Hertz model force-distance curves

At present, there are a variety of theoretical models to describe the mechanical contact between the two bodies under external load and many of such theories have been used to analyze force-distance curves.Among them. Hertz theory has been the most widely used because of its... 

Mapping of the elastic modulus of the glassy and rubbery blocks and clay regions was probed by employing Hertzian and Johnson-Kendall-Roberts (JKR) models from both approaching and retracting parts of the force-distance curves. In order to determine the elastic properties of SEBS nanocomposites in its different constituting zones, the corrected force-distance curve was fitted to the Hertz model ... 

Figure 8.3 shows the typical force-distance curve for a K-carrageenan film. From the slope of the curve, where the AFM tip is in contact with the film surface. Young s modulus of the K-carrageenan film can be estimated by using the Hertz model with the proper measurement of the AFM tip radius using scanning electron microscopy (SEM) and estimated value of Poisson s ratio based on the characteristics of film surface, which is around 1.4 MPa. 

A scanning force instrument also allows for the acquisition of force-distance curves to characterize the local mechanical properties of the sample. Well-defined indentation experiments on soft surfaces like swollen hydrogels in aqueous media are possible with the colloidal probe technique. Raw data are assessed, for example, according to the Hertz model, with the assumption... 

Fig. 1 Single cell elasticity measurements with microindentation technique. (A) AFM allows both live cell imaging and mechanical testing (e.g., microindentation) in near physiological conditions. The AFM tip attached to a cantilever descents slowly to a surface and causes an indentation. The depth of indentation is detected by laser light diffraction pattern. (B) Typical force-distance curves are obtained for hard and soft surfaces and usually analyzed with the classical Hertz model that relates the applied force to the indentation depth.

The approach described above is illustrated by the work of Matzelle et al. (2002). Force distance curves were obtained for the indentation of a colloidal probe in PNiPAAm coatings immersed in water above and below the phase transition temperature (Figure 6.8). The calculation of Young s modulus using the Hertz model revealed a variation of more than two orders of magnitude between the swollen and the collapsed state at 10 C and 35 C, respectively. 

---