate-constant values for selected materials that are relevant to SE1 formation and to lithium batteries. Although many important materials are missing (such as PC, EC, diethyl carbonate (DEC), LiPF6, etc.), much can be learned from a careful study of this table (and its sources). 

In the following sections, we shall explore the applicability of such relationships to experimental data for some simple outer-sphere reactions involving transition-metal complexes. In keeping with the distinction between intrinsic and thermodynamic barriers [eq 7], exchange reactions will be considered first, followed by a comparison of driving force effects for related electrochemical and homogeneous reactions. 

The rate constant and activation parameters for the electron-transfer reactions are given in Table I. The reaction rate of the Cu/3 complex via the inner-sphere was smaller than that of the Cu/ethylimidazole complex. The coordination of the substrate to Cu(II) ion was enthalpically unfavored as compared to the homogeneous Cu complex. On the other hand, the outer-sphere reaction with Fe(II)(phenanthroline)3 proceeded faster for the Cu/3 system than for the homogeneous Cu/ethylimidazole complex. 3 made a significant favorable entropic contribution to the outer-sphere electron-transfer reaction. 

The redox reactions at metal electrodes can be treated in a similar way. Use of the oscillator model for the solvent implies that the solvent reorganization takes place at a fixed separation of the ion from the metal surface. With this condition all results obtained in Sec.3 2.IV for homogeneous outer-sphere and inner-sphere electron-transfer reactions can be directly applied by relating the current density (per unit ion concentration) to the expressions for the rate constant through equation (106.IV). 

The models presented in the preceding section consider only elementary electron-transfer steps. In the same sense, many theories such as those of Marcus and Hush are restricted to outer-sphere reactions. For homogeneous electron transfer, bond breaking was considered in early papers by German and Dogonadze [31], and later by German and Kuznetsov [32]. For... 

The theory outlined here has also been developed to describe homogeneous electron transfer processes. The simplest outer sphere reactions that can be considered involve different oxidation states of the same molecule, e.g. 

---