^{1}and J.-P. Hansen

^{1}

### Abstract

The dielectric response of a simple model of a polar fluid near neutral interfaces is examined by a combination of linear response theory and extensive molecular dynamics simulations. Fluctuation expressions for a local permittivitytensor are derived for planar and spherical geometries, based on the assumption of a purely local relationship between polarization and electric field. While the longitudinal component of exhibits strong oscillations on the molecular scale near interfaces, the transverse component becomes ill defined and unphysical, indicating nonlocality in the dielectric response. Both components go over to the correct bulk permittivity beyond a few molecular diameters. Upon approaching interfaces from the bulk, the permittivity tends to increase, rather than decrease as commonly assumed, and this behavior is confirmed for a simple model of water near a hydrophobic surface. An unexpected finding of the present analysis is the formation of “electrostatic double layers” signaled by a dramatic overscreening of an externally applied field inside the polar fluid close to an interface. The local electric field is of opposite sign to the external field and of significantly larger amplitude within the first layer of polar molecules.

I. INTRODUCTION

II. POLARIZATION IN LINEAR RESPONSE

A. Slab geometry

B. Spherical geometry

III. MOLECULAR DYNAMICS RESULTS

A. Slab geometry

B. Spherical geometry

IV. CONCLUSION

### Key Topics

- Permittivity
- 50.0
- Polarization
- 26.0
- External field
- 23.0
- Liquid dielectrics
- 23.0
- Electric fields
- 19.0

## Figures

Density and orientational profile of a DSS fluid in a slab (, ) for two values of the reduced dipole moment.

Density and orientational profile of a DSS fluid in a slab (, ) for two values of the reduced dipole moment.

Parallel component of the permittivity tensor (same system as in Fig. 1), from fluctuation formula (13) and from the response to an external field along axis.

Parallel component of the permittivity tensor (same system as in Fig. 1), from fluctuation formula (13) and from the response to an external field along axis.

Dipolar fluctuations (thin line) and smoothed curve (thick line) [see text]. Inset: orthogonal component of the permittivity tensor (, , ).

Dipolar fluctuations (thin line) and smoothed curve (thick line) [see text]. Inset: orthogonal component of the permittivity tensor (, , ).

Continuous line: polarization charge density induced inside a slab of polar fluid (, , ) by an external electric field along the direction. Dashed line: ten times the integral .

Continuous line: polarization charge density induced inside a slab of polar fluid (, , ) by an external electric field along the direction. Dashed line: ten times the integral .

Electric field (thick line) and polarization density computed using Eq. (30) (thin line) and from the statistical average (dotted line), for the same system as in Fig. 4. Inset: from Eq. (31) and from fluctuation formula (17) (dashed line).

Electric field (thick line) and polarization density computed using Eq. (30) (thin line) and from the statistical average (dotted line), for the same system as in Fig. 4. Inset: from Eq. (31) and from fluctuation formula (17) (dashed line).

EDL ratio from Eq. (29) (continuous line) and from the fluctuation formula (32) (dashed line) [same system as in Fig. 3].

EDL ratio from Eq. (29) (continuous line) and from the fluctuation formula (32) (dashed line) [same system as in Fig. 3].

Density, orientation, and permittivity profiles of 2076 SPC water molecules confined in a slab of width 4.65 nm by hydrophobic walls (, ).

Density, orientation, and permittivity profiles of 2076 SPC water molecules confined in a slab of width 4.65 nm by hydrophobic walls (, ).

Geometry for the Berendsen formula: a droplet of radius is surrounded by a continuous medium of dielectric constant . Dipolar fluctuations in the fluid are measured inside a concentric subsphere of radius , while the remaining fluid in the outer shell is assumed to behave as a dielectric continuum of permittivity .

Geometry for the Berendsen formula: a droplet of radius is surrounded by a continuous medium of dielectric constant . Dipolar fluctuations in the fluid are measured inside a concentric subsphere of radius , while the remaining fluid in the outer shell is assumed to behave as a dielectric continuum of permittivity .

Density profile [thick curve: ten times ] and estimate of the *bulk* dielectric constant of a droplet of a polar fluid from Eq. (18) with the total dipole moment of a concentric subsphere of radius (thin curve), and from the Berendsen formula (33) (dashed line). The expected bulk value is indicated by the dotted line.

Density profile [thick curve: ten times ] and estimate of the *bulk* dielectric constant of a droplet of a polar fluid from Eq. (18) with the total dipole moment of a concentric subsphere of radius (thin curve), and from the Berendsen formula (33) (dashed line). The expected bulk value is indicated by the dotted line.

Radial electric field, polarization density, molecular density, and permittivity profiles for a spherical droplet of polar fluid (, , ) when an ion of unit electronic charge (reduced charge ) is present at the origin. The dotted line indicates the bulk dielectric constant (divided by 10).

Radial electric field, polarization density, molecular density, and permittivity profiles for a spherical droplet of polar fluid (, , ) when an ion of unit electronic charge (reduced charge ) is present at the origin. The dotted line indicates the bulk dielectric constant (divided by 10).

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