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Effects of Charge
History
Hertz (Circa 1890):Proposed that a rigid indentor, acting under a compressive load P, would cause a deformation of radius a in a substrate having a Young’s modulus E and a Poisson ratio n given by
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(1) |
1930s:Derjaguin and Bradley independently proposed the concept of adhesion-induced deformations between particles and substrates.Derjaguin assumed that the adhesion-induced contact radius can be calculated from Hertzian theory.
1937:Hamaker proposes that surface forces were related to the density of atoms in the particle and substrate, nP and nS, respectively.Hamaker further proposed that the interaction parameter A (commonly referred to as the Hamaker constant) was related to London dispersion forces by
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(2) |
The load P is then given by
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(3) |
By combining this result with the Hertzian indenter model, one sees that the Derjaguin model relates the contact radius to the particle radius by
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(4) |
- 1956:Lifshitz proposes a model relating the London dispersion forces (i.e. the major component of van der Waals interactions in most systems) to the generation of electromagnetic waves caused by instantaneous dipole fluctuations.Surface forces are shown to have an effective range, rather than being contact forces.
- 1967:Krupp proposes adhesion-induced plastic deformations.He proposed that the adhesion-induced stresses between a particle and a substrate could exceed the yield strength of at least one of the contacting materials.
- Circa 1969:David Tabor approaches Ken Johnson about a rather perplexing student Tabor has that does not seem to believe Hertz.
- 1971:The JKR (Johnson, Kendall, and Roberts) theory of adhesion is published.This theory recognized that both tensile and compressive interactions contribute to the total contact radius.JKR model is derived using contact mechanics.It assumes that there are no long-range interactions.
- 1975:Derjaguin, Muller, and Toporov generalize the original Derjaguin model of adhesion to include tensile interactions.This is the DMT theory.
- 1977:Tabor highlights differences in assumptions and predictions between JKR and DMT theories.Also shows that, as long as the meniscus height is large compared to the range of surface forces, the JKR assumption of no long-range interactions is valid.
- 1980:Muller, Yushchenko, and Derjaguin (MYD) propose a general model that purports that both the JKR and DMT theories are subsets of the MYD model.They further divide the universe between small particle, high modulus, low surface energy systems (DMT) and larger particle, lower modulus, higher surface energy (JKR systems).
- 1984:Maugis and Pollock generalize the JKR theory to include adhesion-induced plastic deformations.
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