Existence of the Dielectric Constant in Rigid-Dipole Fluids: The Direct Correlation Function

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Abstract
The question of whether the dielectric constant ε exists (is well defined) for a finite fluid system of rigid dipolar molecules is reconsidered and reformulated. It is found that this question can most simply be expressed in terms of the behavior of the position- and orientation-dependent direct correlation function c(r1, ω1; r2, ω2). It is shown that ε exists if c satisfies the following two conditions: (a) c∼−φ/ kT for |r1−r2| > σ, where φ is the dipole-dipole potential and σ is a length which is large microscopically but small macroscopically. (b) c(r1, ω1; r2, ω2) is of the form c8(|r1− r2|)+ F(r1−r2):e(ω1) e(ω2) for |r1−r2| < σ, where e(ω) is the unit vector with orientation ω. An explicit (and new) expression for ε in terms of c is automatically obtained; its applicability is ensured if the above conditions are satisfied. These results lend new intuition and insight into the question of the existence of ε, and suggest a promising approach for future investigations of this question.