Deflection versus distance curves

Since the first AFM applications, researchers have examined so-called force curves. In the contact mode, these are deflection-versus-distance (DvZ) curves, as seen in Figure 20.2a. Initially, DvZ curves were employed to check whether a particular deflection set point used for imaging corresponds to a net repulsive or net attractive force [25]. This curve can also be obtained in tapping mode... 

Fig. 3 Schematic deflection-versus-piezo translator position curve (Az versus Azc). At large separation, no force acts between tip and sample (a). The cantilever is not deflected. When approaching the surface, it was assumed that a repulsive force is acting (b) and the cantilever is bent upwards. At a certain point, the tip often jumps onto the sample. This happens when the gradient of attractive forces, for example, the van der Waals forces, exceeds the spring constant of the cantilever. After the jump-in, the tip is in contact with the sample surface (c). When retracting the tip, often an adhesion force is observed (d) and the tip has to be pulled off the surface. The deflection-versus-piezo translator position curve has to be transformed as described in the text to obtain a force-versus-distance curve (F versus D).

The concept of measuring forces was further developed in an operational mode called force spectroscopy. Scanning is typically discontinued and the experiment is performed at a given x, y location on the surface. Again, the cantilever support is moved vertically but over a much wider range. Measuring the cantilever deflection gives a force versus distance curve, which is a plot of the force (or cantilever deflection) as a function of the tip-sample separation. In particular, this method can be used to measure the pull-off force (i.e. the force required to separate the tip from the sample surface). In... 

Quantitative evaluation of a force-distance curve in the non-contact range represents a serious experimental problem, since most of the SFM systems give deflection of the cantilever versus the displacement of the sample, while the experimentalists wants to obtain the surface stress (force per unit contact area) versus tip-sample separation. A few prerequisites have to be met in order to convert deflection into stress and displacement into tip-sample separation. First, the point of primary tip-sample contact has to be determined to derive the separation from the measured deflection of the cantilever tip and the displacement of the cantilever base [382]. Second, the deflection can be converted into the force under assumption that the cantilever is a harmonic oscillator with a certain spring constant. Several methods have been developed for calibration of the spring constant [383,384]. Third, the shape of the probe apex as well as its chemical structure has to be characterised. Spherical colloidal particles of known radius (ca. 10 pm) and composition can be used as force probes because they provide more reliable and reproducible data compared to poorly defined SFM tips [385]. 

Interactions between a spherical colloid and a wall can be measured by bringing probe and substrate together and monitoring the cantilever deflection as a function of the interparticle distance. The photodetector voltage versus piezo position curve can be converted into a force-distance curve. The force acting on the cantilever follows from the deflection of the cantilever and its known spring constant. The zero force is defined by the deflection of the cantilever as the colloidal probe is far from the surface of the substrate. To obtain the force-distance dependence on an absolute scale the zero distance, i.e., where the colloid touches the wall, has to be determined. Commonly, the zero distance is obtained from the force curve itself and not through an independent method [68]. 

Fig. 6.16 (A) Potential energy of an atom probe approaching a surface, as a function of separation, and the resulting normal force, the differential of the energy. Point A is the position of equilibrium contact. (B) Enlarged view of the force versus separation curve near the equilibrium contact point. Smaller separations give a repulsive force, and the probe is said to be in contact with the surface. The straight lines correspond to the stiffness of the cantilever, and greater slopes make the probe position unstable. (C) Cantilever deflection as a function of the distance of the cantilever support above the surface. The vertical lines show how the probe will be unstable and jump into and out of contact with the surface. A shffer cantilever would produce the smaller deflection shown as a dotted line, and suppress the instability.

Force Versus Distance Measurements with an AFM Force measurements with AFM, in the contact mode, consist in detecting the deflection of a spring (or cantilever) bearing a tip at its end, when interacting with the sample surface. The deflection of the cantilever is detected by an optical device (four quadrant photodiode) while the tip is vertically moved forward and backward thanks to a piezoelectric ceramic (or actuator). Thus, provided that the spring constant of the cantilever is known, one can obtain a deflection-distance (DD) curve and then a force-distance (FD) curve, by using Hooke s law. The DD curves presented in this chapter were performed in air. A schematic representation of a DD curve obtained when probing a hard surface is reported in Fig. 3.6. 

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