# IImage method for induced surface charge from many-body system of dielectric spheres

## Abstract

Charged dielectric spheres embedded in a dielectric medium provide the simplest model for many-body systems of polarizable ions and charged colloidal particles. We provide a multiple scattering formulation for the total electrostatic energy for such systems and demonstrate that the polarization energy can be rapidly evaluated by an image method that generalizes the image methods for conducting spheres. Individual contributions to the total electrostatic energy are ordered according to the number of polarized surfaces involved, and each additional surface polarization reduces the energy by a factor of (a/R)(3) epsilon, where a is the sphere radius, R the average inter-sphere separation, and. the relevant dielectric mismatch at the interface. Explicit expressions are provided for both the energy and the forces acting on individual spheres, which can be readily implemented in Monte Carlo and molecular dynamics simulations of polarizable charged spheres, thereby avoiding costly computational techniques that introduce a surface charge distribution that requires numerical solution.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science - Office of Basic Energy Sciences - Materials Sciences and Engineering Division

- OSTI Identifier:
- 1390838

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 145; Journal Issue: 12

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Qin, Jian, de Pablo, Juan J., and Freed, Karl F.
```*IImage method for induced surface charge from many-body system of dielectric spheres*. United States: N. p., 2016.
Web. doi:10.1063/1.4962832.

```
Qin, Jian, de Pablo, Juan J., & Freed, Karl F.
```*IImage method for induced surface charge from many-body system of dielectric spheres*. United States. doi:10.1063/1.4962832.

```
Qin, Jian, de Pablo, Juan J., and Freed, Karl F. Wed .
"IImage method for induced surface charge from many-body system of dielectric spheres". United States.
doi:10.1063/1.4962832.
```

```
@article{osti_1390838,
```

title = {IImage method for induced surface charge from many-body system of dielectric spheres},

author = {Qin, Jian and de Pablo, Juan J. and Freed, Karl F.},

abstractNote = {Charged dielectric spheres embedded in a dielectric medium provide the simplest model for many-body systems of polarizable ions and charged colloidal particles. We provide a multiple scattering formulation for the total electrostatic energy for such systems and demonstrate that the polarization energy can be rapidly evaluated by an image method that generalizes the image methods for conducting spheres. Individual contributions to the total electrostatic energy are ordered according to the number of polarized surfaces involved, and each additional surface polarization reduces the energy by a factor of (a/R)(3) epsilon, where a is the sphere radius, R the average inter-sphere separation, and. the relevant dielectric mismatch at the interface. Explicit expressions are provided for both the energy and the forces acting on individual spheres, which can be readily implemented in Monte Carlo and molecular dynamics simulations of polarizable charged spheres, thereby avoiding costly computational techniques that introduce a surface charge distribution that requires numerical solution.},

doi = {10.1063/1.4962832},

journal = {Journal of Chemical Physics},

number = 12,

volume = 145,

place = {United States},

year = {Wed Sep 28 00:00:00 EDT 2016},

month = {Wed Sep 28 00:00:00 EDT 2016}

}