Adhesion of a rigid cylinder to an incompressible film

The adhesion between a rigid cylindrical particle with a flat end of radius a and an incompressible elastic film of thickness h deposited on a rigid substrate was studied. The contact surfaces between the particle and the film and between the film and the substrate are either frictionless (slip) or perfectly bonded (stick). Using integral equations, the stress distribution in the contact area was solved and used to obtain the load required to press the particle onto the thin film. Using a thermodynamic method, the pull-off force to separate the particle from the film was obtained numerically and analytically. For a >>h, the pull-off force is proportional to a²/h^1/2 if it is frictionless on both contact interfaces and is proportional to a³/h^3/2 if it is frictionless between the particle and thin film and bonded between the thin film and the substrate. For a<h/2 the pull-off force is proportional to a^3/2 independent of h and the boundary conditions. To verify this the self adhesion of PDMS [poly(dimethylsiloxane)] was determined experimentally and the a^3/2 relation was confirmed. The self-adhesion of PDMS was found to increase with the square root of contact time suggesting molecular diffusion as the dominant mechanism.