Determination of the dependence of the surface force induced contact radius on particle radius: Cross-linked polystyrene spheres on SiO2/silicon

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Abstract
The contact radii arising from surface forces were determined for cross-linked polystyrene particles having radii between 1.5 and 10 μm in contact with SiO2/silicon substrates using scanning electron microscopy. It was observed that the contact radius varied approximately as the particle radius to the 0.42 ± 0.13 power. These results are consistent with the theories that assume plastic response of the materials, such as that proposed by Maugis and Pollock [D. Maugis and H. M. Pollock, Acta Metall. 32, 1323 (1984)] but are inconsistent with the predictions of models which assume only elastic response, such as that of Johnson, Kendall, and Roberts [K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc. London A 324, 301 (1971)]. The thermodynamic work of adhesion, calculated from the experimental results, was found to be 0.32 J/m2, which is significantly smaller than that reported previously on a similar system.