^{1,a)}, Per Linse

^{1}and Gunnar Karlström

^{2}

### Abstract

Molecular simulations of strongly coupled dipolar systems of varying size have been carried out, using particles confined inside a dielectriccavity and an image charge approach to treat the dielectric response from the surroundings. A simple method using penalty functions was employed to create an isotropic and homogeneous distribution of particles inside the cavity. The dielectric response of the molecular system was found to increase as the number of particles was increased. Nevertheless, a significant surface effect remained even for the largest systems , manifesting itself through a decrease in the dielectric constant of the system as the confining surface was approached. The surface effect was significantly reduced by using a negative dielectric constant of the surrounding dielectric medium, although accomplishing a full dielectric solvation of the molecular system was not possible.

Financial support by the Swedish Research Council (VR) through the Linnaeus grant for the Organizing Molecular Matter (OMM) center of excellence and computer time at LUNARC are gratefully acknowledged. Furthermore, we would like to thank Håkan Wennerström for helpful scientific discussions.

I. INTRODUCTION

II. THEORY

A. Electric fluctuations in dielectric media

B. The method of images

III. MODEL AND METHODS

A. Molecular model

B. Penalty function

C. Correspondence between the dielectric and molecular models

D. Simulation aspects

E. Fluctuating multipole moment analyses

IV. RESULTS AND DISCUSSION

A. Density profiles and orientational ordering

B. Electric fluctuations

C. Energetics

D. Dielectric constant

E. The effect of varying

V. CONCLUSIONS

### Key Topics

- Dielectrics
- 45.0
- Dielectric constant
- 28.0
- Liquid dielectrics
- 7.0
- Monte Carlo methods
- 7.0
- Anisotropy
- 5.0

## Figures

Schematic description of (a) the dielectric model and (b) the simulated systems. The dashed circle in the right panel indicates that appears as a fitting parameter in the simulated systems.

Schematic description of (a) the dielectric model and (b) the simulated systems. The dashed circle in the right panel indicates that appears as a fitting parameter in the simulated systems.

(a) Relative density and orientation distribution and (b) probability distribution of for the outermost 2 Å of an IBC system of particles with without (solid curves) and with (dashed curves) converged penalty functions and , according to Eqs. (17) and (18). The contact value of is ≈39.

(a) Relative density and orientation distribution and (b) probability distribution of for the outermost 2 Å of an IBC system of particles with without (solid curves) and with (dashed curves) converged penalty functions and , according to Eqs. (17) and (18). The contact value of is ≈39.

(a) Radial distribution function and (b) probability distribution of the dipole-dipole angle of particles separated at most 4.2 Å for a system simulated using IBCs (solid curves) and Ewald summation (dashed curves). Homogeneous and isotropic distributions are also shown (dotted curves). For the IBC system, central particles located closer than [15.0 Å for and 4.2 Å for ] to the confining surface were excluded to avoid overlap between the sampling sphere and the surface. In (a), the two curves fully overlap each other.

(a) Radial distribution function and (b) probability distribution of the dipole-dipole angle of particles separated at most 4.2 Å for a system simulated using IBCs (solid curves) and Ewald summation (dashed curves). Homogeneous and isotropic distributions are also shown (dotted curves). For the IBC system, central particles located closer than [15.0 Å for and 4.2 Å for ] to the confining surface were excluded to avoid overlap between the sampling sphere and the surface. In (a), the two curves fully overlap each other.

Reduced multipole moment fluctuations as a function of the reduced parameter from theoretical predictions according to Eqs. (5) and (6) (solid curves) and simulation (symbols) at indicated . The error bars correspond to one standard deviation. The theoretical values at are , , , and .

Reduced multipole moment fluctuations as a function of the reduced parameter from theoretical predictions according to Eqs. (5) and (6) (solid curves) and simulation (symbols) at indicated . The error bars correspond to one standard deviation. The theoretical values at are , , , and .

Total electrostatic energy per particle of the simulated systems as a function of at indicated values of .

Total electrostatic energy per particle of the simulated systems as a function of at indicated values of .

Dielectric constant as a function of the radius of the sampling sphere obtained from Eqs. (2) and (4) using electric moment fluctuations of order from simulated systems at indicated and . The error bars represent one standard deviation. Included also are results from simulations performed using the Ewald summation technique with (dashed curves).

Dielectric constant as a function of the radius of the sampling sphere obtained from Eqs. (2) and (4) using electric moment fluctuations of order from simulated systems at indicated and . The error bars represent one standard deviation. Included also are results from simulations performed using the Ewald summation technique with (dashed curves).

The quota as a function of . According to Eq. (9), this quota determines the strength of the coupling between the molecular system and the dielectric surroundings.

The quota as a function of . According to Eq. (9), this quota determines the strength of the coupling between the molecular system and the dielectric surroundings.

Dielectric constant as a function of the radius of the sampling sphere obtained from Eqs. (2) and (4) using electric moment fluctuations of order from simulated systems with and at indicated . The error bars represent one standard deviation. Included also are results from simulations performed using the Ewald summation technique with (dashed curves).

Dielectric constant as a function of the radius of the sampling sphere obtained from Eqs. (2) and (4) using electric moment fluctuations of order from simulated systems with and at indicated . The error bars represent one standard deviation. Included also are results from simulations performed using the Ewald summation technique with (dashed curves).

## Tables

Some parameters and properties of the simulated systems.

Some parameters and properties of the simulated systems.

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