Wolfgang Schmickler

A theory of adiabatic electron-transfer reactions

Abstract A theory for adiabatic electron-transfer reactions at metal electrodes is presented. The model Hamiltonian is similar to that of the Levich and Dogonadze theory for non-adiabatic reactions, but the rate is not calculated from perturbation theory but by techniques familiar from the Anderson-Newns model for adsorption. In the limit of comparatively weak interactions, this model reduces to the Marcus theory: for stronger interactions there are significant deviations. A possible classification of electrochemical electron-transfer reactions is discussed.

New models for the structure of the electrochemical interface

Abstract Recent progress in the development of models for the structure of the electrochemical interface and their application to capacitance and electrosorption is surveyed. This model of the structure of the double layer includes, for the first time, explicit contributions from the solvent and electronic structure and gives an excellent description of the interfacial capacitance with at most one parameter. The model of electrosorption provides, for the first time, a microscopic definition of the notion of “partial charge transfer,” showing the dependence of this quantity on the relevant microscopic parameters. Our review closes with a discussion of the first quantum model of the surface states in a semiconductor/molten salt interface.

Defining the transfer coefficient in electrochemistry: An assessment (IUPAC Technical Report)

Abstract The transfer coefficient α is a quantity that is commonly employed in the kinetic investigation of electrode processes. In the 3rd edition of the IUPAC Green Book, the cathodic transfer coefficient αc is defined as –(RT/nF)(dlnkc/dE), where kc is the electroreduction rate constant, E is the applied potential, and R, T, and F have their usual significance. This definition is equivalent to the other, -(RT/nF)(dln|jc|/dE), where jc is the cathodic current density corrected for any changes in the reactant concentration at the electrode surface with respect to its bulk value. The anodic transfer coefficient αa is defined similarly, by simply replacing jc with the anodic current density ja and the minus sign with the plus sign. It is shown that this definition applies only to an electrode reaction that consists of a single elementary step involving the simultaneous uptake of n electrons from the electrode in the case of αc, or their release to the electrode in the case of αa. However, an elementary step involving the simultaneous release or uptake of more than one electron is regarded as highly improbable in view of the absolute rate theory of electron transfer of Marcus; the hardly satisfiable requirements for the occurrence of such an event are examined. Moreover, the majority of electrode reactions do not consist of a single elementary step; rather, they are multistep, multi-electron processes. The uncritical application of the above definitions of αc and αa has led researchers to provide unwarranted mechanistic interpretations of electrode reactions. In fact, the only directly measurable experimental quantity is dln|j|/dE, which can be made dimensionless upon multiplication by RT/F, yielding (RT/F)(dln|j|/dE). One common source of misinterpretation consists in setting this experimental quantity equal to αn, according to the above definition of the transfer coefficient, and in trying to estimate n from αn, upon ascribing an arbitrary value to α, often close to 0.5. The resulting n value is then identified with the number of electrons involved in a hypothetical rate-determining step or with that involved in the overall electrode reaction. A few examples of these unwarranted mechanistic interpretations are reported. In view of the above considerations, it is proposed to define the cathodic and anodic transfer coefficients by the quantities αc = –(RT/F)(dln|jc|/dE) and αa = (RT/F)(dlnja/dE), which are independent of any mechanistic consideration.

The interphase between jellium and a hard sphere electrolyte. A model for the electric double layer

A model for the metal/liquid electrolyte interphase is presented, in which metal is modelled as jellium, the electrolyte as an ensemble of hard spheres. An expression is derived for the interfacial capacity at the potential of zero charge. Numerical model calculations are performed for various metal/solvent systems. The model gives good results for the capacity of second and third row sp metals, and for the temperature dependence of the Hg/water interface.

Volcano plots in hydrogen electrocatalysis – uses and abuses

Summary Sabatier’s principle suggests, that for hydrogen evolution a plot of the rate constant versus the hydrogen adsorption energy should result in a volcano, and several such plots have been presented in the literature. A thorough examination of the data shows, that there is no volcano once the oxide-covered metals are left out. We examine the factors that govern the reaction rate in the light of our own theory and conclude, that Sabatier’s principle is only one of several factors that determine the rate. With the exception of nickel and cobalt, the reaction rate does not decrease for highly exothermic hydrogen adsorption as predicted, because the reaction passes through more suitable intermediate states. The case of nickel is given special attention; since it is a 3d metal, its orbitals are compact and the overlap with hydrogen is too low to make it a good catalyst.

A jellium-dipole model for the double layer

Abstract A new model for the double layer at a metal/electrolyte interface is presented. The metal is modelled as jellium, the solvent molecules in the inner layer as an ensemble of dipoles. A set of self-consistent equations for the system is derived and solved numerically. Model calculations for the capacity-charge characteristics are presented, they show a dependence on both the nature of the metal and the solvent, and exhibit capacity humps with a temperature dependent height.

Recent developments in models for the interface between a metal and an aqueous solution

Abstract After a bird’s eye view of double-layer models of interfaces between metals and aqueous solutions from their very beginning, recent developments are reviewed. The role of the metal is examined by considering calculations for metal clusters and the jellium model, both in vacuo and in contact with model solutions. Integral equation approaches to the solution side of the interfaces are reviewed and compared with Monte Carlo and molecular dynamics simulations of analogous molecular models. Computer simulations of metal–water interfaces (including Car-Parinello simulations) and of ionic solution–metal interfaces are considered. Finally, a field-theoretical approach to the double-layer and the treatment of rough electrodes are briefly reviewed.

A unified model for electrochemical electron and ion transfer reactions

Abstract Electron and ion transfer reactions on metal electrodes are considered in an extended Anderson model, in which the interactions of the reactant with the metal and with the solvent depend on the separation from the interface. The model allows the construction of effective potential energy surfaces. Explicit calculations are performed for the transfer of an iodide ion and for the electron transfer reaction of the Fe 2+ /Fe 3+ couple.

Comments on the thermodynamics of solid electrodes

The thermodynamics of solid electrodes are discussed in light of the recent measurements of surface stress. Interfacial tension and surface stress are not even approximately equal, and they generally exhibit a different dependence on the electrode potential. The variation of the interfacial strain with potential is small so that the Lippmann equation for a solid is practically the same as for a liquid electrode. Changes in the interfacial tension can be obtained by integrating the charge density over the potential.

Why is Gold such a Good Catalyst for Oxygen Reduction in Alkaline Media

The two faces of gold: the reduction of oxygen on gold electrodes in alkaline solutions has been investigated theoretically. The most favorable reaction leads directly to adsorbed O(2)(-), but the activation energy for a two-step pathway, in which the first step is an outer-sphere electron transfer to give solvated O(2)(-), is only slightly higher. d-band catalysis, which dominates oxygen reduction in acid media, plays no role. The reason why the reaction is slow in acid media is also explained.