Dielectric Constants of Non-Polar Fluids. I. Theory

The dielectric constant of a classical fluid, composed of spherically symmetric molecules with dipole-dipole interactions, is calculated by a method that leads to formulas previously derived by Yvon but is more direct and yields additional results. The relations of the formulas of Lorentz, Yvon, Kirkwood, and Böttcher to one another are clarified. An accurate calculation of the deviation from the Clausius-Mosotti formula requires knowledge of molecular distribution functions of various orders, but an approximate calculation is possible on the basis of the radial distribution function alone. It is shown that the success of Böttcher's approximation is partly the result of an approximate cancellation of errors, and that a practically equivalent formula can be obtained by another method that lends itself more readily to improvement. The distinctive feature of the present calculation is the introduction of quantities pi(h), the mean moment of molecule i when the positions of it and of h−1 other molecules are specified; Lorentz's formula corresponds to the approximation p1(2)=p1(1), and other formulas to various approximate evaluations of the difference p1(2)—p1(1).