Studying and simulation of ellipsoidal contact models for application in AFM nano manipulation

Four contact models including Hertz, Jamari, Jeng-Wang and Weng-Tang-Zhou-Zhu were considered. To verify the results of contact mechanics, the indentation depth has been compared with spherical geometry. According to the obtained results, by comparing the spherical and elliptical geometries, the indentation depth for spherical geometry is higher than for the ellipsoidal geometry, due to the existence of eccentricity in elliptical contact models which does not exist in spherical geometry. Among the models, the Jeng-Wang and Weng-Tang-Zhou-Zhu are models that are based on the contact of a particle with the substrate. Based on the existing experimental work, Jeng-Wang is the most suitable model for being applied in particle-substrate contact point. The Hertz model has been developed from crowned cylinder equations in order to be implemented for ellipsoidal geometry, moreover the Jamari model investigates two ellipses in contact with each other. By comparing Jeng-Wang and Weng-Tang-Zhou-Zhu models it is obvious that Jeng-Wang has the highest indentation depth while for the Weng-Tang-Zhou-Zhu model it is the lowest. These trends happen for two contact points. Also four materials are compared, among which graphite and chromium have the highest and the lowest indentation depths, respectively. Finally based on the obtained results Jeng-Wang and Jamari are the most suitable contact models that can be implemented in the manipulation of ellipsoidal nanoparticles.