Statistical mechanics of polar fluids in electric fields

Abstract

We have succeeded in deriving microscopically, from the statistical mechanics of a molecular fluid, the thermodynamic relations associated with the dielectric properties of a continuous dielectric medium in the presence of a static electric field, as given, e.g., by Landau and Lifshitz. We do this by extending our earlier formally exact treatment of dipolar fluids in the absence of an electric field to the case in which such a field is present. We begin by giving the dielectric tensor in terms of the pair correlation function and then show the way various thermodynamic quantities of interest are related to the field strength and chemical potentials. In the weak‐field case our results are explicit and include the effects of polarizability as well as a generalization from the fluid to an anisotropic crystal. They are given in two separate developments, one of which yields directly a set of purely thermodynamic results that involve the orientation distribution only through the local number density and the polarization, the other of which involves the statistical mechanics of the orientation distribution itself. Finally, we give the mean‐field results that are obtained upon letting the dipolar pair interaction (both permanent and induced) between fluid particles become infinitely weak and long ranged on the molecular scale.