Contact interactions force-distance curve

Hertzian mechanics alone cannot be used to evaluate the force-distance curves, since adhesive contributions to the contact are not considered. Several theories, namely the JKR [4] model and the Derjaguin, Muller and Torporov (DMT) model [20], can be used to describe adhesion between a sphere and a flat. Briefly, the JKR model balances the elastic Hertzian pressure with attractive forces acting only within the contact area in the DMT theory attractive interactions are assumed to act outside the contact area. In both theories, the adhesive force is predicted to be a linear function of probe radius, R, and the work of adhesion, VFa, and is given by Eqs. 1 and 2 below. 

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. 

The interaction force versus the tip-sample distance can be calculated partly from force-distance curve. The distance-values are transformed such that the contact line F(z) = -k-z + Fo becomes the ordinate of the interaction force curve. 

In the spectroscopy mode of AFM force-distance curves F(z) are recorded at one or more scan points after the z piezo has been adjusted to the force setpoint (contact mode). The classical shape, as illustrated in Section 5.3.4 and Figure 63, is obtained mostly with hard materials or simpler molecules. In air a meniscus of water is formed at the jump-to-contact. Due to the meniscus force the jump-to- and jump-oflf-contact separations differ largely and the area of the hysteresis loop becomes quite large. Force-distance curves can have various appearances. An overview is given in Reference [233]. Spectroscopy is rarely employed in the dynamic mode because with an oscillating probe the tip-sample separation is never well-defined. On the other hand the snap-on is avoided and the complete interaction potential can be inferred from the measured frequency versus distance curve employing simulations [234,235]. 

FIGURE 3.1 Analysis procedure for force-distance curves with and without an adhesive force between the sample and the AFM probe (a) schematic of contact between two bodies when the applied force is positive (repulsive) (b) force-distance curve for the contact between probe and substrate without adhesive interaction (c) corresponding force-deformation plot (d) schematic of adhesive contact especiatly when the applied force is negative (attractive) (e) force-distance curve for adhesive contact (f) corresponding force-deformation plot. 

However, the fact that AFM is sensitive to these weak forces can be turned into an advantage. One of the most common ways to measure the interactions is a force-distance curve measurement, in which the scanner starts to move vertically to make contact with the probe and surface and then reverse to make them separated. During the process, the cantilever deflection is recorded as a function of vertical scanner movement. One can obtain the relation between normal load P and indentation depth 8 using simple relations (the detailed procedure is discussed later). Applying an appropriate contact mechanics theory, one can estimate the mechanical properties of the sample surfaces. 

Another problem in AFM measurements is the difficulty to find the unperturbed surface level, Zq. One can theoretically deduce Zq from the force-distance curve in the DMT model, it is the value of Z at point E, while in the JKR model it is point A in Figure 17.4. However, in practice, the attractive interaction is often not able to be attributed to just one of the two, adhesion inside intimate contact zone and long-range attraction at the perimeter of the contact. Therefore, to determine 8 in absolute terms is difficult. An approach based on the DMT-M model... 

Protems can be physisorbed or covalently attached to mica. Another method is to innnobilise and orient them by specific binding to receptor-fiinctionalized planar lipid bilayers supported on the mica sheets [15]. These surfaces are then brought into contact in an aqueous electrolyte solution, while the pH and the ionic strength are varied. Corresponding variations in the force-versus-distance curve allow conclusions about protein confomiation and interaction to be drawn [99]. The local electrostatic potential of protein-covered surfaces can hence be detemiined with an accuracy of 5 mV. 

In force—displacement measurements, the sample is moved up and down (in and out of contact with the tip) at a fixed position (x, y) (compare also Chap. 2). The resulting force—distance plot (force—displacement curve) displays the bending of the cantilever as a result of tip—sample interaction forces. The interpretation of forces curves has been discussed in detail, e.g., by Cappella and Dietler [3] and by Butt and co-workers [4]. 

It is thus seen that a variety of interfacial forces can be investigated by using AFM. hi the noncontact mode, we mainly estimate the van der Waals forces (image resolution -10 ran). On the other hand, the ionic repnlsion forces are measured in the contact mode. These studies thus would provide an understanding of the interaction forces (attractive and repulsive) in much greater detail. It is seen that by AFM we can determine the magnitnde of distance of separation at which two bodies jump into contact. The exponential and power laws have been found to fit the experimental force curves. 

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