Re-expansion modeling to understand the electrostatic interaction between charged core-shell structured particles

Accurately calculating the electrostatic force is an important step in understanding the interaction between charged core-shell structured particles that have been widely observed in chemistry, physics, biology, and engineering. In this paper, the authors develop a general analytical model to solve for the electrostatic interaction between charged core-shell structured particles that involves a dielectric or conducting core coated with a polarizable dielectric shell. The re-expansion was used method to re-expand the spatial potential in a Legendre polynomial series under interfacial conditions. The electrostatic force was represented as a series based on Maxwell's stress tensor, and was governed by such characteristic parameters as the thickness of the shell, its dielectric constant, and the surface-to-surface separation even at the point of contact. Both unlike-charge and like-charge interactions were considered, and revealed that the polarization of the dielectric shell enhanced attraction but diminished repulsion. Counterintuitively, the electrostatic force was found to rely on the total number of free charges rather than the charge density. A limiting case was provided in which the proposed coated particle-particle model could describe the electrostatic force between a coated particle and a coated plane if the radius of either particle was sufficiently large. The force obtained by the theoretical solution was in exact agreement with that obtained by finite element analysis. The appropriate number of terms required for convergence was also investigated. The model developed here lays the foundation for a general theory of electrostatic interactions between charged particles with multi-shell layers.