Electronic Effects in the Electric Double Layer Wolfgang Schmickler University of Ulm, D-89069 Ulm, Germany Received May 17, 1996 (Revised Manuscript Received August 28, 1996) Contents 1. Introduction 3177 2. Phenomenological Correlations 3178 2.1. The Potential of Zero Charge 3178 2.2. The Helmholtz Capacity 3179 3. The Electronic Density at a Metal Surface 3180 3.1. The Jellium Model 3180 3.2. Jellium with Pseudopotentials 3183 4. Electronic Effects Observed by Optical Techniques 3184 4.1. Electroreflectance Spectroscopy 3184 4.2. Second Harmonic Generation 3185 5. Surface Reconstruction 3187 6. Resistance of Thin Electrodes 3189 7. Tunneling of Electrons through the Electric Double Layer 3190 8. Electronic Effects on Electron Transfer Reactions 3193 8.1. Outer-Sphere Electron Transfer Reactions 3193 8.2. Reaction of Hot Electrons 3194 9. Models for the Electric Double Layer 3195 9.1. The Jellium-Hard Sphere Electrolyte Model 3195 9.2. Models with a Variable Distance between the Metal and the Solution 3197 9.3. Discussion 3198 10. Conclusion 3199 11. References 3199 1. Introduction All electrochemical reactions take place at the interface between an electronic conductor, the elec- trode, and an ionic conductor, the electrolyte. Since the course of these reactions and their variation with the electrode potential depend on the distribution of the particles and the charges in this interfacial region, its structure is of paramount importance for electrochemistry and has been a topic of intensive research since the time of Lippmann 1 and Helm- holtz. 2 It was Helmholtz who pointed out that the high capacity of the interface between a metal and a concentrated electrolyte solution could be explained by the existence of two layers of charges of equal magnitude and opposite sign: a layer of charge on the metal surface, which is balanced by an ionic excess charge in the adjacent solution. This distribu- tion of charges became known as the electric double layer; the use of this term is generally restricted to metal electrodes, and so is this review. Figure 1 shows a picture of the double layer between a single-crystal metal electrode and an aqueous electrolyte solution; this is the interface that is studied in most of the works on which we will report. The circles on the left denote the ion cores of the metal. The polar solvent molecules are indicated by circles with an arrow at their center, and the ions Wolfgang Schmickler was born in Bonn, Germany, in 1946. He studied physics and chemistry at the Universities of Bonn and Heidelberg and at the Imperial College, London. In 1973 he received his Ph.D. in Physical Chemistry from the University of Bonn, graduating summa cum laude. His thesis, which was directed by Professor W. Vielstich, was on the theory of electrochemical electron transfer reactions. After completing his degree he received first a Liebig Fellowship of the Verband der Chemischen Industrie and then a Heisenberg Fellowship of the Deutsche Forschungsgemeinschaft. During this time his home university was at Du ¨ sseldorf, but he used the freedom that these fellowships offered for visits at the Frumkin Institute of Moscow, the Laboratoire d’Electrochimie Interfaciale du CNRS in Meudon, France, and the IBM Research Laboratory in San Jose. While he was in Moscow he became interested in the theory of the electric double layer; for his work on this subject he received the Bodenstein Award of the Deutsche Bunsengesellschaft in 1985. He became assistant professor at the University of Bonn in the same year, but moved to the United States in 1990, where he held the position of an associate professor at the Utah State University in Logan. In 1992, he returned to Germany and took a faculty position at the University of Ulm, where he has been since. His research interests lie in theoretical electrochemistry, but his group also performs experiments on systems that are of interest to theory. Figure 1. Schematic picture of the double layer between a metal surface and an electrolyte solution. 3177 Chem. Rev. 1996, 96, 3177-3200 S0009-2665(94)00408-5 CCC: $25 00 © 1996 American Chemical Society + +