The manipulation of nanoparticles is a current topic of research in the nano world. This is an important subject, since by displacing the nanoparticles, a structure different from the one which is currently available can be obtained. To achieve such a purpose, the atomic force microscope (AFM) is employed as a manipulator to push or pull the target nanoparticles on a substrate and get them to the desired locations. The important point in this process is the amount of force which is necessary to move a particle to the intended spot. Also, to estimate the time for the onset of nanoparticle movement in the sliding mode, it becomes important to obtain the critical time as well. In this paper, through the dynamic simulation of a nanoparticle, its governing manipulation equations have been derived and simulated, so that they can be applied to determine the critical force and time for gold, yeast and platelet nanoparticles in gas, liquid, alcohol, and plasma mediums. Another important issue in the manipulation of nanoparticles is the control of the AFM probe. So, we propose to use an appropriate input such as the torque applied to the probe tip in order to control the probe deviation from its center and to observe the amount of probe displacement along its vertical direction so that, during the moving operation, the AFM probe always remains in contact with the nanoparticle being displaced. This control issue has been investigated for various liquid environments and with different biological and non-biological nanoparticles. Furthermore, the probe of the AFM has been controlled in water, alcohol, and plasma mediums by employing the sliding mode control approach.
