JKR experiment

In the JKR experiments, a macroscopic spherical cap of a soft, elastic material is in contact with a planar surface. In these experiments, the contact radius is measured as a function of the applied load (a versus P) using an optical microscope, and the interfacial adhesion (W) is determined using Eqs. 11 and 16. In their original work, Johnson et al. [6] measured a versus P between a rubber-rubber interface, and the interface between crosslinked silicone rubber sphere and poly(methyl methacrylate) flat. The apparatus used for these measurements was fairly simple. The contact radius was measured using a simple optical microscope. This type of measurement is particularly suitable for soft elastic materials. 

JKR type mea.surement.s on monolayers depo.sited on. soft elastomers. The recent interest in the JKR experiments has been stimulated by the work of Chaudhury and coworkers [47-50J. In a 1991 paper, Chaudhury and White-sides [47] reported their extensive studies on the measurement of interfacial work of adhesion and surface energies of elastomeric solids. The motivation for this work was to study the physico-organic chemistry of solid surfaces and interfaces. 

The experimental and theoretical procedure used by Tirrell et al. is similar to that of Brown and coworkers. Tirrell et al. compared their results from the JKR experiments to 90° peel tests. The details of the experiment may be obtained from the original papers. The obser ations of Tirrell et al. can be summarized as follows ... 

For the Hertzian contact, no force is needed to pull away the contacting sphere from the flat plane in excess of the weight of the sphere. However, for the JKR contact, due to adhesion forces, this does not hold. The value of the nonzero pull-off force represents the adhesion of the contacting sphere with the flat plane. Strictly speaking, this force corresponds to adherence of the surfaces as energy dissipation, surface relaxation, etc. also influence its value. It should be stressed that the value of the JKR pull-off force only depends on the sphere (lens) radius and the work of adhesion in the medium in which the JKR experiment is conducted. Thus, the contact area and mechanical properties for true JKR contacts do not play a role for its value. All the above considerations for contact mechanics were based on pairwise additivity of molecular forces. 

A Landolt pH-oscillator based on a bromate/sulfite/ferrocyanide reaction has been developed with a room temperature period of 20 minutes and a range of 3.1periodic oscillations in volume in a pH responsive hydrogel. A continuously stirred, constant volume, tank reactor was set-up in conjuction with a modified JKR experiment and is used to show that the combination of a pH oscillator and a pH responsive hydrogel can be used to generate measurable force. 

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. 

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... 

Figure 7.13. The JKR experiment for measuring the ideal adhesion energy between a rigid substrate and an elastomer. A hemispherical cap of the elastomer of radius R is brought into contact with the substrate and loaded with a force P. This results in a displacement of the cap <5 and the formation of a circular area of contact radius a.

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 an attempt to determine the applicability of JKR and DMT theories, Lee [91] measured the no-load contact radius of crosslinked silicone rubber spheres in contact with a glass slide as a function of their radii of curvature (R) and elastic moduli (K). In these experiments, Lee found that a thin layer of silicone gel transferred onto the glass slide. From a plot of versus R, using Eq. 13 of the JKR theory, Lee determined that the work of adhesion was about 70 7 mJ/m". a value in clo.se agreement with that determined by Johnson and coworkers 6 using Eqs. 11 and 16. 

The study of acid-base interaction is an important branch of interfacial science. These interactions are widely exploited in several practical applications such as adhesion and adsorption processes. Most of the current studies in this area are based on calorimetric studies or wetting measurements or peel test measurements. While these studies have been instrumental in the understanding of these interfacial interactions, to a certain extent the interpretation of the results of these studies has been largely empirical. The recent advances in the theory and experiments of contact mechanics could be potentially employed to better understand and measure the molecular level acid-base interactions. One of the following two experimental procedures could be utilized (1) Polymers with different levels of acidic and basic chemical constitution can be coated on to elastomeric caps, as described in Section 4.2.1, and the adhesion between these layers can be measured using the JKR technique and Eqs. 11 or 30 as appropriate. For example, poly(p-amino styrene) and poly(p-hydroxy carbonyl styrene) can be coated on to PDMS-ox, and be used as acidic and basic surfaces, respectively, to study the acid-base interactions. (2) Another approach is to graft acidic or basic macromers onto a weakly crosslinked polyisoprene or polybutadiene elastomeric networks, and use these elastomeric networks in the JKR studies as described in Section 4.2.1. 

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 a typical experiment, Israelachvili deposited monolayers of surfactants onto cleaved mica sheets, and evaluated the surface energies using the JKR equation. Fig. 11 contrasts results for mica coated with monolayers of (a) L-a-dipalmitoyl-phosphatidylethanolamine (DMPE) where j/a = = 27 mJ/m and (b) hexa-decyltrimethylammonium bromide (CTAB) where = 20 mJ/m and = 50 mJ/m. ... 

Also adhesion between the tip and sample can cause deformation of the sample. Several theories have been developed to include the effect of adhesive forces. In the JKR theory adhesion forces outside the contact area are neglected and elastic stresses at the contact line are infinite [80]. Even under zero load, the adhesion force results in a finite contact radius a=(9jtR2y/2 E)1/3 as obtained from Eq. 7 for F=0. For example, for a tip radius R=10 nm, E=lGPa, typical surface energy for polymers y=25 mN/m, and typical SFM load F=1 nN, the contact radius will be about a=9.5 nm and 8=9 nm, while under zero load the contact radius and the deformation become a=4.5 nm and 8=2 nm, respectively. The experiment shows that under zero load the contact radius for a 10 nm tungsten tip and an organic film in air is 2.4 nm [240]. The contact radius caused only by adhesion is almost five times larger than the Hertzian diameter calculated above. It means, that even at very small forces the surface deformation as well as the lateral resolution is determined by adhesion between the tip and sample. 

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. 

When attempting to relate the adhesion force obtained with the SFA to surface energies measured by cleavage, several problems occur. First, in cleavage experiments the two split layers have a precisely defined orientation with respect to each other. In the SFA the orientation is arbitrary. Second, surface deformations become important. The reason is that the surfaces attract each other, deform, and adhere in order to reduce the total surface tension. This is opposed by the stiffness of the material. The net effect is always a finite contact area. Depending on the elasticity and geometry this effect can be described by the JKR 65 or the DMT 1661 model. Theoretically, the pull-off force F between two ideally elastic cylinders is related to the surface tension of the solid and the radius of curvature by... 

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