Force-displacement modifiers

Since the first experiment, where Bhushan and Koinkar [265] have measured the hardness of silicon with a modified SFM, researchers have been using force-displacement curves more for the determination of certain sample properties, e.g. hardness and stiffness, than for the structuring of surfaces. 

Repair of damaged SBR concrete specimens using of epoxy resin and of the hard flexible polymer PT. According to the first approach, three pairs of specimens from each group of modified concrete (C5% le and C5% lpt, C10% 2e and C10% 2pt, C20% 3e and C20% 3pt) were tested up to damage with measurements of force and vertical displacement (deflection). Obtained results are presented in form of force-displacement diagrams in Fig. 12a,b,c. Specimens repaired in each pair with the epoxy resin (e5 l, e5 2, e5 3) and the polymer PT (pt5 l, pt5 2, pt5 3) were tested also up to damage. Obtained results are presented as comparison in Fig. 12a,b,c. Every specimen was broken in concrete in a certain distance from the repair joint (Fig. 13a,b). 

The main shortcoming, reported by Anderson [12] for the Amott methods, is their insensitivity near neutral wettability. In addition, the RDI relates relative volnmes of imbibition, but one also needs to look at these individual volumes to obtain a better understanding of flnid displacement as represented by this index. More recently, Ma [15] reported that the Amott test also does not discriminate adequately at strongly water-wet conditions and proposed an imbibition rate method for wettability (see below). Other shortcomings include variations in laboratory procednres. The temperatnre and length of time employed for the spontaneons imbibition and the pressure used during the forced displacement cycle are often modified to match specific field parameters or for ease of measurement in the laboratory. Consequently, the qnantitative values that are obtained can differ from one laboratory to another for reasons that are not related just to the wettability of the rock sample. 

Covalently modified nanotube tips also offer the possibility of probing biological systems at the nanometer scale this was demonstrated using biotin-streptavidin. 5-(Biotinamido)pentylamine was covalently linked to nanotube tips through amide bonds, and force-displacement measurements were completed on mica surfaces containing immobilized streptavidin. A well-defined binding force of 200 pN per biotin-steptavidin pair was obtained. Control experiments were carried out with an excess of free biotin, which blocks all receptor sites of the protein, and unmodified nanotube tips showed no adhesion within the noise limits of the experiments. Thus the observed binding force resulted from the interaction of nanotube-linked biotin with the surface of streptavidin. 

Figure 19.3 shows representative force—displacement curves obtained from quasistatic indentation tests for each material configuration. As seen in Figure 19.3, the first damage of pristine and 1 wt% GB-modified GFRP occurred at 3.4 and 3.7 kN, respectively, whereas for 1 wt% NC, the first damage was observed at approximately 2.5 kN. 

Figure 19.6 shows representative force—displacement curves found from quasistatic indentation tests for pristine and GB-modified GFRP. As can be observed, the... 

Figure 19.6 Comparison of reaction force—displacement curves of pristine and GB-modified GFRP under a quasi-static indentation test.

Seismic Collapse Assessment, Fig. 1 Force-displacement relations from a monotonic and a cyclic test (Modified from Gatto and Uang 2002 With permission from Prof. Uang, UC San Diego)... 

Thomas et al. [72] used a modified force microscope in which a compensatory force was applied to the probe to keep its displacement at zero. With this system they studied interactions between organomercaptan molecules with CH3, NH2, or COOH end groups. All measurements were performed in dry nitrogen. From SEM-measured tip radii and pull-off force they calculated the work of adhesion using the DMT model. They found that the work of adhesion values qualitatively scaled as expected for van der Waals, hydrogen bonding,... 

They are, in fact, two possible perturbative approaches. In the first approach, one considers two (or any number) reagents A and B as a single system where A and B are two fragments in interactions. The total density is p(r ) = p4(r/) I p/ (r/) [24]. Displacement of A relative to B is an internal mechanical deformation of the complete system it is related to response function of A I B. For instance, a small displacement U/f of an atom K of B will modify the force on the other atoms by... 

Based on the concepts of intermolecular forces and shear modulus introduced in the previous section, it is relatively easy to estimate the theoretical stress required to cause slip in a single crystal. We call this the critical shear stress, Ocr. Refer to Figure 5.10a, and consider the force required to shear two planes of atoms past each other. In the region of small elastic strains, the stress, t, is related to the displacement, x, relative to the initial interplanar spacing, d, according to a modified form of Eq. (5.10) for the shear modulus, G ... 

Figure 4 clearly illustrates that polarizability is a function of the frequency of the applied field. Changing the restoring force constant, k (equation (2)) is another way to modify the linear polarizability. Another alternative is to add anharmonic terms to the potential to obtain a surface such as that shown in Figure 13. The restoring force on the electron is no longer linearly proportional to its displacement during the polarization by the light wave, it is now nonlinear (Figure 14). As a first approximation (in one dimension) the restoring force could be written as ...

On the other hand, the application of a static or slowly varying electric field will be able to displace ions and electrons away from their equilibrium positions and, as a consequence, the polarizability of the electrons will be modified. In the description of H. A. Lorentz s electronic oscillators, the small shifts in the ionic positions modify the spring constants and restoring forces of the electronic oscillators. 

One generally attempts to reduce the capillary forces restraining the oil and/or alter viscosity of the displacing fluid in order to modify the viscous forces being applied to drive oil out of the pores. The ratio of viscous forces to capillary forces actually correlates well with residual oil saturation and is termed the capillary number. One formulation of the capillary number is,... 

If the Hellmann-Feynman theorem is to be valid for forces on nuclei, the Coulomb cusp condition must be satisfied. However, if the nuclei are displaced, the orbital Hilbert space is modified. Hurley [179] noted this condition for finite basis sets, and introduced the idea of floating basis functions, with cusps that can shift away from the nuclei, in order to validate the theorem for such forces. 

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