A quantum mechanical theory is employed to describe heterogeneous ferrocene (Fc)/ferrocenium (Fc + ) electron transfer across Au(111)/[bmim][BF 4 ] and Au(111)/acetonitrile interfaces. Classical molecular dynamics simulations were performed to calculate the potential of mean force for Fc and Fc + and to estimate the solvent reorganization energy. The structure of the reaction layer and the solvent shell of Fc and Fc + as derived from molecular dynamics are thoroughly investigated. The molecular structure of ferrocene and ferrocenium species, as well as the reactant−electrode orbital overlap are addressed on the basis of a quantum chemical approach. The experimental dielectric spectra for both types of solvents are used for quantum corrections of the outer-sphere reorganization energy as well as for estimations of the effective frequency factor in the limit of strong and weak electronic coupling. The dependence of the electronic transmission coefficient on the electrode−reactant distance is calculated for several orientations of the ferrocenium cation relative to the electrode surface which was represented by a cluster. Emphasis is put on the molecular nature of the elementary act and its qualitatively interesting features for both interfaces. The electron transfer rate constants are calculated and discussed in the viewpoint of available experimental data.
Intensive research in the field of lithium ion intercalating systems over the last several decades resulted in the design of hundreds of active material and electrolyte systems for practical battery applications. [1][2][3] Given the high priority of achieving maximum capacity, energy density, and rate capability characteristics of the Li-ion batteries, as well as emerging Na-ion and K-ion batteries, the focus of the majority of studies on the Electrochemical metal-ion intercalation systems are acknowledged to be a critical energy storage technology. The kinetics of the intercalation processes in transition-metal based oxides determine the practical characteristics of metal-ion batteries, such as the energy density, power, and cyclability. With the emergence of post lithium-ion batteries, such as sodium-ion and potassium-ion batteries, which function predominately in nonaqueous electrolytes of special formulation and exhibit quite varied material stability with regard to their surface chemistries and reactivity with electrolytes, the practical routes for the optimization of metal-ion battery performance become essential. Electrochemical methods offer a variety of means to quantitatively study the diffusional, charge transfer, and phase transformation rates in complex systems, which are, however, rather rarely fully adopted by the metal-ion battery community, which slows down the progress in rationalizing the ratecontrolling factors in complex intercalation systems. Herein, several practical approaches for diagnosing the origin of the rate limitations in intercalation materials based on phenomenological models are summarized, focusing on the specifics of charge transfer, diffusion, and nucleation phenomena in redox-active solid electrodes. It is demonstrated that information regarding rate-determining factors can be deduced from relatively simple analysis of experimental methods including cyclic voltammetry, chronoamperometry, and impedance spectroscopy.
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