Lennard–Jones interactions between nano-rod like particles at an arbitrary orientation and an infinite flat solid surface

An analytical expression for the Lennard–Jones interaction between nano-rods and an infinite flat solid surface is presented. Starting from the elementary Lennard–Jones interaction between two particles, and taking the shape of the nano-rod to be a filled cylinder of radius r and length L, the obtained expression was valid for arbitrary orientation of the nano-rod at variable elevation from the surface. By differentiating the potential with respect to the orientation and elevation we were able to extract the torque and force, respectively, exerted on the nano-rods when approaching a flat surface. The derivation is subjected to the assumption of additivity and approximated for some limiting case.