Lateral or frictional force

Figure 11.7 Working principle of the lateral or friction force microscope (LFM or FFM).

The lateral forces result in a torsion of the cantilever, and this can be measured using the same optical detection system that measures vertical deflection (see Fig. 2.8). This signal from the tip-specimen interaction leads to another operational mode, the lateral or frictional force microscope (LFM or FFM) [142, 143]. In LFM the cantilever is designed to be... 

In lateral or frictional force microscopy (FFM) [120,121], lateral deflection of the cantilever is the signal of interest. The single-beam cantilever is scanned in a direction perpendicular to its long axis to enhance the twisting motion. The top to bottom signal remains under feedback control to keep the normal force constant while the right to left signal is monitored (see Fig. 3.23). 

FIGURE 3 Different AFM imaging modes. (A) Contact or normal force mode. (B) Lateral or friction force mode. (C) Intermittent contact mode, also known as noncontact or tapping mode. (D) Force modulation mode. 

MFM (magnetic force microscope), LFM (lateral force, or friction force microscope), etc. None of the above finds wide use for particle size determination. The AFM has however been used to determine the shape, size and types of particle on a polished silicon wafer surface [203]. 

Lateral force microscopy (LFM) or Friction force microscopy (FFM)... 

Mate [6] first obtained the friction force signal as well as the normal load signal by modifying an AFM in 1987. The modified AFM was called FFM or LFM (lateral force microscopy). The friction force signal was obtained by detecting the tor-... 

In 1987 Mate et al. [468] used, for the first time, an atomic force microscope (AFM) to measure friction forces on the nanometer scale (review Ref. [469]). This technique became known as friction force microscopy (FFM) or lateral force microscopy (LFM). To measure friction forces with the AFM, the fast scan direction of the sample is chosen perpendicular to the direction of the cantilever. Friction between the tip and the sample causes the flexible cantilever to twist (Fig. 11.7). This torsion of the cantilever is measured by using a reflected beam of light and a position-sensitive detector in the form of a quadrant arrangement of photodiodes. This new method made it possible for the first time to study friction and lubrication on the nanometer scale. 

Considering the ratio of inertia forces to friction forces, a parameter is obtained called the Reynolds number, or Reynolds law, in honor of Osborne Reynolds, who presented it in a publication of his experimental work in 1882. However, it was Lord Rayleigh 10 years later who developed the theory of dynamic similarity. 

Solidlike behavior abounds when the surface-to-volume ratio is very high,1 that is, when the particulates are even mildly compacted, surface-charged, or wet all contribute to large frictional forces and to nonuniform, often unstable stress fields in both flowing and compacted particulate assemblies, as we discuss later in this chapter. We begin by discussing some of the unique properties of polymer particulates relevant to processing. Comprehensive reviews can be found in the literature f 1 —4). 

Sufficiently large normal or lateral stresses can lead to plastic deformation and wear. Both processes contribute to the friction force. The simple geometry... 

When the tip was slid laterally at v= 100 m/s during indentation, the friction or cutting force fluctuated around zero as long as the substrate did not yield (Fig. 14). This nearly frictionless sliding can be attributed to the fact that the... 

Pressures in bins and silos. When granular solids are placed in a bin or silo, the lateral pressure exerted on the walls at any point is less than predicted from the head of material above that point. Furthermore there usually is friction between the wall and the solid grains, and because of the interlocking of the particles, the effect of this friction is felt throughout the mass. The frictional force at the wall tends to offset the weight of the solid and reduces the pressure exerted by the mass on the floor of the container. 

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