Modeling and simulation of contact parameters of elliptical and cubic nanoparticles to be used in nanomanipulation based on atomic force microscope

•Modeling complex cubic and elliptic contact theory.•Development of contact relations for AFM tip and particle contact and particle contact with surface.•Consider the roughness for modeling the contact.•Using laboratory results to validate the results. Regarding the contact mechanics of smooth nanoparticles, two new geometries, specifically elliptical and cubic are chosen for nanoparticles. The results of elliptical contact simulation show that the JKR theory induces a greater indentation depth in both contact geometries since it includes the adhesion forces. Moreover, the Jamari theory shows a lesser indentation depth because it assumes larger contact area. The results of cubic nanoparticles simulation exhibit a significant difference between the contact of tip and nanoparticle compared to the contact of nanoparticle and surface. This can be attributed to the large contact area between the cubic nanoparticle and the reference surface. The JKR and DMT theories, however, show greater indentation depths in the tip contact with nanoparticle. Furthermore, the Lundberg theory yields the maximum indentation depth in the nanoparticle contact with reference surface. Finally, in order to validate the results, experimental and FEM approaches are incorporated. Concerning the experimental results, a certain number of silver nanoparticles are placed on a polystyrene surface. After obtaining the experimental force-displacement curves, the results of presented models are compared with them. The experimental results indicate that for silver nanoparticles and polystyrene surface, the Hertz theory with 1.11% of error and the JKR theory with 8.7% of error show the best output, respectively. Regarding rough nanoparticles contact, the geometry of roughness are taken as elliptical. Meanwhile, analytical relations are presented to solve force and contact area integrals while noting the problem dimensions. The results of simulation show that the JKR theory yields the highest roughness force, followed by the Hertz and Jamari theories, and regarding rough contact area, the Hertz theory creates the largest contact area, followed by the Jamari and JKR theories. The presented analytical method is compared with numerical results as a means of validation.