Retractive force, variation

Another contact technique that can be used to analyze multiphase polymer films (i.e., local variations in the elastic properties of the surface) is force-distance spectroscopy. In this mode, the force-distance curves are plots of distance dependent on the forces that act on the tip in the vicinity of the surface. They are registered when the tip approaches the surface or is retracted from it (Maver et al. 2013). Typical approach/retract force-distance curves and their stages are presented in Figure 8.4 (1) the cantilever starts to approach the surface (2) the tip approaches the surface ... 

This thermodynamic swelling force is counterbalanced by the retractive force of the crosslinked structure. The latter is usually described by the Flory rubber elasticity theory and its variations [9]. Equilibrium is attained, in a particular solvent at a particular temperature, when the two forces become equal. Thermodynamically, this equilibrium translates to the requirement that the total change of the chemical potential, (A be equal to zero. For the case described above, that term contains chemical potential contributions from mixing, (A i)f jx, and from the elastic force, (A i)g. Thus, at equilibrium we can write ... 

The results of Cohan on the force of retraction r at a = 1.5 for GR-S synthetic rubbers vulcanized with various proportions of a calcium carbonate filler are shown in Fig. 104. The agreement with the theoretical curve drawn according to Eq. (52) is good. In further confirmation of the theory, variations in average particle diameter... 

The diagrams in Fig. llc-f can be measured by the force probe method, when the amplitude and phase are measured as the tip approaches and retracts the surface vertically. In the non-contact range, both the amplitude and the phase retain their constant values (Fig. llc,e). When the tip enters the intermittent contact range (Zphase reduces almost linearly on approaching the surface. The deviation of the amplitude signal from a certain set-point value As is used by a feedback loop to maintain the separation Zc between the tip and sample constant, and hereby visualise the surface structure. When the surface composition is uniform, the amplitude variation is mainly caused by the surface topography. However, if the surface is heterogeneous, the variation in the amplitude can be affected by local differences in viscoelasticity [108-110 ] and adhesion [111] of the sample (Sect. 2.2.2). 

When the tip-CL system vibrates far from the surface, it oscillates with its free amplitude Af. When the attractive force field b omes large enough (typically for distances between the tip and the surface smaller than 2nm), if the drive frequency is slightly below the resonant one, the oscillation amplitude increases. At this point the sample is retracted. For its retraction, the oscillation amplitude takes a new route than for the approach the variation of the oscillation amplitude shows an hysteresis between the approach and the retraction of the tip from the sample. The retraction route depends on the drive amplitude as shown in Figure 10b which repre nts only retractions for clarity purposes. The smaller the drive amplitude the smaller the hysteresis cycle, to a point where no hysteresis cycle can be detected. 

All those experimental results can be satisfactorily described by the study (with analytical expressions or simulations) of the oscillating behavior of the tip-cantilever system in interaction with the sample through an attractive force field (20, 28). When the tip is close to the sample, the non linear dynamical behaviour of the oscillator gives a bifurcation from a monostable to a bistable state. Theoretical work shows that it is very informative to follow not only the variations of the amplitude during the approach and retraction but also the phase variations (20,29,63). 

Representative AFM force curves for Sample 1 and Sample 2 are shown in Figures 4 and 5, respectively. The measured adhesive force between the silicon tip and the composite surface was similar for both samples, although substantial variation was noted in the measurement. These findings indicate that the AFM tip interacts primarily with the resin-rich composite surface on both samples. Force measurements for Sample 3 and Sample 4 indicated substantially greater adhesive forces between the AFM tip and the composite surfaces when compared to Samples 1 and 2. In fact, it was not possible to obtain reproducible force of adhesion measurements for Sample 3 or Sample 4 using the same conditions used for Sample 1 and Sample 2 because the tip remained imbedded in the composite surfaces for almost the entire retraction cycle. Substantial differences between the force curves for Sample 3 and Sample 4 were not observed. 

Figure 8 (Left) Force spectroscopy Shear forces between poly(ethylene propylene) end functionalized with a zwitterionic group (PEP-X) brush-bearing surfaces at separation D=7.0 0.4nm. Upper trace, applied lateral motion (AXo) of top mica surface lower trace, shear force fs transmitted to the lower mica surface. The horizontal broken line represents the midpoint between the shear forces on the back and forth cycles, and is therefore the position of zero shearforce when the shear springs are unbent. Inset (i) illustrates the chain configuration in the initial force rise regime a- b. Inset (ii) illustrates the relaxation of a chain following cessation of the applied motion at point d (lower trace) the thick part is as yet unrelaxed, while the thin part has relaxed by arm retraction. (Right) The variation of the plateau normalized shearforce (kinetic normalized friction force, fnin IR, in units of pN m" ) with sliding velocity. Vs, taken from traces as on the left. The cartoons indicate schematically the effect of the self-regulation mechanism on the interpenetration zone S (see also Section 2.24.3.5). Adapted from Tadmor, R. Janik, J. Fetters, L. J. Klein, J. Phys. Rev. Lett. 2003, 91,115503. ...

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