On the Role of Dipole-Dipole Coupling in Dielectric Media

The mathematical treatment of dipole-dipole coupling in my previous article on magnetism applies with but little modification to the electric case. Because of fluctuation effects, the use of the usual Lorentz local field E+4πP/3 and of the Clausius-Mossotti formula cannot be justified except as a first approximation valid at low density. Consequently one need not accept the C-M prediction that polar liquids should exhibit the electric analogue of ferro-magnetism. A Gaussian approximation, or better still, a formula based on Onsager's field would never allow ferro-magnetism. Consequently the hypothesis of hindered rotation, as in the theories of Fowler and Debye, may not be necessary to explain the absence of spontaneous polarization, as well as the non-occurrence of much saturation curvature in strong applied fields. It is a weakness of their theory that this hypothesis cannot consistently be employed both for such purposes and to explain discontinuities in dielectric constants and specific heats at lower temperatures (e.g., 100° in HCl). It is surprising that the Clausius-Mossotti formula works so exceedingly well as it does in nonpolar liquids, since it is theoretically valid at high densities only for an artificial model of harmonic oscillators which cannot be regarded as an accurate representation of the induced polarization. The calculations of Kirkwood on the translational fluctuation effect, causing deviations from the C-M expression in gases, are extended to include polar molecules, and agree adequately with recent measurements of Keyes and collaborators on NH3.