Abstract
This article considers the problem of finding the electrostatic potential that is given in terms of a scalar function called Green function in dielectric cylindrical nanoparticles with core-shell structure using the image charge method. By using this method that allows us to solve differential form of electric potential problem by the Green function, we investigate the distribution of the electric field in the configuration of a cylindrical nanoparticle surrounded by a continuum dielectric medium. By utilizing this well-known method, we obtain exact analytical formulas for the electrostatic potential and the electric field inside the shell, core and surrounding space of nanoparticle that can be applied to analysis of electromagnetic problems, electrostatic interactions in biomolecular simulations and also computer simulations of condensed-matter media.
Highlights
The electrostatics play an important and dominant role in many physical/chemical problems, biological and nanoscale systems.[1]
By using this method that allows us to solve differential form of electric potential problem by the Green function, we investigate the distribution of the electric field in the configuration of a cylindrical nanoparticle surrounded by a continuum dielectric medium
To gain insight into the summation in the electrostatic potential equations, we will investigate the behavior of intermediate functions because the electrostatic potential depends on the intermediate functions that into the series expansions
Summary
The electrostatics play an important and dominant role in many physical/chemical problems, biological and nanoscale systems.[1]. A simple and direct calculation of the electrostatic potential and the electric field is called image charge method or method of image charge (IC).[2,3] IC method is an approach for finding and describing the electric potential and field distributions in structures with special geometries, without solving a differential equation.[4] It is an analytical method for solving some electrostatic problems (specific types of boundary value problems in electrostatics) which can be used for calculating the electric field.[5] Method of IC can be applied to study different problems such as analysis of electron or ion trajectories, field-induced diffusion in scanning tunneling microscope experiments and field-emission diodes.[6] In particular, image charges play an important role in charge transport through molecules and single-molecule junctions, the electrostatic interactions in computer simulations of biomolecules, the surface tension of electrolyte solutions and the adsorption of polyelectrolytes.[7,8,9]. Distribution at different regions of a dielectric core-shell nanoparticle with cylindrical geometry by using the IC method
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