Adhesion and Wetting of Nanoparticles on Soft Surfaces

We study adhesion of spherical and cylindrical nanoparticles on soft (gel-like) substrates using a combination of the molecular dynamics simulations and theoretical calculations. The substrate deformation is obtained as a function of the gel shear modulus, nanoparticle size, surface tension of nanoparticles and substrate, and work of adhesion. It was shown recently that the classical JKR model can only be applied to describe nanoparticle adhesion on relatively stiff substrates. In this so-called adhesion regime the deformation of the substrate is determined by balancing the elastic energy of indentation and the work of adhesion between a nanoparticle and a gel. However, in the case of soft gels when substrates undergo moderate deformations the depth of the indentation produced by a nanoparticle is determined by the surface tension of the gel and the work of adhesion (the wetting regime). We present an analytical model describing crossover between adhesion and wetting regimes. In the framework of this model a crossover between different interaction regimes is controlled by a dimensionless parameter gamma(s)(GR(p))W--2/3(-1/3), where gamma(s) and G are the surface tension and shear modulus of the gel, W is the work of adhesion between gel and nanoparticle, and R-p is the nanoparticle radius. Nanoparticle adhesion regime corresponds to small values of this parameter, gamma(s)(GR(p))W--2/3(-1/3) << 1, while the wetting regime takes place at gamma(s)(GR(p))W--2/3(-1/3) >> 1. We applied our model to obtain work of adhesion between silicon substrates and silica microspheres and to obtain surface tension of silicon gels from particle indentation experiments.