The fundamental equation of electrostatics, i.e. the integral equation for the polarization of a macroscopic dielectric in an arbitrary external field, is written in a form that allows explicit inclusion of the toroidal boundary conditions as well as the cutoff of dipolar interactions often used in the computer simulation of polar systems. The toroidal boundary conditions are accounted for in a natural way if the integral equation is formulated (and solved) in Fourier space. Rigorous expressions for the polarization induced by a homogeneous field as well as for the equilibrium dipole moment fluctuations, both as a function of the dielectric constant, are then easily derived for general systems in two and three dimensions. The equations obtained for spherical cutoff geometry with reaction field are identical to those valid for an infinite periodic system (Ewald sum plus reaction field). When applied to the case of a highly polar Stockmayer system (μ*2=3·0, θ*=0·822, T*=1·15) the formulas lead to a consiste...

Dipole moment fluctuation formulas in computer simulations of polar systems

Revue des etudes sur la constante dielectrique et la permittivite des molecules a l'etat liquide. Etudes theoriques

A Consistent Molecular Treatment of Dielectric Phenomena

Recently a computer adapted theory suitable for evaluating the dielectric properties of polar systems has been proposed. It rests on the assumption that the system behaves like a macroscopic dielectric and that the modifications of dipolar interactions do not affect its dielectric constant. In the present paper these assumptions are tested, for a system of 512 Stockmayer particles with μ*2 = 3·0 and I* = 0·025 at ρ* = 0·822 and T* = 1·15, in a series of extensive simulations, in which the boundary conditions (spherical reaction field (RF) vs. lattice summation technique (LS)) have been varied in a systematic way. Within the limits of statistical accuracy all simulations give identical results for the static as well as for the frequency dependent dielectric constant, namely e(0) = 66 and a relaxation time of τD* ≃ 1·0 for the almost Debye-like behaviour of e(ω). For particle numbers of 256 and upward the system studied behaves like a macroscopic dielectric; the bulk dielectric constant is independent of N ...

Consistent calculation of the static and frequency-dependent dielectric constant in computer simulations

Computer simulation of the static dielectric constant of systems with permanent electric dipoles.

Dielectric Constants of Fluid Models: Statistical Mechanical Theory and its Quantitative Implementation

Molecular dynamics (MD) simulations of an isolated dipolar system (made of Stockmayer molecules) has been performed. A two dimensional system has been adopted, using a ‘2-D electrostatics’ dipolar interaction. The isolated system was a disc in vacuo. The autocorrelation function (ACF) of the moment of the disc was extracted from our runs, together with the ACF of the moment of a small inner disc (‘microscopic’ or ‘multimolecular’ ACF). Comparison of these two ACF has allowed us to compute the response function of the annulus between the two discs. The behaviour of the latter was that predicted by the theory of Fatuzzo and Mason. It is thus shown, for the first time, that one can obtain, by numerical simulation of a few hundred molecules, reliable values of the complex permittivity of highly polar fluids, despite the long range character of the dipolar interaction. Its behaviour is surprisingly realistic when compared with that of real 3-D polar liquids. Monomolecular ACF have also been extracted from the ...

Molecular dynamics calculation of the dielectric constant

Molecular dynamics simulation of a sample of a two-dimensional fluid of Stockmayer molecules (i.e. particles interacting via a central Lennard-Jones interaction plus a point dipole interaction) are reported. The dipolar interaction adopted is that required by two-dimensional electrostatics, so that the convergence problem is conserved. The sample (≈13 molecular diameters in size) is kept in vacuo by a steep circular potential barrier. It is first shown that for distances greater than 3 to 5 molecular diameters the macroscopic laws of electrostatics apply, by checking that the mean squared moment of an inner disc, as a function of the diameter of the disc, can be fitted with a single dielectric constant, which is thus determined. The Kirkwood correlation factor for an infinite sample is then evaluated. For highly polar systems, it is greater than unity. Also the radial vector correlation function h Δ(r), which describes the weight of in an expansion of the angle-dependent pair distribution f...

Molecular dynamics calculation of the dielectric constant: II. Static properties of a fluid of two-dimensional Stockmayer molecules

In the previous papers of this series it was shown, by molecular dynamics simulations, that 2D fluid systems of pure Stockmayer molecules have a higher dielectric constant than predicted by the Onsager model or, equivalently, that their Kirkwood orientational correlation factor g k is greater than unity. In this paper this observation is further considered; it is shown that it is due to the fact that the longitudinal positive correlations are enhanced, while the negative correlations in the transverse direction are diminished, compared with those induced in a continuum by a polar molecule. Modified Stockmayer model molecules are then studied. The adopted modifications are of two kinds: (i) the molecular point dipole is excentred and (ii) a central quadrupole is added to the central dipole. In both cases g k is found to be closer to unity than for the pure Stockmayer systems. However, this is not due to a better local validity of the Onsager picture: rather, the map of the local polarization around a refer...

G. Bossis

Papers

Molecular dynamics calculation of the dielectric constant

Molecular dynamics calculation of the dielectric constant: II. Static properties of a fluid of two-dimensional Stockmayer molecules

Molecular dynamics calculation of the dielectric constant: IV. 2D fluids of various modified Stockmayer molecules