Nonclassical dynamic modeling of nano/microparticles during nanomanipulation processes

Since the manipulation of particles using atomic force microscopy is not observable in real-time, modeling the manipulation process is of notable importance, enabling us to investigate the dynamical behavior of nanoparticles. To model this process, previous studies employed classical continuum mechanics and molecular dynamics simulations which had certain limitations; the former does not consider size effects at the nanoscale while the latter is time consuming and faces computational restrictions. To optimize accuracy and computational costs, a new nonclassical modeling of the nanomanipulation process based on the modified couple stress theory is proposed that includes the size effects. To this end, after simulating the critical times and forces that are required for the onset of nanoparticle motion on the substrate, along with the dominant motion mode, the nonclassical theory of continuum mechanics and a developed von Mises yield criterion are employed to investigate the dynamical behavior of a cylindrical gold nanoparticle during manipulation. Timoshenko and Euler–Bernoulli beam theories based on the modified couple stress theory are used to model the dynamics of cylindrical gold nanoparticles while the finite element method is utilized to solve the governing equations of motion. The results show a difference of 90% between the classical and nonclassical models in predicting the maximum deflection before the beginning of the dominant mode and a difference of more than 25% in the dynamic modeling of a 200 nm manipulation of a gold nanoparticle with a length of 25 µm and aspect ratio of 30. This difference increases with each increment of the aspect ratio and reduction of manipulation distance. Furthermore, by applying an extended von Mises criterion on the modified couple stress theory, it is found that the failure aspect ratio of a cylindrical gold nanoparticle based on nonclassical models is 212% more than that of the classical model. In the end, the results are compared with those of the classical method on polystyrene nanorods. The results for cylindrical gold nanoparticles indicate that the material length scale has a major effect on the exact positioning of cylindrical nanoparticles.