Andrey V. Dobrynin, University of Connecticut
Adhesion and contact phenomena play an important role in colloidal science, tribology, pharmaceutical science and technology, biophysics and biochemistry. They provide us with understanding of mechanisms for friction between surfaces, adhesion and deformation of cells, liposomes, micro and nanocapsules. Furthermore, they are of paramount importance for nanofabrication and nanomolding.
Using molecular dynamics simulations and theoretical analysis we study static and dynamics of peeling off of nanoparticles from adhesive substrates. The critical detachment force, f*, is calculated as a function of the nanoparticle radius, Rp, shear modulus, G, surface energy, γp, and work of adhesion, W. The magnitude of the detachment force is shown to increase from πWRp to 2.2πWRp with increasing nanoparticle shear modulus and nanoparticle size. This variation of the detachment force is a manifestation of a 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, surface energy of the neck, and nanoparticle adhesion energy to a substrate. It is a function of the dimensionless parameter δ~γp(GRp)-1/3 W-2/3 which is proportional to the ratio of the surface energy of a neck and the elastic energy of 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 which is usually the case for strongly crosslinked large nanoparticles. However, in the opposite limit, corresponding to soft small nanoparticles, for which δ>>1, the critical detachment force, f*, scales as f*~γp3/2Rp1/2G-1/2δ-1.89.
We applied Kramers theory of the stochastic barrier crossing in the effective one dimensional potential to study dynamics of nanoparticle detachment. The activation energy, ΔE, for nanoparticle detachment first decreases linearly with increasing the magnitude of the applied force, f, then it follows a power law ΔE0~(f*-f)3/2 as magnitude of the pulling force f approaches a critical detachment force value, f*. These two different regimes in activation energy dependence on the magnitude of the applied force are confirmed by analyzing nanoparticle detachment in effective one dimensional potential obtained by Weighted Histogram Analysis Method. In the framework of the scaling approach we show that detachment of nanoparticle proceeds through neck formation and magnitude of the activation energy is determined by balancing surface energy of the neck connecting particle to a substrate with elastic energy of nanoparticle deformation. In this regime the activation energy at zero applied force, ΔE0~γp5/2Rp1/2G-3/2δ-3.75, is a universal function of the parameter δ .