On the dielectric constant of non-polar Lennard-Jones fluids according to the Kirkwood-Yvon theory

Abstract

We have calculated the fractional increase in the Clausius-Mossotti expression for the dielectric constant of a non-polar fluid on the basis of the Kirkwood-Yvon theory, assuming that the structure of the fluid is that appropriate to a Lennard-Jones interatomic potential. The triplet distribution function which occurs in the Kirkwood-Yvon theory was replaced by the superposition approximation. Pair distribution functions, and relevant thermodynamic properties, for a Lennard-Jones fluid were taken from the machine simulation studies of Verlet and co-workers. We present the results at the two reduced temperatures T* = 1·5 and T* = 2·5, and compare them with (i) predictions based on the dielectric virial expansion (curtailed at the three-particle term), and (ii) some estimates by Alder, Strauss and Weis, obtained by the method of molecular dynamics. We conclude that, subject to the assumptions of the Kirkwood-Yvon theory, the dielectric virial expansion approach is adequate when the reduced density, ρ*, is less than about 0·25, and that the present method, embodying the superposition approximation, is adequate up to ρ* = 0·5. For ρ* > 0·5 the molecular dynamic work indicates that the superposition approximation over-estimates departures from the Clausius-Mossotti law (which are always positive, and greatest at about ρ* = 0·5). We have discussed the experimental data on argon at 25°C (i.e. T* = 2·5) in the light of these results.