Analytical Modeling of Electrostatic Toner Adhesion

Abstract

Persistent conflicts between toner adhesion measurements and theory have prompted scientists and engineers to propose a myriad of models for particle adhesion. Adhesion, generally consisting of an electrostatic component and a non-electrostatic component (i.e. van der Waals), is a critical factor in determining transfer efficiency in laser printers. The electrostatic component of adhesion depends upon many factors: toner size, shape, and composition; development and transfer voltages; and design parameters such as component materials, geometry, and process speed. Many of these factors are directly related to the charge distribution and dielectric properties of the particles. In order to account for these factors, different analytical models have been proposed that separately consider dielectric polarization, charge distribution, and neighboring particles. Still, measurements of electrostatic adhesion force tend to be as much as one order of magnitude higher than calculations. We propose a fully analytic model of particle adhesion that incorporates many of these factors including, multiple particle and image force interactions, non-uniform charge distribution, and dielectric polarization. The multi-particle force model consists of a field expansion in the spherical basis followed by integration of the Maxwell stress tensor. Combining these physical mechanisms bring the predicted adhesion on spherical particles closer to measured results.