Dynamic modeling of manipulation of micro/nanoparticles on rough surfaces

In this paper, the dynamic behavior of spherical micro/nanoparticles, while being pushed on rough substrates, is studied by means of an Atomic Force Microscope (AFM). For this purpose, first, the contact adhesion force, and the areas and penetration depths of rough surfaces are derived based on the Johnson-Kendall-Roberts (JKR) theory, the Schwarz method, and the Rumpf/Rabinovich models. Then, the dynamic model of particle manipulation on rough substrates is revised using the specified contact theory for rough surfaces. And finally, the pushing of spherical particles with 50, 100, 200, 500, and 10000 nm radii is simulated. The results show that the critical force and the critical time of manipulation decrease when the particles are pushed on the rough surfaces as compared to the smooth ones. It is also observed that the critical force for a rough substrate containing asperities of low height and large radius approaches a comparable critical force magnitude to the smooth substrate, as is expected. Also, when the asperity radius in the substrate is within the range of 0.5 < r < 5 nm, the critical force of pushing decreases; however, as the asperity radius becomes larger than 5 nm, the critical force begins to increase again. Furthermore, the critical values are generally more sensitive to the changes of the asperity radius than the height. It is also found that the difference between the critical values based on the Rumpf and Rabinovich models is negligible. However, the estimation of particles’ dynamic behavior using the Rumpf model could be wrong for the rough substrates with small radius asperities, which is considerable in the manipulation and assembly practices. Moreover, the dynamic behavior of particles of small radius (r < 500 nm) change during the pushing process on rough surfaces, and the rolling behavior could be possible on the surfaces that have small radius asperities. The probability of this occurrence is increased in the pushing of larger particles on rougher substrates.