# Atomic Force Spectroscopy on Ionic Liquids
## 4 Principles of Atomic Force Spectroscopy
At first, one must consider that in conventional AFMs, the force is recorded as a function of the position of the piezo scanner, \(z\). This is, however, not the real distance between the tip and surface. As the cantilever is also moved by the piezo scanner when in contact with the surface, one must subtract the cantileverdeflection \(\delta_{c}\), which has been measured by the optical lever method, from the scanner movement \(z\) in order to obtain the true distance, called separation \(s\), between the tip and sample [77]. \[s=z-\delta_{c} \tag{3}\]  
Secondly, one must consider that during approach and retraction, instabilities in cantilever motion can develop, leading to jumps [78]. When the gradient of the force between the tip and surface during the approach becomes larger than the spring constant of the cantilever, a jump-to-contact (JTC) occurs. Similarly, a jump-off-contact (JOC) occurs when the spring constant of the cantilever becomes larger than the gradient of adhesive forces between the tip and sample [79]. These two instabilities, related to the maximum adhesive forces called pull-on force and pull-off force, mark a hysteresis between the approach and the retraction curve, containing information about the material properties of the sample [78]. When approaching solid surfaces in a liquid, the tip is not necessarily in direct contact with the surface after the jump-to-contact occurs, as solvation layers constitute an additional barrier that the tip must puncture before reaching the solid surface. Thanks to the high sensitivity of an AFM in the \(z\) direction, this effect can be used to resolve the internal structure of the interface layer. In the case of ionic liquids, dense alternating anion and cation layers are present at the interface that cause additional characteristic jumps in the force curve, preferentially during the approach, as illustrated in Figure 7b [80]. At each layer, the force increases at constant separation until it is high enough that the tip can puncture the layer and jump to the next layer. These jumps are strongly dependent on the charging of the system. In the case that the tip or surface is not charged, the measured thicknesses of the layers correspond to the dimension of the anion or cation, respectively, but when a charged surface is investigated with a charged tip, the observed jumps correlate with the dimension of an ion pair [81]. In this manner, detailed information about mechanical properties and the thicknesses of the interface layers of ionic liquids can be collected with sub-nN and sub-nm resolution. In order to achieve such a high resolution, the condition of the tip is the key parameter. While extremely sharp Si tips can be prepared via microfabrication, their morphology is significantly altered by impurities. When handling the tips in ambient conditions, organic adsorbates can be adsorbed on the tip, impairing its performance. Hence, tip preparation methods involving plasma treatment, sputtering, or UV irradiation have been found to significantly increase the quality of AFM measurements in liquids [82]. A further source of tip contamination can be solid state impurities such as elements from the backside coating of the cantilever that have diffused to the tip apex [83]. Similar contaminations can also evolve in the course of the measurement if material from the solid surface or particles already present in the liquid get attracted to the tip and thus changing its geometry [84]. Besides these  
Figure 7: **(a)** Lennard–Jones potential describing the force between the tip and a solid surface related to attractive and repulsive interaction; **(b)** schematic illustration of a typical static-mode force curve obtained during approach and retraction of a solid surface in an ionic liquid. unwanted effects, controlled tip modification by adsorbates can also be used to increase the sensitivity and selectivity of the tip as shown below [85]. A further parameter that can influence the measured forces is the velocity of the tip during approach and retraction.