Theory of electric field detachment of charged toner particles in electrophotography

In the electrophotographic process, electric fields are used to detach and move charged toner particles from one surface to another. In principle, electric field detachment occurs when the applied electrostatic force overcomes the toner adhesion force to a surface. For triboelectrically charged toner, many measurements have indicated that the electrostatic adhesion force is much greater than that calculated for a uniformly charged dielectric sphere, suggesting that the surface charge distribution on a toner particle is nonuniform. In the present work, the physics of the electrostatic force is described and a dumb-bell type charge distribution on triboelectrically charged toner particles is proposed as an approximation of nonuniformly charged particles. The electrostatic force on an isolated toner particle with a dumb-bell type charge distribution is computed by means of a recently developed computational method based on a Galerkin finite-element technique. The effect of the electrode spacing on the electric field detachment of charged toner particles is examined in particular. The results show that the magnitude of electrostatic force is rather insensitive to the electrode spacing when the particle is nonuniformly charged, unless the spacing is so small that the counter electrode is nearly touching the particle. The electrostatic force for detaching a charged particle is shown to become maximized when the particle charge and applied field strength satisfy a certain relationship. Formulas are also derived for the minimum electric field strength and the corresponding particle charge that are required for the maximized electrostatic detaching force to overcome the non-electrostatic components of adhesion. For triboelectrically charged toner particles, the components of the electrostatic force components are shown to be much greater than nonelectrostatic force components. If the particle charge is proportional to the particle surface area and the non-electrostatic force component is relatively insignificant, the detachment of toner particles in response to an applied electric field should be independent of the particle size.