A fast algorithm for treating dielectric discontinuities in charged spherical colloids

Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction

Electrostatic polarization is important in many nano- and micro-scale physical systems such as colloidal suspensions, biopolymers, and nanomaterials assembly. The calculation of polarization potential requires an efficient algorithm for solving 3D Poisson's equation. We have developed a useful image charge method to rapid evaluation of the Green's function of the Poisson's equation in the presence of spherical dielectric discontinuities. This paper presents an extensive study of this method by giving a convergence analysis and developing a coarse-graining algorithm. The use of the coarse graining could reduce the number of image charges to around a dozen, by 1-2 orders of magnitude. We use the algorithm to investigate the interaction force between likely charged spheres in different dielectric environments. We find the size and charge asymmetry leads to an attraction between like charges, in agreement with existing results. Furthermore, we study three-body interactions and find, in the presence of an external interface, that the interaction force depends on the curvature of the interface and performs a nonmonotonic electrostatic force.