Contact Mechanics of Nanoparticles: Pulling Rigid Nanoparticles from Soft, Polymeric Surfaces

Detachment of rigid nanoparticles from soft, gel-like polymeric surfaces is studied by using a combination of the molecular dynamics simulations and theoretical calculations. Simulations show that detachment of nanoparticles from soft surfaces proceeds through a neck formation. Analysis of the simulation results demonstrates that the magnitude of the detachment force f* depends on the nanoparticle radius R(p), shear modulus of substrate G(s), surface tension of substrate γ(s), and work of adhesion W. It is controlled by the balance of the elastic energy, surface energy of the neck, and nanoparticle adhesion energy to a substrate and depends on the dimensionless parameter δ ∝ γ(s)(G(s)R(p))(-1/3)W(-2/3). In the case of small values of the parameter δ ≪ 1, the critical detachment force approaches a critical detachment force calculated by Johnson, Kendall, and Roberts for adhesive contact, f* = 1.5πWR(p). However, in the opposite limit, corresponding to soft substrates, for which δ ≫ 1, the critical detachment force f* ∝ γ(s)(3/2)R(p)(1/2)G(s)(-1/2). All simulation data can be described by a scaling function f* ∝ γ(s)(3/2)R(p)(1/2)G(s)(-1/2)δ(-1.89).