On the dielectric constant of dipolar hard spheres

Abstract

An interaction-graph theory for the dielectric constant ε of a fluid of hard spheres, each of diameter d and with central point dipole moment μ, is developed. In particular, we consider the Debye function (ε - 1)/(ε + 2) expanded as Σa_n (ρ*)yⁿ , where y = 4πρμ²/9kT, ρ is the number density, ρ* = ρd ³. a ₁(ρ*) = 1, a ₂(ρ*) = 0 and a ₃(ρ*) = -15/16 + 0·0313 ρ* + …. The dominant term -15/16 was derived earlier by Jepsen by a different method. The coefficients of the terms in ρ*^-2 y ⁴ and ρ*^-1 y ⁴ are calculated (and are small). It is proved that the coefficients of terms proportional to yⁿ (without further powers of ρ*) are the same in Partey's recent LHNC theory as in Wertheim's mean spherical approximation: and the implication of this for Patey's theory is discussed. Independent support for the validity of Patey's predictions at high densities is cited. It is argued that ε for water can never be accounted for by treating the molecules as (polarizable) dipolar hard spheres: charge separation must play a dominant role in determining ε.