On the Molecular Theory of Dielectric Polarization in Rigid-Dipole Fluids

A molecular theory is developed for the polarization P(r) produced by a weak position-dependent external electric field E0(r) in a finite fluid system, of arbitrary shape, composed of rigid polar molecules. The theory differs from earlier work in that no assumption is made concerning the form of the electrostatic constitutive relation. [The usual assumption in this regard is that P(r) = (ε − 1)E(r) / 4π, where E(r) is the total Maxwell electric field. The “dielectric constant” ε is well defined only if the relation between P(r) and E(r) is in fact one of constant local proportionality.] The result of the present theory is a non-local relation between P(r) and the external field E0(r). The contribution to P(r1) produced by E0(r2) (r1 ≠ r2) is determined by the orientational correlation which exists in zero applied field between two representative dipoles located at r1 and r2. In principle this result may be used to investigate the conditions under which the dielectric constant is well defined, a question of considerable interest but one which has received little attention. The probable existence of long-range orientational correlations in polar fluids unfortunately precludes at present such an investigation for dense fluids, although for dilute gases the investigation can proceed by means of a density expansion. In this way it is demonstrated that the dielectric constant is well defined at least to second order in the density. This demonstration provides some insight into the connection between long-range dipolar effects on the macroscopic and molecular levels. It also yields automatically expressions for the first and second “dielectric virial coefficients”; these expressions agree with results obtained by previous workers under the assumption that the dielectric constant is well defined.