Universal pull-off force for separating a rigid sphere from a membrane

Abstract

A pull-off force $F_c$ is required to separate two objects in adhesive contact. For a rigid sphere on an elastic slab, the classic Johnson–Kendall–Roberts (JKR) theory predicts $F_c=\frac{3}{2}\pi \gamma R_s$, where $\gamma$ represents the interface adhesion or toughness and $R_s$ is the radius of the sphere. Here, we investigate an alternative, extreme scenario: the pull-off force required to detach a rigid, frictionless sphere from a thin membrane, a scenario observed in a wide range of nature and engineering systems, such as nanoparticles on cell membranes, atomic force microscopy probes on atomically thin 2D material sheets, and electronic devices on flexible films. We show that, within the JKR framework, the pull-off forces in axisymmetric soap films, linearly elastic membranes, and nonlinear hyperelastic membranes are all given by $F_c=\pi \gamma R_s$. This result is remarkable as it indicates that the pull-off force for membranes is independent of the material’s constitutive law, size, pretension, and solid surface tension.