Contributions of Fluctuations and Anisotropy to Dielectric Polarization in Polar Substances

The theory of dielectric polarization in polar substances is extended to include the effect of fluctuations in the dipole moments of the individual molecules. The effect of optical anisotropy is also taken into account. The resulting expression for the dielectric constant is identical in its leading terms to an earlier result of Harris and Alder, in which fluctuations are neglected, but differs significantly from an equation derived by Frohlich, which is here explicitly shown to involve an additional approximation. Application of the theory to gases is discussed briefly. It is pointed out that Onsager's formula for relating the permanent dipole moment of a molecule to its average moment in the dielectric involves an approximation which produces an incorrect limiting behavior at large volumes, so that it should not be applied to polar gases at normal pressures. Calculations are presented showing the various contributions to the dielectric polarization of gaseous ammonia. The fluctuation term contributes of the order of 20% of the term expressing the correlation in orientation of the average dipole moments. The theory is also applied to liquid water, using Pople's bendable hydrogen bonded model for that substance. In water the fluctuation term is but 6% of the direct correlation term, and opposite in sign. The results are discussed briefly.