Lateral contact stiffness

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].

In analogy to indentation experiments, measurements of the lateral contact stiffness were used for determining the contact radius [114]. For achieving this, the finite stiffness of tip and cantilever have to be taken into account, which imposes considerable calibration issues. The lateral stiffness of the tip was determined by means of a finite element simulation [143]. As noted by Dedkov [95], the agreement of the experimental friction-load curves of Carpick et al. [115] with the JKR model is rather unexpected when considering the low value of the transition parameter A(0.2Further work seems to be necessary in order to clarify the limits of validity of the particular contact mechanics models, especially with regard to nanoscale contacts. 

Fig. 7 Development of fatigue cracks in an epoxy/glass contact under gross slip condition (1Hz, displacement amplitude 60 xm) (from [97]). White arrows indicate the occurrence of crack initiation and propagation at the edge of the contact under the action of tensile stresses. The lateral contact stiffness, K, is essentially a measurement of the elastic response of the epoxy substrate within the contact zone. Brittle crack propagation is associated to a drop in stiffness due to the additional accommodation of the imposed displacement provided by crack opening mechanisms...

Lateral contact. stiffness and glass transition temperature... 

The harmonic drive approach which is basic in rheological experiments was first implemented by Colchero et al. (25) for an AFM. The basic idea couples a lock-in technique with the lateral force microscope and has been essentially used for measuring the lateral contact stiffness (26,27). If the tip is modulated periodically in successive back and forth scans the lateral force signal is periodic too. The lock-in technique is particularly appropriate to analyze a signal in reference to another signal of the same frequency. 

Behavior of gels was first calculated from the elastic properties of a single contact between two spheres in 1985 and presented in a lecture which was published a year later.The contact stiffness arises because the spheres move together as a eompression load F is applied to the two spheres. Under zero load the distance between the sphere centres is D, as shown in Fig. 11.6(a), but when a force F is applied (Fig. 11.6(b)) the spheres move together an extra distance 5 which depends on the adhesion between the spheres. The stiffness is defined as... 

Thin hexafluoropropylene (HFP) films were deposited applying different reactor conditions by a radio frequency plasma enhanced chemical vapor deposition process onto photolithographic masked silicon surfaces, (a) depicts the crosslink density calculated from ESCA experiments (28). (b) shows the normalized amplitude response. The difference between silicon and HFP response was measured from recorded images allowing for an accurate statistical averaging, and converted into the difference in contact stiffness ks. The SFM measurements were carried in a nitrogen atmosphere (humidity < 4 %) at room temperature. Scan speed was 50 jjm/s, applied lateral modulation amplitude 3.5 nm, and modulation frequency 13 kHz. No external load was applied to the cantilever. 

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... 

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... 

The studies on adhesion are mostly concerned on predictions and measurements of adhesion forces, but this section is written from a different standpoint. The author intends to present a dynamic analysis of adhesion which has been recently published [7], with the emphasis on the mechanism of energy dissipation. When two solids are brought into contact, or inversely separated apart by applied forces, the process will never go smoothly enough—the surfaces will always jump into and out of contact, no matter how slowly the forces are applied. We will show later that this is originated from the inherent mechanical instability of the system in which two solid bodies of certain stiffness interact through a distance dependent on potential energy. 

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