Contact electrification between randomly rough surfaces with identical materials

Abstract

We put a flat and a rough surface in contact and then separate them by the distance d. We calculate the work and the force needed to separate two surfaces. The theory is an extension of earlier researches by Persson, Scaraggi, and Volokitin. In addition to the effects of the roughness, we consider the effect of the fluctuations of charge density in the work of adhesion. The roughness increases the area of the surface and, consequently, an enhancement in the charge, growth in the force, and work of adhesion. When the density of charges is not constant, the roughness imposes a balanced distance between plates. As the balanced distance decreases, the roughness of the surface increases. To reach the distance less than the balanced, a downward force is needed. The comparison between the force of constant charge density and fluctuations of charges displays that the force of charge fluctuations has the larger magnitude than the constant charge, even with a charge density power spectrum 10-13 less than the square of the constant charge density.