Lateral forces

Lateral force microscopy (LFM) has provided a new tool for the investigation of tribological (friction and wear) phenomena on a nanometre scale [110]. Alternatively known as friction force microscopy (FFM), this variant of AFM focuses on the lateral forces experienced by the tip as it traverses the sample surface, which... 

One of the most important extensions is the measurement of lateral forces (friction). Friction measurements have accompanied tlie SFA teclmique since its early begiimings in the Cavendish laboratory in Cambridge [37] and a variety of different lateral force measurements are practised throughout tlie SFA conmumity. 

The measurement of lateral forces (friction and shear) in the SFA has recently been reviewed by Kumacheva... 

Adechanical stahility. ChemisoriDtion to tire surface, intennolecular interactions and crosslinking between adjacent compounds—if possible—all contribute to tire resulting stability of tire monolayer film. Lateral force microscopy investigations revealed tliat tire mechanical stability towards lateral forces on tire nanometre scale is likely to be detennined by tire defect density and tire domain size on a nano- to micrometre scale [163, 1731. 

The periodic shedding produces lateral forces of the same period on the cylinder. Should the cylinder be weakly supported and have a natural frequency close to the shedding frequency, it oscillates strongly in concert with the vortex street. Such behavior is responsible for the singing of power lines, the oscillation of tall smokestacks, and, most spectacularly, for the coUapse in 1940 of the newly built Tacoma Narrows suspension bridge, in Washington state, under the influence of a steady 65 km/h wind. 

A very practical way to infer the contact area was later developed by Carpick et al. [65] and Lantz et al. [66]. In these experiments, a small (up to nanometer) lateral modulation, djc, is applied to the sample, and torsion of the cantilever is monitored with a lock-in amplifier to detect the lateral force response, dF (Fig. 5). In this way, the lateral stiffness, [51], given by... 

Then, from the lateral force condition that Ny = 0,... 

From Figure D-6 for lateral forces, force equilibrium in the z-direction yields... 

From moment equiiibrium about the x-axis to which the moments of Figure D-7 and the lateral forces of Figure D-6 contribute (but not the in-plane forces of Figure D-5 because they are either parallel to or perpendicular to the x-axis),... 

To minimize effects of friction and other lateral forces in the topography measurements in contact-modes AFMs and to measure topography of the soft surface, AFMs can be operated in so-called tapping mode [53,54]. It is also referred to as intermittent-contact or the more general term Dynamic Force Mode" (DFM). A stiff cantilever is oscillated closer to the sample than in the noncontact mode. Part of the oscillation extends into the repulsive regime, so the tip intermittently touches or taps" the surface. Very stiff cantilevers are typically used, as tips can get stuck" in the water contamination layer. The advantage of tapping the surface is improved lateral resolution on soft samples. Lateral forces... 

Fig. 27—The images of three-dimensional morphologies, (a) and lateral force (b) of Au film [9],...

The system could be energy conservative if the atoms moved smoothly over the potential field. In that case, an atom, when traveling over one period of the potential, would experience a symmetrically distributed lateral force so that its time average and the net work done by the force would be zero. In reality, however, this is not going to happen that way. The author will demonstrate in the following how the system becomes unstable which inevitably leads to energy dissipation and friction. 

It can be seen from Fig. 15(a) that the atom moves in a stick-slip way. In forward motion, for example, it is a stick phase from A to B during which the atom stays in a metastable state with little change in position as the support travels forward. Meanwhile, the lateral force gradually climbs up in the same period, leading to an accumulation of elastic energy, as illustrated in Fig. 15(fo). When reaching the point B where a saddle-node bifurcation appears, the metastable... 

Following the approach similar to that of the atomic-scale model, the evolution of the system state and the lateral force on the asperity can be determined in terms of AUldrj = 0. If we chose V rj)= VQ cos ir rj) as the potential function for the repulsive and attractive pinning center, respectively, the lateral force F=-dy/d7 can be plotted as a function of the traveling distance p, as shown in Fig. 17. 

The changes of lateral force F in forward and backward motions follow the curve 1 and 2, respectively. It can be observed that there is one saddle-node bifurcation for the repulsive pinning center, but two bifurcations for the attractive piiming center. This suggests that the interfacial instability results from different mechanisms. On one hand, the asperity suddenly looses contact as it slides over a repulsive pinning center, but in the attractive case, on the other hand, the... 

Fig. 17 —Lateral force acting on the asperity versus the traveling distance r, (a) for repulsive pinning center, the dotted area corresponds to the net work done by the force, (b) for attractive pinning center.

Fig. 21—Changes in lateral force and tilt angle for SAMs in sliding, (a) results for commensurate monolayers, (b) results for incommensurate case.

The example demonstrates that the instability and consequent energy dissipation, similar to those in the Tomlinson model, do exist in a real molecule system. Keep in mind, however, that it is observed only in a commensurate system in which the lattice constants of two monolayers are in a ratio of rational value. For incommensurate sliding, the situation is totally different. Results shown in Fig. 21(b) were obtained under the same conditions as those in Fig. 21 (a), but from an incommensurate system. The lateral force and tilt angle in Fig. 21(b) fluctuate randomly and no stick-slip motion is observed. In addition, the average lateral force is found much smaller, about one-fifth of the commensurate one. 

The molecule initially sits in potential energy minimum. A lateral force F is required to overcome attractive interac-... 

---