Noted that nanomaterials have sizes ranging from about one nanometer up to several hundred nanometers, comparable to many biological molecules such as antibodies, proteins and etc. Since molecules are very small and typically just several nanometers in size, we consider a core-shell nanoparticle with a = 5 nm and b = 10 nm. The position of charge is 2 b 3 while b = 2a. The numerical results are calculated for m = 0, 1, 2, 3, 4. THEORY AND FORMULATIONįigures 2-4 show the variation of the functions Σ m( k), Θ m( k) and Λ m( k) versus variable kb by varying the dielectric constant of core, shell and the surrounding medium. 12 In the present paper, we will obtain the electric potential and field distribution at different regions of a dielectric core-shell nanoparticle with cylindrical geometry by using the IC method. used the IC Method for a three-dielectric-layer hybrid solvation model of biomolecules. It is important to note that a multilayer dielectric structure often play a determinant role for their physical-chemical properties. Since the fundamental problem in electrostatics is to find the electric field that plays a significant role in design of electromagnetic devices. 11 In this work, the IC method is developed to cylindrical core-shell nanostructures for finding the electrostatic potential, and therefore the electric field in dielectric media. studied reaction fields due to a point charge in a hybrid ion-channel model using the IC method. For example, an analytical expression for the electric potential produced by a point charge located inside and outside of a cylindrical pore studied by Cui. So far, only a few of researches were investigated the method of image charges to study of cylindrical structures. 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. 5 Method of IC can be also 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. 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. 2,3 IC method is an approach for finding and describing the electric potential and field distributions in structures with special geometries, without specifically solving a differential equation. A simple and direct calculation of the electrostatic potential and therefore the electric field is called image charge method or method of image charge (IC). 1 One of the basic problems in electrostatic is to obtain the electrostatic potential and the electric field. The electrostatics play an important and dominant role in many physical/chemical problems, biological and nanoscale systems.
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