Statistical Pull Off of Nanoparticles Adhering to Compliant Substrates

It is widely known in adhesive contact mechanics that a spherical particle will not detach from an elastic half-space unless a critical level of pulling force is reached, as already revealed by JKR- or DMT-type deterministic models. This article focuses on the scenario of particle-substrate adhesion where the size of particles is down to the nanometer scale. A consequence of particle size reduction to this range is that the energy scale confining the state of system equilibrium becomes comparable to the unit of thermal energy, leading to statistical particle detachment even below the critical pull-off force. We describe the process by Kramers' theory as a thermally activated escape from an energy well and develop a Smoluchowski partial differential equation that governs the spatial-temporal evolution of the adhesion state in probabilistic terms. These results show that the forced or spontaneous separation of nanometer-sized particles from compliant substrates occurs diffusively and statistically rather than ballistically and deterministically as assumed in existing models.