Contact stiffness

A series of force-distance curves for various materials pairs examined (gold/ nickel, diamond/graphite, diamond/diamond) are shown in Fig. 4 [39]. For an indentation, the unloading slope (dF/dr) of the force-displacement curve is a measure of the contact stiffness and can be used to determine the modulus if the contact area (A) is known using a variant of Eq. 3 below. 

Fig. 7. Voigt model analysis of (a) lateral contact stiffness and (b) the response time, t, for a silicon nitride tip vs. poly(vinylethylene) as a function of frequency and polymer aging times. Reprinted with permission from ref [71].

Fig. 11. Load-displacement data and contact stiffness for poly-isoprene. Reprinted with permission from ref. [102],...

We have recently been exploring this technique to evaluate the adhesive and mechanical properties of compliant polymers in the form of a nanoscale JKR test. The force and stiffness data from a force-displacement curve can be plotted simultaneously (Fig. 13). For these contacts, the stiffness response appears to follow the true contact stiffness, and the curve was fit (see [70]) to a JKR model. Both the surface energy and modulus can be determined from the curve. Using JKR analyses, the maximum pull off force, surface energy and tip radius are... 

Asif, S.A.S., Wahl, K.J. and Colton, R.J., Nanoindentation and contact stiffness measurement using force modulation with a capacitive load-displacement transducer. Rev. Sci. Instrum., 70, 2408-2413 (1999). 

The key quantities are the peak load, the displacement at peak load, and the initial unloading contact stiffness,... 

Fig. 13.5. Quantitative measurements of contact stiffness by UFM (a) theoretical calculation of the UFM response on Si (1) and Ge (2) surface, using the engineering parameters ESi = 164 GPa, EGe = 121 GPa, surface energy in an ambient environment y = 1 N m-1, and the manufacturer s data for cantilever stiffness kc = 2.8 nN nm-1 and tip radius Rt = 10 nm (b) experimentally measured UFM response of a silicon surface (c) schematic illustration of the differential UFM approach to the measurement of contact stiffness (Kolosov and Yamanaka 1993), from the threshold amplitude values (ai and a2) for two different normal force values (Fi and P2), the contact stiffness Seff is given by Seff = (F2 — -Fi)/(a2 — ) (d) experimental stiffness measurements... 

The shape of the force versus indentation curve depends on surface adhesive and elastic properties. Variations in these parameters affect the ultrasonically induced deflection. Conversely, the variations in the shape of the ultrasonically induced normal deflection contain information on surface adhesive and elastic properties. Figure 13.3 illustrates how the threshold amplitude should depend on the normal force value. If the normal force is set at a higher value F2 > Fi, then the threshold amplitude a2 = h2) needed to reach the pull-off point should be higher than the threshold amplitude (fli = hi) for Fi. If the threshold amplitude values (fli and a2) are measured for two different normal force values (Fi and F2), the contact stiffness is... 

The beauty of the differential UFM approach is that the absolute value of the contact stiffness of a nanoscale contact at a known force level F is directly measured in terms of the ultrasonic vibration amplitude and the applied force, and is practically independent of the adhesion or other contact parameters. The contact geometry would need to be known in order to determine the elastic stiffness of the sample. 

D scattering function from a crack reference signal in frequency domain signal in frequency domain reference signal in time domain signal in time domain differential contact stiffness... 

To minimise the friction effect, it has been proposed to use smaller amplitudes and higher frequencies [122,137]. The so-called scanning local-acceleration microscopy (SLAM) is another modification of contact-mode SFM which was implemented by vibrating the sample at a frequency above the highest tip-sample resonance (region III in Fig. 13b). In this frequency range (around 1 MHz), the cantilever response to the sample excitations becomes independent of the cantilever stiffness and depends linearly on the contact stiffness and reciprocally on the cantilever mass m (Fig. 13b) ... 

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