Adhesion of small spheres

J.A. Greenwood (1)

1 CAM - University of Cambridge [UK]

ABSTRACT Bradley(1931) calculated the adhesive force between rigid spheres in terms of a surface force law: Johnson, Kendall & Roberts (1971) calculated the adhesive force between elastic spheres in terms of the surface energy. Oddly, both approaches predicted a pull-off force proportional to [but with different coefficients or ], and no dependence on the elastic modulus. Interpretation of AFM measurements of nanoscale contacts has relied on the Bradley and JKR theories for the limiting values of the Tabor parameter , and on detailed numerical calculations, or more conveniently on the Maugis theory, to bridge the gap between these extremes. A map presented by Johnson & Greenwood (1997) delineating the regions of applicability has been modified by Yao et al (2006) to take into account the ‘strength limit '. Yao et al, repeating the numerical calculations but using the exact sphere shape instead of the paraboloidal approximation dating back to Hertz, find that the pull-off force may be less than one-tenth of the JKR value.. Yao et al's numerical calculations using a Lennard-Jones law of force between an exact sphere and a plane are repeated and their values confirmed: but it is shown that the drastic reductions found occur only for spheres which are smaller than atomic dimensions, and that for conditions for which continuum calculations can be believed, the reductions are rather small. The limitations imposed by large strain elasticity, by the ‘Derjaguin approximation', and by the discrete nature of atomic interactions, are discussed.

Mots clés: Physical Sciences

J.A. Greenwood. Adhesion of small spheres. Philosophical Magazine, 2009, 89 (11), pp.945-965. ⟨10.1080/14786430902832765⟩. ⟨hal-00514016⟩