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 α γ_p(GR_p)^-1/3W ^-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*α γ_p ^3/2R_p^1/2G^-1/2. Simulation data are described by a scaling function f*α γ_p ^3/2R_p^1/2G^-1/2δ ^-1.89.