Ions confined in spherical dielectric cavities modeled by a splitting field-theory

Leo Lue, Per Linse

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The properties of ions confined within spherical dielectric cavities are examined by a splitting field-theory and Monte Carlo simulations. Three types of cavities are considered: one possessing a uniform surface charge density, one with a uniform volume charge density, and one containing mobile ions. In all cases, mobile counterions are present within the dielectric sphere. The splitting theory is based on dividing the electrostatic interaction into long- and short-wavelength contributions and applying different approximations on the two contributions. The splitting theory works well for the case where the dielectric constant of the confining sphere is equal to or less than that of the medium external to the sphere. Nevertheless, by extending the theory with a virial expansion, the predictions are improved. However, when the dielectric constant of the confining sphere is greater than that of the medium outside the sphere, the splitting theory performs poorly, only qualitatively agreeing with the simulation data. In this case, the strong-coupling expansion does not seem to work well, and a modified mean-field theory where the counterions interact directly with only their own image charge gives improved predictions. The splitting theory works best for the system with a uniform surface charge density and worst for the system with a uniform volume charge density. Increasing the number of ions within the sphere, at a fixed radius, tends to increase the ion density near the surface of the sphere and leads to a depletion region in the sphere interior; however, varying the ion number does not lead to any qualitative changes in the performance of the splitting theory.
LanguageEnglish
Article number144902
Number of pages13
JournalJournal of Chemical Physics
Volume142
Issue number14
Early online date14 Apr 2015
DOIs
Publication statusPublished - 2015

Fingerprint

Ions
cavities
Charge density
ions
Surface charge
confining
Permittivity
permittivity
Wavelength
Mean field theory
expansion
data simulation
predictions
Coulomb interactions
wavelengths
depletion
electrostatics
radii
approximation
simulation

Keywords

  • mean field theory
  • dielectrics
  • carrier density
  • surface charge
  • electrostatics

Cite this

@article{f0aa4769526848b7b3d34eb2d791930d,
title = "Ions confined in spherical dielectric cavities modeled by a splitting field-theory",
abstract = "The properties of ions confined within spherical dielectric cavities are examined by a splitting field-theory and Monte Carlo simulations. Three types of cavities are considered: one possessing a uniform surface charge density, one with a uniform volume charge density, and one containing mobile ions. In all cases, mobile counterions are present within the dielectric sphere. The splitting theory is based on dividing the electrostatic interaction into long- and short-wavelength contributions and applying different approximations on the two contributions. The splitting theory works well for the case where the dielectric constant of the confining sphere is equal to or less than that of the medium external to the sphere. Nevertheless, by extending the theory with a virial expansion, the predictions are improved. However, when the dielectric constant of the confining sphere is greater than that of the medium outside the sphere, the splitting theory performs poorly, only qualitatively agreeing with the simulation data. In this case, the strong-coupling expansion does not seem to work well, and a modified mean-field theory where the counterions interact directly with only their own image charge gives improved predictions. The splitting theory works best for the system with a uniform surface charge density and worst for the system with a uniform volume charge density. Increasing the number of ions within the sphere, at a fixed radius, tends to increase the ion density near the surface of the sphere and leads to a depletion region in the sphere interior; however, varying the ion number does not lead to any qualitative changes in the performance of the splitting theory.",
keywords = "mean field theory, dielectrics, carrier density, surface charge, electrostatics",
author = "Leo Lue and Per Linse",
year = "2015",
doi = "10.1063/1.4917256",
language = "English",
volume = "142",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
number = "14",

}

Ions confined in spherical dielectric cavities modeled by a splitting field-theory. / Lue, Leo; Linse, Per.

In: Journal of Chemical Physics , Vol. 142, No. 14, 144902, 2015.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Ions confined in spherical dielectric cavities modeled by a splitting field-theory

AU - Lue, Leo

AU - Linse, Per

PY - 2015

Y1 - 2015

N2 - The properties of ions confined within spherical dielectric cavities are examined by a splitting field-theory and Monte Carlo simulations. Three types of cavities are considered: one possessing a uniform surface charge density, one with a uniform volume charge density, and one containing mobile ions. In all cases, mobile counterions are present within the dielectric sphere. The splitting theory is based on dividing the electrostatic interaction into long- and short-wavelength contributions and applying different approximations on the two contributions. The splitting theory works well for the case where the dielectric constant of the confining sphere is equal to or less than that of the medium external to the sphere. Nevertheless, by extending the theory with a virial expansion, the predictions are improved. However, when the dielectric constant of the confining sphere is greater than that of the medium outside the sphere, the splitting theory performs poorly, only qualitatively agreeing with the simulation data. In this case, the strong-coupling expansion does not seem to work well, and a modified mean-field theory where the counterions interact directly with only their own image charge gives improved predictions. The splitting theory works best for the system with a uniform surface charge density and worst for the system with a uniform volume charge density. Increasing the number of ions within the sphere, at a fixed radius, tends to increase the ion density near the surface of the sphere and leads to a depletion region in the sphere interior; however, varying the ion number does not lead to any qualitative changes in the performance of the splitting theory.

AB - The properties of ions confined within spherical dielectric cavities are examined by a splitting field-theory and Monte Carlo simulations. Three types of cavities are considered: one possessing a uniform surface charge density, one with a uniform volume charge density, and one containing mobile ions. In all cases, mobile counterions are present within the dielectric sphere. The splitting theory is based on dividing the electrostatic interaction into long- and short-wavelength contributions and applying different approximations on the two contributions. The splitting theory works well for the case where the dielectric constant of the confining sphere is equal to or less than that of the medium external to the sphere. Nevertheless, by extending the theory with a virial expansion, the predictions are improved. However, when the dielectric constant of the confining sphere is greater than that of the medium outside the sphere, the splitting theory performs poorly, only qualitatively agreeing with the simulation data. In this case, the strong-coupling expansion does not seem to work well, and a modified mean-field theory where the counterions interact directly with only their own image charge gives improved predictions. The splitting theory works best for the system with a uniform surface charge density and worst for the system with a uniform volume charge density. Increasing the number of ions within the sphere, at a fixed radius, tends to increase the ion density near the surface of the sphere and leads to a depletion region in the sphere interior; however, varying the ion number does not lead to any qualitative changes in the performance of the splitting theory.

KW - mean field theory

KW - dielectrics

KW - carrier density

KW - surface charge

KW - electrostatics

U2 - 10.1063/1.4917256

DO - 10.1063/1.4917256

M3 - Article

VL - 142

JO - Journal of Chemical Physics

T2 - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 14

M1 - 144902

ER -