Marcus Theory of Outer-Sphere Heterogeneous Electron Transfer Reactions: Dependence of the Standard Electrochemical Rate Constant on the Hydrodynamic Radius from High Precision Measurements of the Oxidation of Anthracene and Its Derivatives in Nonaqueous Solvents Using the High-Speed Channel Electrode

The validity of Marcus theory for outer-sphere heterogeneous electron transfer for the electrooxidation of a range of anthracene derivatives in alkyl cyanide solvents is investigated. The precision measurement of these fast electron transfers (k ≥ 1 cm s ) is achieved by use of the high-speed channel electrode and, where necessary, fast-scan cyclic voltammetry. First, the solvent effect on the rate of electron transfer is studied by considering the first oxidation wave of 9,10-diphenylanthracene in the alkyl cyanide solvents: acetonitrile, propionitrile, butyronitrile, and valeronitrile. Second, the variation of k for a series of substituted anthracenes is investigated by analyzing the voltammetric response of the one-electron oxidations of 9-phenylanthracene, 9,10-dichloroanthracene, 9-chloroanthracene, 9,10-dicyanoanthracene, 9-cyanoanthracene, 9-nitroanthracene, 9,10-diphenylanthracene, and anthracene in acetonitrile. It is shown that the rate of electron transfer of a single compound in different alkyl cyanides is determined by the longitudinal dielectric relaxation properties of the solvent, while differences in rate between the substituted anthracenes in acetonitrile can be quantitatively rationalized by considering their relative hydrodynamic radii. This makes possible the accurate prediction of electron-transfer rates for a molecule by interpolation of rate constants known for related molecules.