Johnson-Kendall-Roberts experiment

Perhaps the most significant complication in the interpretation of nanoscale adhesion and mechanical properties measurements is the fact that the contact sizes are below the optical limit ( 1 t,im). Macroscopic adhesion studies and mechanical property measurements often rely on optical observations of the contact, and many of the contact mechanics models are formulated around direct measurement of the contact area or radius as a function of experimentally controlled parameters, such as load or displacement. In studies of colloids, scanning electron microscopy (SEM) has been used to view particle/surface contact sizes from the side to measure contact radius [3]. However, such a configuration is not easily employed in AFM and nanoindentation studies, and undesirable surface interactions from charging or contamination may arise. For adhesion studies (e.g. Johnson-Kendall-Roberts (JKR) [4] and probe-tack tests [5,6]), the probe/sample contact area is monitored as a function of load or displacement. This allows evaluation of load/area or even stress/strain response [7] as well as comparison to and development of contact mechanics theories. Area measurements are also important in traditional indentation experiments, where hardness is determined by measuring the residual contact area of the deformation optically [8J. For micro- and nanoscale studies, the dimensions of both the contact and residual deformation (if any) are below the optical limit. 

In order to eventually be able to produce nanoscale machines and pumps, the swelling behaviour of the gel to be harnessed in order for mechanical work to be done. In order demonstrate the ability of the system to produce work, a modified version of the experimental set-up devised by Johnson-Kendall-Roberts (JKR experiment) (77) is used. 

An easier way to measure Go for weakly adhering soft elastomers is the JKR (Johnson, Kendall, Roberts) technique (119,120), which usually involves contacting a hemispherical cap of elastomer with a planar substrate. Contact mechanics are employed to relate contact area to intrinsic adhesion. Using the JKR technique, a value of Go has been obtained of 0.12 J/m, about a factor of 2 higher than the expected work of adhesion (121). In other works (122,123) JKR experiments have been employed to determine threshold adhesion energies as low as 0.05 J/m2. 

In recent years it has been demonstrated that also adhesion (or adhesion hysteresis) plays an important role in friction. Israelachvili and coworkers could show that friction and adhesion hystereses are, in general, directly correlated if certain assumptions are fulfilled. These authors have proposed models based on data obtained by surface forces apparatus (SFA) experiments, e. g. the cobblestone model of interfacial friction (4). In addition, several groups described the application of continuum contact mechanics (e.g. Johnson-Kendall-Roberts (JKR) theory (5)) to describe friction data measured between flat surfaces and nanometer sized contacts (d). 

A third experiment which shows unequivocally that molecules leap into adhesive contact was performed by Johnson, Kendall and Roberts in 1970. This experiment was similar to Newton s original test on glass telescope lenses (Fig. 3.1) but used rubber surfaces because they adhere much more reliably than glass. Roberts had developed a way of moulding rubber in concave glass lenses to produce remarkably smooth elastomeric spherical surfaces as shown in Fig. 3.12. The rubber composition was mixed and then pressed hot into the glass lens. After... 

The importance of viscoelastic effects in adhesion as measured by methods such as peeling tests means that it is quite difficult to measure the limiting fracture energy Gq. One method that has been used successfully for elastomers was developed by Johnson, Kendall and Roberts (Johnson et al. 1971) and is commonly known as the JKR experiment. The experimental arrangement is... 

Johnson, Kendall, and Roberts (JKR) calculated the Hertzian contact area between two spherical surfaces when the adhesion energy could not be disregarded [15]. They verified their theory by their own experiments using the material combination of rubber and glass. In the JKR theory, it is assumed that adhesion energy is proportional to the contact area and that the attractive force acting on the outside of the contact area can be ignored. The JKR theory is outlined below. 

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