Electrostatic proximity force, toner adhesion, and atomic force microscopy of insulating particles

It has recently been shown [Czarnecki and Schein, J. Electrostat. 61 (2004) 107] that the electrostatic adhesion of a discrete distribution of charge points that are symmetrically distributed around a sphere in contact with a conductive plane is larger than the conventional result, (1/4πε0)(Q2/4r2), (which describes the adhesion of a spherically symmetric charge distribution to a conductive plane) by (1+4/π) where Q is the total charge and r is the radius of the spherical particle. This is a surprising result since it is conventionally assumed that a charged insulating particle can be modeled as a spherically symmetric charge distribution which is equivalent to a single charge point Q located in the center of the sphere. This new electrostatic force, the 4/π term which is due to quantized nature of charge, is called the electrostatic proximity force. Previously published, poorly understood toner adhesion data and atomic force microscopy experiments with insulating particles can be accounted for using the proximity force.