Force curves

Finally, Berger et al [192] have developed a teclmique whereby an array of force curves is obtained over the sample surface ( force-curve mapping ), enabling a map of the tip-sample adliesion to be obtained. The autiiors have used this approach to image differently oriented phase domains of Langimiir-Blodgett-deposited lipid films. 

A typical force curve showing the specific avidin-biotin interaction is depicted in figure Bl.20.10. The SFA revealed the strong influence of hydration forces and membrane undulation forces on the specific binding of proteins to membrane-bound receptors [81]. 

Figure Bl.20.10. Typical force curve for a streptavidin surface interacting with a biotin surface in an aqueous electrolyte of controlled pH. This result demonstrates the power of specific protein interactions. Reproduced with pennission from [81].

Figure Bl.20.11. Force curves of DMPC/DPPE (dimyristoyl phosphatidylcholine and dipalmitoyl phosphatidylethanolainine) bilayers across a solution of PEG at different concentrations. Clearly visible is a concentration-dependent depletion attraction, with pennission from [17],...

Fig. 3. Attraction—repulsion potentials as a function of distance between particle centers. Curve 1 represents the attractive potential caused by van der Waals forces, curve 2 is the repulsive potential caused by double-layer forces, and curve 3 is the resultant force experienced by the two particles.

TTie force-curve mapping technique is often referred to as force-volume mapping commercially, although sample volume is not probed unless stiff levers or compliant surfaces are used. 

Fig. 4. AFM force curves (using double-cross configuration) showing unloading slope differences for various material pairs. Reprinted with permission from ref. [39]. Copyright 1994 Institute of Physics.

An example of interaction stiffness and force curves for a Si surface with a native oxide at 60% relative humidity (RH) is shown in Fig. 12 [104]. The stiffness and force data show an adhesive interaction between the tip and substrate. The hysteresis on retraction is due to a real change in contact area from surface oxide deformation and is not an experimental artifact. The adhesive force observed during retraction was consistent with capillary condensation and the surface energy measured from the adhesive force was close to that of water. 

To illustrate the relationship between the microscopic structure and experimentally accessible information, we compute pseudo-experimental solvation-force curves F h)/R [see Eq. (22)] as they would be determined in SEA experiments from computer-simulation data for T z [see Eqs. (93), (94), (97)]. Numerical values indicated by an asterisk are given in the customary dimensionless (i.e., reduced) units (see [33,75,78] for definitions in various model systems). Results are correlated with the microscopic structure of a thin film confined between plane parallel substrates separated by a distance = h. Here the focus is specifically on a simple fluid in which the interaction between a pair of film molecules is governed by the Lennard-Jones (12,6) potential [33,58,59,77,79-84]. A confined simple fluid serves as a suitable model for approximately spherical OMCTS molecules confined... 

Fig. 19 —A schematic force curve as a function of film thickness for the liquid of linear chain molecules.

The mechanical instability, jump-in and pull-off phenomenon, can also be observed in a macroscopic system, and both the trajectory and force curves exhibit similar patterns to those in Fig. 6. As a comparison, Fig. 9 shows a force curve obtained from SFA experiments of mica surface separation in diy air [8]. The pattern of the force variation, the... 

Fig. 19—Force curve in a AFM experiment as the probe travels along the surface of NaCI crystal (from Ref. [14]).

Fig. 23—A schematic force curve plotted as a function of sliding velocity. A viscous friction forms the background of the force curve upon which the frictions from superharmonic and parametric resonance are superposed.

At finite velocity kinetic friction behaves quite differently in the sense that the commensurability plays a less significant role. Besides, the system shows rich dynamic properties since Eq (16) may lead to periodic, quasi-periodic, or chaotic solutions, depending on damping coefficient y and interaction strength h. Based on numerical results of an incommensurate case [18,19], we outline a force curve of F in Fig. 23 asafunction ofv, in hopes of gaining a better understanding of dynamic behavior in the F-K model. 

A similar process can be observed at the asperity level, as shown in Fig. 33, where a lateral force F pulls the upper solid forward by a distance, u, while the asperity attached to the solid body remains in contact with the lower asperity. The value of u at the moment when the asperity is suddenly pulled out of contact gives rise to creep length of static friction. By referring to the force curve shown in the inserted panel of Fig. 33, the creep distance for this system is estimated to be similar with the asperity dimension in the sliding direction, which is in agreement with the measured creep length, 1 fim, as reported in Ref. [30]. 

SPM force curves are acquired by moving the tip toward the sample and recording the cantilever deflection as a function of the so-called Z position. Cantilever deflection is directly proportional to the force exerted on the sample by the tip. If the spring constant (fc) of the cantilever is known, the force can be calculated. The Z position defines the distance from the sample to the piezo, to which the base of the cantilever is attached (Figure 9.13). By convention the closest point of approach by the piezo is designated as zero on the x-axis. Note that for some instruments the piezo is attached to the sample stage and thus moves the sample up toward the tip however, this does not change the analysis. 

FIGURE 9.14 Typical approach force curve (solid line) for a sample which is penetrated by the scanning probe microscope (SPM) tip. Also shown is the force curve (dashed line) when the tip encounters a hard surface (glass) and schematic drawings of the relative positions of the SPM tip and the sample surface as related to the force curves. (From Huson, M.G. and Maxwell, J.M., Polym. Test., 25, 2, 2006.)... 

Figure 9.14 shows a typical approach force curve along with schematic drawings of the relative positions of the SPM tip and the sample surface, as related to the force curve. At the start of the experiment, i.e., position A on the right-hand side of the figure, the tip is above the surface of the sample. As it approaches the surface the Z value decreases until at position B the tip contacts the surface. With further downward movement of the piezo the cantilever starts to be deflected by the force imposed on it by the surface. If the surface is much stiffer than the cantilever, we get a straight line with a slope of — 1, i.e., for every 1 nm of Z travel we get 1 nm of deflection (Une BC in Figure 9.14). If the surface has stiffness similar to that of the cantilever, the tip wUl penetrate the surface and we get a nonlinear curve with a decreased slope (line BD in Figure 9.14). The horizontal distance between the curve BD and the line BC is equal to the penetration at any given cantilever deflection or force. The piezo continues downward until a preset cantilever deflection is reached, the so-called trigger. The piezo is then retracted a predetermined distance, beyond the point at which the tip separates from the sample.

Figure 9.15 shows typical force curves for a chlorobutyl mbber (CUR) and a namral rubber (NR) sample. It is immediately obvious that the CIIR sample is softer and, as expected, shows much greater hysteresis and hence poorer resilience than the NR sample. 

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... 

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