Friction loop

Figure Bl.19.24. Friction loop and topography on a heterogeneous stepped surface. Terraces (2) and (3) are composed of different materials. In regions (1) and (4), the cantilever sticks to the sample surface because of static friction The sliding friction is tj on part (2) and on part 3. In a torsional force image, the contrast difference is caused by the relative sliding friction, Morphological effects may be...

It can be shown that relations between measured lateral forces (half width of friction loop W = (Mu-Md)/2) and the friction loop offsets (A (Mu + Md)/2) for sloped and flat surfaces at a given load (2.7-2.10) can be used to calculate the friction force calibration factor a [nN/V]. M denotes the torsion moment involved, the subscripts u and d denote uphill and downhill scan directions, and the subscripts. v and/denote sloped and flat surfaces, respectively. 

Fig. 2.32 Left Schematic of calibration specimen Right Example of experimental data measured with a Si3N4 tip on both sloped and flat surfaces (a) topography image (vertical scale from black to white 800 nm), (b) cross section of topography (vertical scale 800 nm), (c) difference friction image (trace - retrace, vertical scale 0.5 V), (d) off-set of the friction loops (trace + retrace, vertical scale 0.5 V) and (e) friction loop corresponding to cross section shown in panel (b) (the off-sets for sloped and flat surface, As and /1r, respectively, have been marked). Reproduced with permission from reference [18]. Copyright 2006. American Chemical Society...

Fig. 4.13 Friction loop (friction signal [V] vs. scanned distance [nm] plot) measured perpendicular to the polymer chain direction of oriented polyethylene with a -CF3 modified tip. [31]...

Friction data in the form of friction loops are captured at a constant load for various scan rates (that are converted to velocity taking the scan size into consideration) and sizes at room temperature and at 5°C. The friction force as half width of the friction loop is calculated and then plotted against velocity. 

The corresponding output of the (lateral) photodiode signal is shown in Figure 10. The so-called friction loop (108) displayed allows one to calculate the... 

One commonly measures of the friction force at a constant velocity using the friction loop. The tip is forced to slide in the lateral direction by the cantilever. The friction force makes the cantilever twist by an angle that is proportional to the friction force. When the movement is reversed and the tip slides in the opposite direction, the cantilever bends by the same but opposite angle. This friction loop corresponds to the difference of the lateral force signal between the back and forth scans. Therefore, the friction force equals half the amplitude of the friction loop. 

Figure 4 The shape of the friction loop obtainedfor an oscillatory drive at constant velocity.

In the local microscopy s field, a large effort is dedicated to study the mechanical properties which can be accessed with a nanotip. Within this context, soft materials are well adapted to probe mechanical response at the nanometer scale. After a discussion of some experimental and technical key points, we present three different types of experiments done on one model polymer polystyrene films with different molecular weights. In the experiments, the tip may scan the sample surface (friction loops), or move upward and downward in the vicinity of the sample -in contact mode (force curve) or in an oscillating mode (approach-retract curves)-. The comparison of the results shows the sensitiveness of the tip to local mechanical properties. New routes to explore mechanical properties without touching the sample are proposed. 

In this paper we will compare different experiments in contact and with an oscillating tip to show their contribution for the study of soft material. In static contact mode, force curves and friction loops are recorded while in tapping a systematic investigation of approach-retract curves is presented. A model sample is used monodisperse polystyrene films of different molecular weights (MJ bulk mechanical properties and molecular weight dependence of the glass transition temperature. In order to emphasize the inherent difficulties encountered with an AFM, we begin with a detailed discussion of the technical conditions. 

A more sensible way for a tribological experiment, is to routinely perform a friction loop (Figure 3) on the reference surface. If the magnitude of the friction loop remains constant at any stage of the experiment, this means that even if any molecules or polymers have been stuck on the apex there are only few and unable to produce a significant additional cantilever deflection within the range of the available sensitivity. 

Figure 3 Friction loop tip friction deflection AZf variation during the scan of a flat sample parallel to the cantilever symmetry axis for a fixed tip-sample vertical position. The dashed line gives the tip-CL equilibrium position. When the flat sample moves to the left (trace, part a), the tip deflection AZf due to friction is positive, whereas it is negative when the sample moves to the right (retrace, part b). Between part a and b, when the scan way changes, the tip remains glued on the sample, it is called static friction contrarily to part a or b where dynamic friction takes place. The static friction may be masked when larger scans are done, like for the following friction experiments. Experimental friction loop obtained on a = 94500 PS sample, with a 20nm scan.

It is the lateral force signal of the detection scheme and corresponds to the photo diode current taken from the friction loop (47), li =AIt /AFn is attained, with the same cantilever, from lateral force measurements on a silicon calibration sample (c.f, silicon surface treatment in Appendix). Note that there are no cantilever length dimensions necessary for the lateral force calibration. 

In the chain-parallel direction, only the HOPE showed a periodic stick slip behavior with a repeat distance of ca. 2.5 A. This distance is equal to the repeat unit of polyethylene (16, 20). For PTFE the LFM friction loops in our experiments did not reveal any stick slip behavior. Thus, in this case, we cannot determine the value of do in the chain-parallel direction. In this case we can, however, assume that the value of d is close to 0. Based on equation 1, the friction anisotropy is therefore expected to be larger for PTFE, than that for HDPE. For a semi-quantitative comparison of friction forces predicted by equation (1) on one hand and experimental results obtained on highly oriented polymer surfaces on the other hand, one should be... 

Figure 3.9 Example of the friction force of the so-called friction loop correspond to the...

---