Models of Electron Transfer at Different Electrode Materials.

Electron transfer is the most important electrochemical process. In this review, we present elements of various aspects of electron transfer theory from the early work of Marcus and Hush to recent developments. The emphasis is on the role of the electronic, and to a lesser extent the geometrical, properties of the electrode. A variety of experimental works are discussed in light of these theoretical concepts. Because the field of electron transfer is so vast, this review is far from comprehensive; rather, we focus on systems that offer a special interest and illuminate aspects of the theory.

Catalysis of hydrogen evolution on Pt(111) by absorbed hydrogen.

The activity of Pt(111) electrodes for the hydrogen evolution reaction (HER) in 0.5M H2SO4 solution is found to increase with continuous potential cycling in the HER potential region. In addition, the basic cyclic voltammograms obtained in 0.5M H2SO4 saturated with N2 after HER show several characteristic changes: the current waves for hydrogen adsorption in the region of0.2 < E < 0.35 V and for sulfate adsorption at 0.35 < E < 0.5 V decrease and the current spike at 0.44 V for the phase transition of the sulfate adlayer gradually disappears. We suggest that these changes are caused by the absorption of a small amount of hydrogen in the subsurface layer and propose a mechanism by which this enhances hydrogen evolution.

The Crucial Role of Local Excess Charges in Dendrite Growth on Lithium Electrodes.

Much theoretical effort has been spent on the causes of dendrite formation in lithium metal batteries, but a decisive factor has been overlooked: Lithium is deposited on an electrode which carries a sizable negative charge, and this charge is not distributed homogeneously on the surface. We show by explicit model calculations that the excess charge accumulates on small protrusions and creates a strong electric field, which attracts the Li+ ions and induces further growth on the tip and finally the formation of dendrites. Even a small tip consisting of a few atoms will carry an excess charge of a tenth of a unit charge or more. In addition, the negative charge on the tips locally reduces the surface tension, which further fosters dendrite growth. The same principles can also explain dendrite formation on other metals with deposition potentials below the potential of zero charge.

A model for the effect of ion pairing on an outer sphere electron transfer.

Ion pairing can strongly affect the rates of electron transfer reactions. To explain this effect, we propose a model Hamiltonian that describes the interactions between the pairing ion and the reactant, solvent and inner sphere reorganization, and bond breaking. Explicit expressions for the energies of the initial and final states, and for the energy of activation are derived in the weak adiabatic limit. The model is applied to the reduction of Cu(ii) in the presence of chloride ions. For this purpose, the pertinent system parameters are obtained from density functional theory. Our model explains why the chloride ion enhances the rate of the first electron transfer in copper deposition.

Interactions of ions across carbon nanotubes.

The interactions between a pair of Li+ ions across a semiconducting (8,0)CNT and a conducting (5,5)CNT has been investigated by density functional theory. The direct Coulomb interaction between the ions is almost completely screened. The band structure of the CNTs is not affected by the Li+ ions, but the Fermi level is raised to accommodate the extra electrons. Because of the unique band structure of CNTs this results in an effective attraction between the ions, which is greater for the (8,0)CNT. In contrast, a Cl- ion inside a CNT forms a chemical bond which modifies the band structure. Again, the electrostatic field of the ion is almost completely screened outside of the tube. Nevertheless, the adsorption of a Li+ ion outside is favored by a Cl- ion inside. This apparent attraction is mainly caused by a lowering of the work function of the CNT by the presence of the Cl-.

The Pre-exponential Factor in Electrochemistry.

Like many branches of science, not to mention culture in general, electrochemistry has a number of recurring topics: Areas of research that are popular for a certain time, then fade away as their possibilities seem to have been exhausted, only to return decades later as progress in experimental or theoretical techniques offer new possibilities for their investigation. A prime example are fuel cells, which have undergone five such cycles, but here we discuss a general concept of kinetics-the pre-exponential factor of a rate constant-which has undergone two such cycles. The first cycle was in the 1950-1980s, when the methods of electrochemical kinetics were developed, and the interpretation was based on transition-state theory. The second was triggered by the re-discovery of Kramers theory for reactions in condensed phases. This Minireview will show that the time has come for a third cycle based on recent progress in electrocatalysis.

Adiabatic Electron-Transfer Reactions on Semiconducting Electrodes.

Theoretical treatments of electrochemical reactions at semiconductors are usually based on theories that presume a weak interaction between the reactant and the electrode. Herein a theory is developed that is valid for arbitrary interaction strengths, and its consequences are explored within a simple coupling scheme. This model can be used as a framework for the investigation of specific catalytic reactions including photoelectrocatalysis.

On the capacitance of narrow nanotubes.

The storage of ions in narrow nanotubes is investigated by grand-canonical Monte Carlo simulations. The interaction between the ions is screened by the image charge on the wall of the tube, but at close distances it is still much larger than the thermal energy. Depending on the electrochemical potential imposed by the contact with an electrolyte solution, two different regimes can be distinguished at the potential of zero charge: for low values corresponding to an ionophobic pore the tube is almost empty; for high values - ionophilic pore - a one dimensional salt is formed. The two regions are separated by a narrow transition zone marked by strong fluctuations. Depending on the regime and on the value assumed for the dielectric constant, the interfacial capacity shows four, two, or in rare cases three maxima. The results are compared to a reference system of non-interacting ions, and discussed with respect to recent calculations within classical density functional theory.

Determining Electrochemical Surface Stress of Single Nanowires.

