Particle Adhesion to Highly Compliant Substrates: Anomalous Power-Law Dependence of the Contact Radius on Particle Radius

Abstract

The adhesion-induced contact radius and meniscus height between soda-lime glass particles and three highly compliant polyurethane substrates (Young's modulus between 4 kPa and 0.7 MPa) were measured using scanning electron microscopy as a function of particle radius. Two distinct power-law exponents were found. A value of about 2/3, which is in good agreement with the predictions of the JKR theory (Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc., London Ser. A 1971, 324, 301), was found for larger particles. However, the experimentally obtained exponent for smaller particles was found to be approximately 3/4. The present results are compared with the predictions of the large-scale deformation model of Maugis (Maugis, D. Langmuir 1995, 11, 679) as well as a self-consistent surface-energy model. Although both models contain some interesting features, neither theory can fully account for the observed behavior.