A theory of the dielectric polarization of polar substances

Abstract With the aid of classical statistical mechanics, a general expression for the static dielectric constant is derived. It is found, as in earlier work, that the dielectric constant is dependent upon the mean-square dipole moment of a macroscopic spherical sample of the substance. This mean-square moment is expanded as a series in powers of the mean molecular polarizability, and the terms proportional to the zero and first powers are evaluated in detail and in such a way that the long- and the short-range effects are separated. The former are determined with the aid of macroscopic arguments, so that a purely molecular theory remains. In the limit when short-range directional forces are zero, the formula reduces to the well-known Onsager equation. It is found that it is not in general legitimate to replace the surroundings of a macroscopic sample by a continuum having the bulk properties of the substance, and for this reason the approximate equation of Harris & Alder is found to lead to doubtful conclusions. The general equations are applied to the experimental data for water and other liquids, and the results are not unsatisfactory.