Existence of the dielectric constant in fluids of classical deformable molecules

Abstract

The existence of the dielectric constant ε is investigated for fluids composed of classical deformable (polarizable) molecules. The development is based upon generalized functional-derivative relations which involve joint distributions in molecular positions rk and dipole moments μk. Sufficient conditions for the existence of ε are expressed in terms of the generalized direct correlation function c(12) = c(r₁, μ₁; r₂, μ₂). It is found that ε exists if -kTc( 12) depends only on relative positions and dipole moment directions (in addition to │μ₁│and │μ₂│, and becomes asymptotic to the dipole-dipole potential at long range. An expression for ε in terms of a short-ranged total correlation function h₀(12) emerges automatically from the development. An expression for ε in terms of c(12) is also derived. The latter expression involves an inverse kernel in (│μ₁│,│μ₂│) space. The case of rigid polar molecules is reconsidered as a special case of the present formulation.