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

Abstract

Electrostatic polarization is important in many nano-/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 an 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 interaction and find in the presence of an external interface, the interaction force depends on the curvature of the interface, and behavior a non-monotonic electrostatic force.

Comparison of efficient techniques for the simulation of dielectric objects in electrolytes

“…To satisfy the boundary conditions on the other surfaces ∂S j ( j = i), L 2 additional (second-level) image charges are generated in S j ( j = i) for each of the L 1 image charges in S i . Recursive iteration of this procedure yields the polarization potential [31],…”

“…In the model investigated in Sections 5 and 6, the dielectric ratio is 1 / m = 0.025, so (35) is used. When P > 1, the polarization potential can be constructed by a procedure of iterative image-charge reflections [67,31], as illustrated in Fig. 1.…”

“…The BEM for general mobile dielectric objects was proposed and implemented in [25,12] for MD simulations. The ICM for multiple spheres was presented in [31]; here we present its first implementation within a MC simulation. For the BEM, surface bound charge is obtained from the solution of a dense linear system via the generalized minimum residual (GMRES) method [40], using a formulation that is particularly well conditioned [41,25].…”

“…In certain cases, it is possible to avoid the evaluation of harmonic series via an image-charge representation of the closed-form Green's functions [26][27][28][29][30]. Recently, this image-charge method (ICM) has been extended to the treatment of multiple spheres via recursive reflections [31]. This approach not only provides a fast approximation to the Green's function, but also can be easily accelerated by well-known algorithms, because the approximation is a sum of Coulomb potentials.…”

Depletion forces due to image charges near dielectric discontinuities

“…where G free (r, r ′ ) = (ε|r − r ′ |) −1 is the Green's function in the absence of any dielectric bodies, and δG(r, r ′ ) represents the influence of any dielectric bodies proposed [12,13]. In order to account for the dispersion interaction, however, further work is required to numerically evaluate the determinant of the Green's function.…”