Electrochemical surface stress is important in nanomaterials because of their large surface-to-volume ratios, which lead to unique mechanical and electrocatalytic properties, but directly measuring this quantity has been challenging. Here we report on experimental determination of the surface stress, and associated electrochemical processes of a single gold nanowire with an optical imaging technique. We show that surface stress changes linearly and reversibly with the potential between 0 and 0.8 V versus Ag/AgCl, but abruptly with large hysteresis, associated with the oxidation and reduction of the nanowire, between 0.8 and 1.5 V. The potential derivative of the surface stress closely resembles the cyclic voltammograms. We described the observations in terms of anion adsorption and surface oxidation/reduction. This work demonstrates a new approach to study electrochemical processes and the associated surface stress changes of nanomaterials.

On the Energetics of Ions in Carbon and Gold Nanotubes.

We investigate the insertion of halide and alkali atoms into narrow single-walled carbon nanotubes with diameters <9 Šby density functional theory; both chiral and non-chiral tubes are considered. The atoms are stored in the form of ions; the concomitant charge transfer affects the band structure and makes originally semiconducting tubes conducting. The electrostatic interaction between a charge and the walls of the tube is explicitly calculated. The insertion energies and the positions of the ions are determined by a competition between electrostatic energy and Pauli repulsion. For comparison, we consider ions in gold nanotubes. Alkali ions follow the same principles in gold as in carbon tubes, but chloride is specifically adsorbed inside gold tubes.

Oxygen Reduction on Ag(100) in Alkaline Solutions--A Theoretical Study.

Silver is much more reactive to oxygen than gold; nevertheless, in alkaline solutions, the rates of oxygen reduction on both metals are similar. To explain this phenomenon, the first, rate-determining step of oxygen reduction on Ag(100) is determined by a combination of DFT, molecular dynamics, and electrocatalysis theory. In vacuum, oxygen is adsorbed on Ag(100), but in the electrochemical environment, the adsorption energy is offset by the loss of hydration energy as the molecule approaches the surface. As a result, the first electron transfer should take place in an outer-sphere mode. Previously, the same mechanism for oxygen reduction on Au(100) has been predicted, and these calculations have been repeated by using a more advanced version of the electrocatalysis theory discussed herein to confirm previous conclusions. The theoretical results compare well with experimental data.

On the electrochemical deposition and dissolution of divalent metal ions.

The deposition of Cu(2+) and Zn(2+) from aqueous solution has been investigated by a combination of classical molecular dynamics, density functional theory, and a theory developed by the authors. For both cases, the reaction proceeds through two one-electron steps. The monovalent ions can get close to the electrode surface without losing hydration energy, while the divalent ions, which have a stronger solvation sheath, cannot. The 4s orbital of Cu interacts strongly with the sp band and more weakly with the d band of the copper surface, while the Zn 4s orbital couples only to the sp band of Zn. At the equilibrium potential for the overall reaction, the energy of the intermediate Cu(+) ion is only a little higher than that of the divalent ion, so that the first electron transfer can occur in an outer-sphere mode. In contrast, the energy of the Zn(+) ion lies too high for a simple outer-sphere reaction to be favorable; in accord with experimental data this suggests that this step is affected by anions.

Electrochemical adsorption of OH on Pt(111) in alkaline solutions: combining DFT and molecular dynamics.

The adsorption of OH on Pt(111) in alkaline solution has been investigated by a method that combines density functional theory, molecular dynamics, and quantum statistical mechanics. In particular, we have calculated the free energy surface for the reaction. A physisorbed hydroxide ion in a metastable state and a stable adsorbed uncharged OH group are observed. The energy of activation at equilibrium is comparatively low, so that the reaction is fast.

Chlorine-enhanced surface mobility of Au(100).

Motivated by experimental studies of two-dimensional Ostwald ripening on Au(100) electrodes in chlorine-containing electrolytes, we have studied diffusion processes using density functional theory. We find that chlorine has a propensity to temporary form AuCl complexes, which diffuse significantly faster than gold adatoms. With and without chlorine, the lowest activation energy is found for the exchange mechanism. Chlorine furthermore reduces the activation energy for the detachment from kink sites. Kinetic Monte Carlo simulations were performed on the basis of extensive density functional theory calculations. The island-decay rate obtained from these Monte Carlo simulations, as well as the decay rate obtained from the theoretical activation energies and frequency factors when inserted into analytical solutions for Ostwald ripening, are in agreement with experimental island-decay rates in chlorine-containing electrolytes.

Why silver deposition is so fast: solving the enigma of metal deposition.

A perfect match: Silver deposition is one of the fastest electrochemical reactions, even though the Ag(+) ion loses more than 5 eV solvation energy in the process. This phenomenon, an example of the enigma of metal deposition, was investigated by a combination of MD simulations, DFT, and specially developed theory. At the surface, the Ag(+) ion experiences a strong interaction with the sp band of silver, which catalyzes the reaction.

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.

Hydrogen electrocatalysis on single crystals and on nanostructured electrodes.

We investigate hydrogen evolution on plain and nanostructured electrodes with a theory developed by us. On electrodes involving transition metals the most strongly adsorbed hydrogen is often only a spectator, while the reaction proceeds via a weakly adsorbed species. For Pt(111) the isotherms for both species are calculated. We explain why a nanostructure consisting of a monolayer of Pd on Au(111) is a good catalysts, and predict that Rh/Au(111) should be even better. Our calculations for a fair number of metals are in good agreement with experiment.