Debye–Hückel theory for rigid-dipole fluids

Abstract

The dipolar analog of classical linearized Debye–Hückel theory is formulated for a finite fluid system of arbitrary shape composed of rigid polar molecules. In contrast to the ionic case, the dipolar Debye–Hückel (DDH) theory is nonunique due to an inherent arbitrariness in the choice of a local field E*. This nonuniqueness is expressed in terms of a parameter ϑ related to the ellipticity of the spheroidal cavity used to define E*. The theory then leads to an expression for the direct correlation function c (ϑ) as a function of ϑ. Only the short‐range part of c (ϑ) depends upon ϑ; the long‐range part equals −φ_d/kT for all ϑ, where φ_d is the bare dipole–dipole potential. This result for c (ϑ) implies the existence of the dielectric constant ε for all ϑ and leads to a formula for ε (ϑ). The DDH results for c (ϑ) and ε (ϑ) are formally identical to the ’’mean‐field’’ results of Ho/ye and Stell (obtained for an infinite system by a γ→0 limiting procedure) in which ϑ represents a ’’core parameter.’’