Physical Explanation of the Universal (Separation)?3 Law Found Numerically for the Electrostatic Interaction Between Two Protruding Nanostructures

摘要

This conference poster relates to the electrostatic interaction between (a) a “central” nanostructure standing on one of a pair of widely separated parallel planar plates of large lateral extent, and (b) a distant nanostructure standing on the same plate. The effect of the distant nanostructure is to reduce the apex field enhancement factor for the central nanostructure from the value it would have in the absence of the distant nanostructure. Using the Floating Sphere at Emitter Plate Potential (FSEPP) model to represent a pair of identical post-like structures, Forbes showed that, at large separations, the fractional reduction fell off as the inverse third power of the sphere separation. De Assis and Dall'Agnol used numerical solution of Laplace's equation to investigate six different kinds of distant nanostructure and concluded that the inverse third-power law was a universal law. This poster uses first-principles arguments, based on the physics of electrostatic depolarization effects associated with dipoles, to show that this universal law is expected. Further, it is suggested that arguments of this kind apply on any scale and can also be applied to macroscopic objects.