On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane

Müller, Veronika; Yushchenko, V. S.; Derjaguin, B.V.

doi:10.1016/0021-9797(80)90419-1

Cited by 673 publications

(318 citation statements)

References 9 publications

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“…Table 2 summarizes the relations between contact radius, the deformation of the sample, and the adhesion force for a spherical tip on a plane surface according to the three most used theories. These theories have been developed by Hertz [245], Johnson-Kendall-Roberts (JKR) [246], and Derjaguin-Müller-Toporov (DMT) [247][248][249].…”

Section: Theory: Hertz Jkr Dmt and Beyondmentioning

confidence: 99%

Force measurements with the atomic force microscope: Technique, interpretation and applications

Butt

Cappella

Kappl

2005

Surface Science Reports

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Section: Theory: Hertz Jkr Dmt and Beyondmentioning

confidence: 99%

Force measurements with the atomic force microscope: Technique, interpretation and applications

Butt

Cappella

Kappl

2005

Surface Science Reports

3,242

2,949

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“…For two spheres of radius and pressed together under a load the radius of the circle of contact is given by: (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) where and are the elastic constants of the material of the spheres:…”

Section: Fig24 Two Spherical Particles In Contactmentioning

confidence: 99%

“…Differences in the relations between the applied load force and the contact area or surface deformation are due to the role played by the adhesion in the considered system. These theories have been developed by Hertz that adhesion is neglected [6], Johnson-Kendal-Roberts (JKR) [7], Derjaguin-Müller-Toporov (DMT) [8][9][10], and Maugis [6,7,11,12]. In the Hertz model the adhesion is neglected, whereas the two other theories take account of it outside (DMT) or inside (JKR) the contact area.…”

Section: Introductionmentioning

confidence: 99%

On the Adhesion between Fine Particles and Nanocontacts: An Atomic Force Microscope Study

et al. 2006

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To optimize the handling of fine powders in industrial applications, understanding the interaction forces between single powder particles is fundamental. The forces between colloidal particles dominate the behavior of a great variety of materials, including paints, paper, soil, and many industrial processes. With the invention of the atomic force microscope (AFM), the direct measurement of the interaction between single micron-sized particles became possible. The adhesional contact between a particle and a substrate is a parameter for analyzing pull-off force data generated by AFM. The aim of this study was to understand surface interactions between fine particles. I measured the adhesion forces between AFM tips or particles attached to AFM cantilevers and different solid samples. Smooth and homogeneous surfaces such as silicon wafer, mica, or highly oriented pyrolytic graphite (HOPG), and more rough and heterogeneous surfaces such as iron particles or patterns of TiO 2 nanoparticles on silicon wafer were used. First, I addressed to the wellknown issue that AFM adhesion experiment results show wide distributions of adhesion forces rather than a single value. My experimental results show that variations in adhesion forces comprise fast (i.e., from one force curves to the next) random fluctuations and slower fluctuations, which occur over tens or hundreds of consecutive measurements. Slow fluctuations are not likely to be the result of variations in external factors such as lateral position, temperature, humidity, and so forth because those were kept constant. Even if two solid bodies are brought into contact under precisely the same conditions (same place, load, direction, etc.) the result of such a measurement will often not be the same as for the previous contact. The measurement itself will induce structural changes in the contact region which can change the value for the next adhesion force measurement.In the second part I studied the influence of humidity on the adhesion of nanocontacts. Humidity was adjusted relatively fast to minimize tip wear during one experiment. For hydrophobic surfaces, no signification change of adhesion force with humidity was observed. Adhesion force-versus-humidity curves recorded with hydrophilic surfaces either showed a maximum or continuously increased. I demonstrate that the results can be interpreted with simple continuum theory of the meniscus force. The meniscus force is calculated based on a model that includes surface roughness and takes into account different AFM tip (or particle) shapes by a two-sphere-model.Experimental and theoretical results show that the precise contact geometry has a critical influence on the humidity dependence of the adhesion force.Changes of tip geometry on the sub-10-nm length scale can completely change adhesion force-versus-humidity curves. Our model can also explain the differences between earlier AFM studies, where different dependencies of the adhesion force on humidity were observed.Keywords: Atomic force microscopy (AFM), cantile...

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“…Therefore the pressure dependence of t can be obtained by measuring F f and knowing the relation between A and the applied load L. In most cases, this relation is calculated from elastic continuum mechanics models which describe the contact area between a sphere (tip) and a plane (sample) [9]. However, the load dependence of the contact area not only depends on the exact tip geometry but also on the strength of the adhesive forces compared to the elastic deformations [8,[19][20][21].…”

Section: Atomic Force Microscopy Study Of An Ideally Hard Contactmentioning

confidence: 99%

Atomic Force Microscopy Study of an Ideally Hard Contact: The Diamond(111)/Tungsten Carbide Interface

et al. 1998

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A comprehensive nanotribological study of a hydrogen-terminated diamond(111)/tungsten carbide interface has been performed using ultrahigh vacuum atomic force microscopy. Both contact conductance, which is proportional to contact area, and friction have been measured as a function of applied load. We demonstrate for the first time that the load dependence of the contact area in UHV for this extremely hard single asperity contact is described by the Derjaguin-Müller-Toporov continuum mechanics model. Furthermore, the frictional force is found to be directly proportional to the contact area. Comments

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On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane

Cited by 673 publications

References 9 publications

Force measurements with the atomic force microscope: Technique, interpretation and applications

Force measurements with the atomic force microscope: Technique, interpretation and applications

On the Adhesion between Fine Particles and Nanocontacts: An Atomic Force Microscope Study

Atomic Force Microscopy Study of an Ideally Hard Contact: The Diamond(111)/Tungsten Carbide Interface

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