# Atomic Force Spectroscopy on Ionic Liquids
## 3 The Electric Double Layer at Solid-Liquid Interfaces  
Investigations of the electric double layer formed in a liquid electrolyte close to an electrified interface range back to the early days of electrochemistry. In 1853, [PERSON] described the electric double layer as a simple capacitor formed by ions of the electrolyte being attracted by the oppositely-charged surface [49]. Later, [PERSON] and [PERSON] improved this conception by taking into account the fact that entropic effects lead to a smearing of the region that screens the surface charge and described the double layer as a diffuse space charge zone [50; 51]. This model has been found to work well in describing electrolytes with low ion concentrations at moderate voltages. [PERSON] further improved understanding of the interface by re-introducing a \"Helmholtz-like\" layer directly at the surface, thus removing the deficiencies that the Gouy-Chapman model revealed at high voltages, as it does not account for the finite size of the ions [52]. In this Gouy-Chapman-Stern model, a linear potential drop in the inner compact layer occurs before a quasi-exponential decrease in the outer layer does. An illustration of the discussed models of the electrical double layer is shown in Figure 4. These models are so-called \"primitive models\", as they treat the ions as charged spheres, the solvent as a dielectric continuum, and the electrode as an ideal metal. When trying to understand the interface between an electrified solid surface and an ionic liquid, the above-mentioned models could not be successfully applied, mainly because they were developed for diluted electrolytes where the ion distribution can be described by Poisson-Boltzmann statistics [13]. To obtain a more comprehensive insight into the mechanism of the double layer, so-called \"non-primitive models\" were developed to take into account the properties of the metal electrode and the discrete nature of the solvent [53]. For instance, the ion-dipole-jellium model treats the solvent and solute as an ensemble of hard spheres interacting with the electron gas of the electrode [54; 55]. In this way, it became possible to describe the processes at the interface with particular consideration of the charge transfer from a quantum mechanical perspective. However, for modelling ionic liquids, further parameters must be considered, as the electrolyte forms a kind of \"ionic plasma\" [56]. It was found that their electric double layer shows similarities to conventional molten salts, where overscreening or crowding effects become relevant [57]. Describing such a complex interface structure is challenging, and approaches using mean-field theory, Landau-Ginzburg theory, and molecular dynamics have been considered [13; 58; 59; 57]. Figure 4: Models of the formation of the electrical double layer in an electrolyte in contact with a positively charged solid electrode. As ionic liquids are entirely composed of ions, one can assume in a simplified approximation that ions with a charge opposite to the electrified electrode will be attracted to the interface. As illustrated in Figure 5 for a positive electrode, the first layer would be formed by anions, followed by a cation layer. Depending on the strength of the coulomb interaction, this layering will be repeated towards the bulk several times. With increasing distance from the interface, the disorder will decrease until, finally, the bulk structure is adopted. In ionic liquids composed of asymmetric ions, the orientation of the molecules also becomes relevant, and the interaction between charged head groups and uncharged tail groups can result in complex field-induced charge arrangement processes [60]. In order to verify or improve on these theories, direct experimental insight into the double layer structure is essential. In particular, the mechanical methods, AFM and SPA, have contributed significantly to elucidating the interface structure in recent years.