Adhesion forces from force curve analysis

PFT Mode AFM Related to this dynamic pulsed force mode is the so-called PFT mode. Using a cantilever with intermediate spring constant ( lN/m), a somewhat altered intermittent contact mode experiment is carried out during which the entire force-displacement curve is being captured. Unlike the intermittent contact mode, however, in which the amphtude is used as the feedback parameter, in this mode the force is controlled directly by using the maximum exerted force, the peak force, as the feedback parameter. This mode allows exquisite control of the force exerted with the tip/cantilever and provides information on sample deformation, stiffness, and adhesive forces from an analysis of the force-displacement curve (Fig. 6.8). 

NR with standard recipe with 10 phr CB (NR 10) was prepared as the sample. The compound recipe is shown in Table 21.2. The sectioned surface by cryo-microtome was observed by AFM. The cantilever used in this smdy was made of Si3N4. The adhesion between probe tip and sample makes the situation complicated and it becomes impossible to apply mathematical analysis with the assumption of Hertzian contact in order to estimate Young s modulus from force-distance curve. Thus, aU the experiments were performed in distilled water. The selection of cantilever is another important factor to discuss the quantitative value of Young s modulus. The spring constant of 0.12 N m (nominal) was used, which was appropriate to deform at rubbery regions. The FV technique was employed as explained in Section 21.3.3. The maximum load was defined as the load corresponding to the set-point deflection. 

SFM also enables us to measure specific interaction forces between a small silicon tip and the surface. The pull-off forces between the tip and the surface estimated from Force vs Distance Curves (FDC) can be correlated to the adhesive interactions between tip and surface [9]. Recording of FDCs line-by-line allows us to image surface topography and adhesive surface properties simultaneously [10]. This technique has some disadvantages, like the requirement for a large amount of data acquisition and analysis, which have been alleviated by the invention of the Pulsed Force Mode (PFM). The PFM simplifies and accelerates the measurements of adhesive properties with high lateral resolution [11, 12]. 

Table 3. Adhesion Forces Obtained from Force Curve Analysis...

As mentioned earlier, the Gc value required to define the CZ model is obtained from TDCB tests. The remaining parameter Gm is chosen as the UTS, and was extracted from the stress-strain curves at the corresponding rates. This was an arbitrary choice, since the level of the constraint near the crack tip is higher than that in uniaxial tensile tests used to obtain the stress-strain curves. Therefore, a sensitivity study on this parameter was performed. For illustration purposes, a numerical analysis carried out on TDCB test specimens bonded with the two adhesives under investigation is shown in this section. The value of a was varied from 20 to 80 MPa and numerical predictions of load versus time were compared against the experimental results. Fig. 5 shows a comparison of the FV and experimental results for different values for TDCB tests performed at 0.1 mm/min. The best fit G value should be able to predict correctly both the experimental force and crack history. (Note that the latter was found to be less sensitive to changes of the cohesive strength.)... 

Consequently, ( )x is a function of disturbing stress. Go dist- An analysis of the form of the function can be useful in calculating the strength of adhesion, Possible dependences of( )x andOodist are shown in Figure 2.5. Curve 1 characterizes the case of filler separation when a certain a is reached, followed by catastrophic failure. A characteristic point of the curve is that corresponding to the Oo dist value at which a sharp increase in the separation rate occxu s. Proceeding from the assumption that the entire sample s resistance force is concentrated solely at the cross-sectional area of all the filler particles in the sample cross-sectional plane, one can calculate o, from the formula ... 

It is tempting to try to relate directly the peel master curve to one or another rheological function. However, such attempts have been unsuccessful. Although the G"(co) function is similar in shape to the peel force vs. rate function from the onset of interfacial failure onward, the magnitude of the variations in G" are much larger than the peel force variations. Of course, no such simple analysis could predict the location of the transition from cohesive to adhesive failure. 

---