Contact mechanics of nanoparticles.

We perform molecular dynamics simulations on the detachment of nanoparticles from a substrate. The critical detachment force, f*, is obtained as a function of the nanoparticle radius, R(p), shear modulus, G, surface energy, γ(p), and work of adhesion, W. The magnitude of the detachment force is shown to increase from πWR(p) to 2.2πWR(p) with increasing nanoparticle shear modulus and nanoparticle size. This variation of the detachment force is a manifestation of neck formation upon nanoparticle detachment. Using scaling analysis, we show that the magnitude of the detachment force is controlled by the balance of the nanoparticle elastic energy, neck surface energy, and energy of nanoparticle adhesion to a substrate. It is a function of the dimensionless parameter δ ∝ γ(p)(GR(p))(-1/3)W(-2/3), which is proportional to the ratio of the surface energy of a neck and the elastic energy of a deformed nanoparticle. In the case of small values of the parameter δ ≪ 1, the critical detachment force approaches a critical Johnson, Kendall, and Roberts force, f* ≈ 1.5πWR(p), as is usually the case for strongly cross-linked, large nanoparticles. However, in the opposite limit, corresponding to soft small nanoparticles for which δ≫1, the critical detachment force, f*, scales as f*∝ γ(p)(3/2)R(p)(1/2)G(-1/2). Simulation data are described by a scaling function f*∝ γ(p)(3/2)R(p)(1/2)G(-1/2)δ(-1.89).