Atomic force distance curve

As we showed in Chapter 6 (on the modulus), the slope of the interatomic force-distance curve at the equilibrium separation is proportional to Young s modulus E. Interatomic forces typically drop off to negligible values at a distance of separaHon of the atom centres of 2rg. The maximum in the force-distance curve is typically reached at 1.25ro separation, and if the stress applied to the material is sufficient to exceed this maximum force per bond, fracture is bound to occur. We will denote the stress at which this bond rupture takes place by d, the ideal strength a material cannot be stronger than this. From Fig. 9.1... 

Cappella B, Dietler G (1999) Force-distance curves by atomic force microscopy. Surf Sci Rep 34(1-3) 101-104... 

Alternatively, one may employ colloidal probe atomic force microscopy (AFM) to measure force distance curves such as the ones plotted in Fig. 5.1 [162]. The important difference between SFA and colloidal probe AFM experiments is that in the latter the entire force distance curve is accessible rather than only that portion satisfying Eq. (5.66) [163, 164]. In Ref. 164 a comparison is presented between theoretical and experimental data for confined poly-electrolyt.e systems. 

The atomic force microscope (AFM) is a promising device for the investigation of materials surface properties at the nanoscale. Precise analysis of adhesive and mechanical properties, and particularly of model polymer surfaces, can be achieved with a nanometer probe. This study distinguishes the different contributions (chemical and mechanical) included in an AFM force-distance curve in order to estabhsh relationships between interfacial tip-polymer interactions and the surface viscoelastic properties of the polymer. 

Adhesive forces were measured to analyze the interaction between Si atomic force microscope (AFM) tips and the deposited films from the force-distance measurement with the AFM. The force-distance curve is expected to elucidate the adsorption behavior of PAM on the deposited films. In the force-distance measurement, there is no interaction until the tip is close enough to be attracted to the surface. As the tip approaches to the surface, it contacts with the surface. After the contact, the tip is retracted from the surface, the cantilever is bent, and a repulsive force (positive) is measured. When the tip is being retracted, an attractive force is measured (negative). When the critical force is reached, the tip is separate from the surface and this point is called the pull-off point. Therefore, the pull-off point, which corresponds to the point of the critical force, is determined by the degree of the adhesive force between the tip and the surface. The higher the adhesive force between the tips and the films, the lower the pull-off point. Figure 6.14a shows the force-distance curves of the tips and poly Si film at pH 10 as a function of the PAM concentration. In the absence of the absorbed PAM molecule, an adhesive force was observed at approximately 20 nm of separation distance. It is of interest that there is no significant difference between the surface forces of the tip and poly Si film even with the presence of PAM. This result is almost the same for all samples, irrespective of the concentration, which means that PAM is scarcely adsorbed on poly Si film. 

Close to ro the force-distance curve approximates a tangent when the applied forces are small the displacement of the atoms is small and proportional to the force. We can define the stiffness of the bond. So, as the slope of this line ... 

FIGURE 4.1 (a) Bond-energy cun/e for KCt At infinite separation, the energy is that required to form and Cl" from the corresponding atoms, (b) Force-distance curves for two materials one where the bonding Is strong and one where it is weak. 

The potential energy for a pair of atoms at a separation distance of r can be obtained as the integral (area) under the force-distance curve between infinity and the distance r (see Fig. 3). 

Force distance curves measured in pure water with these fimctionalized tips on SAMs of p-CD 1 on atomically smooth Au(lll) showed multiple pull-off events as shown in Figure 5 (top). After replacing the water by an aqueous solution of the external guest (1,8-ANS, 100 pM), the number of resolved pull-off events was drastically reduced. In ca. 50 % of the force distance curves single pull-offs were observed (Figure 5, bottom). The other force-distance curves showed up to three pull-offs, indicating some residual free p-CD cavities. 

Figure 3.5.30 Exploring short-range interaction forces on Si(lll) surfaces covered with Sn and Pb atoms, (a) Sets of short-range force-distance curves obtained over structurally equivalent Sn and Si atoms acquired with tips differing in their detailed atomic structure, (b) The same force-distance curves as in (a) but normalized to the absolute value of the minimum short-range force of the Si curve. (c,d) Similar sets of short-range force curves for Pb and Si, obtained before (c) and after (d) normalization. The average relative interaction ratios obtained from the normalized data for Sn (77%) and Pb (59%) are characteristic val-tfes for the chemical identification, (e-h) Single-atom chemical identification, (e)...

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