# Atomic Force Spectroscopy on Ionic Liquids
## 4 Principles of Atomic Force Spectroscopy  
Shortly after the epoch-making invention of the scanning tunneling microscope (STM), [PERSON] et al. developed the atomic force microscope (AFM) in the 1980s [62]. It utilizes a sharp tip attached to a microcantilever scanning the surface. In the standard contact mode, the deflection of the cantilever is measured via optical lever amplification when approaching the surface, thus serving as a force sensor based on [PERSON]'s law:  
\[F=-k\delta_{c}, \tag{1}\]  
where \(F\) is the force, \(k\) the spring constant, and \(\delta_{c}\) the cantilever deflection [63]. Using a feedback loop, the force can be kept constant and thus the topography of solid samples can be mapped by moving the sample via piezo elements. With this relatively simple measurement technique, impressive results on the micro- and nanoscale, even up to atomic resolution, have been obtained [64]. As further measurement modes, the non-contact and intermittent or tapping mode have been developed based on the fact that the resonance frequency of the cantilever changes when the tip comes in the vicinity of a surface [65]. They are dynamic measurement modes, where the cantilever is oscillated and the frequency or amplitude of the oscillation is used as an input signal of the feedback loop. These techniques have the advantage that the direct interaction between the tip and sample is minimized, and thus more reliable measurements at higher scan speeds are possible. Dynamic measurements are not only possible using the optical lever technique but also with piezoelectric sensors such as the qPlus tuning fork, allowing for measurements with utmost signal-to-noise ratio [66; 67]. AFM measurements can be performed in various environments without complex sample preparation and do not rely on the presence of vacuum conditions, which are required for other high-resolution microscopy techniques such as electron microscopy. Hence, the AFM has also become a versatile tool for the investigations of liquid samples in chemistry and life science [68]. It has been extensively employed for investigating the morphology changes of metallic surfaces during electrochemical polarization in various electrolytes, including ionic liquids [69; 70; 71; 72; 73]. Here, we focus on the investigation of the spatial extension of the electric double layer at a solid/liquid interface, where information about the structure out-of-plane, normal to the surface in particular, is needed. Therefore, the tip is approached and subsequently retracted from the surface and the force between the tip and sample is recorded as a function of their separation [74]. This mode is called atomic force spectroscopy (AFS), as the force-separation relationship depends on the material properties, thus allowing for mapping of the material contrast [63]. In recent years, AFS has become the method of choice for the investigation of interfaces in liquid and is in particular applied in nanobiology for investigating, e.g., cells, proteins, or antigen-antibody interactions [75]. During these investigations, where the samples are typically immersed in an ionic buffer, effects of interface modifications at charged surfaces have already become obvious [76]. Theoretically, the interaction between the tip and a solid surface can be approximated by the Lennard-Jones potential \(U_{LJ}\) (see Figure 7a), which was calculated by a two-atom approach. It includes an attractive van der Waals interaction and a repulsive interaction related to Coulomb forces and the Pauli Exclusion Principle:  
\[U_{LJ}=-4\varepsilon\left(\frac{\sigma^{6}}{s^{6}}-\frac{\sigma^{12}}{s^{12}}\right) \tag{2}\]  
Here, \(\varepsilon\) is the minimum of the potential well, \(s\) is the separation between the two atoms, and \(\sigma\) describes the separation of zero force [74]. On a real surface in contact with an ionic liquid, the situation can be more complex, as is illustrated by the schematic force curve shown in Figure 7b.