Velocity-dependent adherence: An analytical approach for the JKR and DMT models

Recent surface forces apparatus experiments on organic monolayers deposited on mica surfaces (Ruths, M.; Granick, S. Langmuir 1998, 14, 1804) have evidenced an increase of the pull-off force with driving velocity, which has been interpreted as due to local viscoelastic dissipation at the contact edge. Following Maugis and Barquins, this phenomenon is modeled through a combination of the Johnson-Kendall-Roberts equations for the adhesive contact of elastic bodies and the Gent-Schultz approach to viscoelastic crack dissipation. We provide an approximate analytical solution for the pull-off force as a function of the driving velocity, which is supported by the result of direct numerical integrations of the equations in a large range of velocities. We discuss the application of this model to the adherence of two mica surfaces supporting surfactant monolayers.