The interaction of an atomic force microscope tip with a nano-object: a model for determining the lateral force

A calculation of the lateral force interaction between an atomic force microscope (AFM) tip and a nano-object on a substrate is presented. In particular, the case where the AFM tip is used to manipulate the nano-object is considered; i.e., the tip is displaced across the nano-object with the feedback off. The Hamaker equations are used to calculate the force when the tip and sample are not in contact and the Johnson, Kendall and Roberts (JKR) or Derjaguin, Muller and Toporov (DMT) formalisms are used for the contact force. The effect of the material parameters, the choice of contact theory and the shape of the nano-object on the resulting lateral forces are explored. The calculation is applied to an experimental system consisting of a cadmium selenide nanorod on graphite.