On the dielectric constant of dipolar hard spheres

An interaction-graph theory for the dielectric constant e 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 (e - 1)/(e + 2) expanded as Σan (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 e for water can never be accounted for by treating the molecules as (polarizable) dipolar hard spheres: charge separation must play a dom...

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