The analytical relations between particles and probe trajectories in atomic force microscope nanomanipulation

Analytical expressions relating the trajectories of spherical nanoparticles pushed by an atomic force microscope tip to the scan pattern of the tip are derived. In the case of a raster scan path, the particles are deflected in a direction defined by the geometries of tip and particles and the spacing b between consecutive scan lines. In the case of a zigzag scan path, the particles are deflected in a range of directions around 90 degrees, also depending on the parameter b. Experimental results on gold nanoparticles manipulated on silicon surfaces in ambient conditions confirm the predictions of our model.