Molecular dynamics calculation of the dielectric constant

Abstract

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 <u_i (0)u_j (r)> in an expansion of the angle-dependent pair distribution function, has been obtained. This function attains its theoretical macroscopic limit at ≈5 molecular diameters, and is consistent with the Kirkwood factor derived from the dielectric constant. Finally it is shown that the angle averaged pair distribution function g(r) depends on the strength of the dipoles. Also, partially averaged functions g(r, θ) and h _Δ(r, θ) are given. These show that the number of neighbours, and their mean polarization parallel to the reference molecule, are much greater in a longitudinal direction than in a transverse direction.