Modeling the adhesion of spherical particles on rough surfaces at nanoscale

In this paper, the Van der Waals force acting between a spherical nanoparticle and a surface with random distribution of asperities has been simulated using the Johnson-Kendall-Roberts (JKR) contact mechanics model. To predict the adhesion force in different mediums and under different contact conditions, it is necessary to calculate the adhesion force in micro/nano systems. For this purpose, four different cases of surface roughness have been studied. The geometries of these rough surfaces have been defined taking into account the two key parameters of asperity radius and asperity height, and the necessary equations to determine the contact area and the magnitude of the adhesion force have been derived. Based on the geometries of the surface cap/trough, the interaction force between a spherical nanoparticle and a rough substrate has been obtained by applying Van der Waals theory. Then, the adhesion force for spherical nanoparticle has been modeled with respect to its height above the rough surface. Finally, the behavior of nanoparticles with different radii on four different rough substrates have been simulated and analyzed. The simulation results show that more precise adhesion forces can be obtained by modelling the surface roughness at the nanoscale. For small distances between spherical nanoparticle and the substrate, the adhesion force determined with the new roughness models is larger for rough substrates than for smooth ones.