Electrochimica Acta 45 (2000) 2317 – 2338 Recent developments in models for the interface between a metal and an aqueous solution Rolando Guidelli a, *, Wolfgang Schmickler b a Dipartimento di Chimica, Uniersita ` di Firenze, Via Gino Capponi, 9 -50121 Florence, Italy b Abteilung Elektrochemie, Uniersity of Ulm, D-89069 Ulm, Germany Papers received in Newcastle, 20 December 1999 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 simula- tions) 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. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: Double layer; Jellium; Monte Carlo simulations; Molecular dynamics simulations; Integral equations www.elsevier.nl/locate/electacta 1. A bird’s eye view of double-layer models Ten years before Debye and Hu ¨ ckel, Gouy [1] and Chapman [2] represented the electrolyte solution adja- cent to a planar charged wall as a cloud of point ions embedded in a dielectric continuum and solved the differential equation resulting from the combination of the Poisson equation of electrostatics and Boltzmann statistics. Their diffuse layer theory accounts satisfacto- rily for the thermodynamic surface excesses of non-spe- cifically absorbed ions such as F - and K + ions on a mercury electrode. This theory predicts that the differ- ential capacity C, namely the derivative of the charge density  M with respect to the applied potential E, once plotted against  M or else the applied potential E, should have the shape of an inverted parabola, with the minimum at the potential of zero charge (pzc ) and increasing progressively with an increase in the elec- trolyte concentration. This prediction is verified only in the proximity of the potential of zero charge and at low electrolyte concentrations. However, as we depart from these conditions, the differential capacity no longer satisfies the Gouy – Chapman (GC) theory, and be- comes independent of the electrolyte concentration. To account for this behaviour, the interface was regarded as consisting of a charge-free layer of water molecules enclosed between the metal surface and the plane of closest approach to the metal surface of the centers of charge of the solvated ions; this layer, called the inner or compact layer, is bounded by the diffuse layer on the solution side [3]. The inner and diffuse layers are in series, and hence the reciprocal of the overall capacity is the sum of the reciprocals of the capacity C i of the inner layer and of the capacity C d , of the diffuse layer, the latter being expressed by the GC theory. In this way, as C d becomes greater than C i , C tends to coincide with the capacity C i of the inner layer. It soon became apparent that C i contains a wealth of structural infor- mation; thus, it depends characteristically on the nature of the metal and of the solvent and, for a given interface, on the electrode charge and on the tempera- ture. In particular, at metal – water interfaces C i shows a * Corresponding author. Tel.: +39-55-2757540; fax: +39- 55-244102. E-mail address: guidelli@unifi.it (R. Guidelli) 0013-4686/00/$ - see front matter © 2000 Elsevier Science Ltd. All rights reserved. PII:S0013-4686(00)00335-2