Automating the task of nanomanipulation is extremely important since it is tedious for humans. This paper proposes an atomic force microscope (AFM) based force controller to push nano particles on the substrates. A block phase correlation-based algorithm is embedded into the controller for the compensation of the thermal drift which is considered as the main external uncertainty during nanomanipulation. Then, the interactive forces and dynamics between the tip and the particle, particle and the substrate including the roughness effect of the substrate are modelled and analysed. Further, a neural network (NN) is employed to approximate the unknown nanoparticle and substrate contact dynamics. Using the NN-based adaptive force controller the task of pushing nanoparticles is demonstrated. Finally, using the Lyapunov-based stability analysis, the uniform ultimate boundedness (UUB) of the closed-loop tracking error, NN weight estimates and force errors are shown.