Image Charge Method for Reaction Fields in a Hybrid Ion-Channel Model

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.

A fast algorithm for treating dielectric discontinuities in charged spherical colloids

Electrostatic interactions between multiple colloids in ionic fluids are attracting much attention in studies of biological and soft matter systems. The evaluation of the polarization surface charges due to the spherical dielectric discontinuities poses a challenging problem to highly efficient computer simulations. In this paper, we propose a new method for fast calculating the electric field of spaced spheres using the multiple reflection expansion. The method uses a technique of recursive reflections among the spherical interfaces based on a formula of the multiple image representation, resulting in a simple, accurate and close-form expression of the surface polarization charges. Numerical calculations of the electric potential energies of charged spheres demonstrate the method is highly accurate with small number of reflections, and thus attractive for the use in practical simulations of related problems such as colloid suspension and macromolecular interactions.

Fast Analytical Methods for Macroscopic Electrostatic Models in Biomolecular Simulations

We review recent developments of fast analytical methods for macroscopic electrostatic calculations in biological applications, including the Poisson-Boltzmann (PB) and the generalized Born models for electrostatic solvation energy. The focus is on analytical approaches for hybrid solvation models, especially the image charge method for a spherical cavity, and also the generalized Born theory as an approximation to the PB model. This review places much emphasis on the mathematical details behind these methods.

Multiple-image treatment of induced charges in Monte Carlo simulations of electrolytes near a spherical dielectric interface

The polarization-induced charges of a dielectric sphere are studied for charged colloidal systems in electrolyte solutions with a primitive model. The method of constructing multiple-image charges is used to approximate the polarization potential of a microion outside the sphere; it is based on a numerical discretization of the potential's analytical integral representation, and can systematically approximate the exact potential with desired accuracy by varyiation of the number of point images. Different aspects of the image effects are then investigated by Monte Carlo simulations for several colloidal systems, in both salt-free and salty environments. Furthermore, we studied the influence of discrete surface charges of different valences, and demonstrate that the polarization charges can significantly strengthen charge reversal for the colloid-microion complex, especially for multivalent interfacial ions.