The Optical Properties of Nonpolar Liquids

A theory of the refraction, Kerr effect and light scattering for liquids with nonpolar axially symmetric molecules is developed. The molecules are assumed to possess a limited freedom of rotation. This assumption alone does not alter the classical equations. It is necessary to consider the quasi-crystalline grouping of neighboring molecules which produces an anisotropic polarization field. The anisotropy of the Lorentz forces is calculated by combining the classical cavity method with Ewald's lattice theory. It is shown that the procedure of Raman and Krishnan is not justified. With a low potential barrier the quasi-crystalline grouping gives an increase of the refraction, Kerr effect, depolarization and intensity of the Rayleigh scattered light. This is true also for an arbitrarily high potential barrier, provided the anisotropy of the Lorentz force is sufficiently large. These results agree with the observed increase of the refraction in compressed gases and in some solids, and with the observed increase of the depolarization in compressed gases and in liquids near the critical temperature. The observations in liquids are explained by considering a moderate anisotropy of the Lorentz force and a potential barrier of finite height. In this case the molar refraction is slightly smaller than that of the ideal gas. No large deviations from the Lorentz-Lorenz equation can be expected even if the anisotropy is considerable. The refraction changes with pressure and temperature and its dispersion differs from that of the gas. The depolarization and the intensity of the scattered light are considerably smaller than, and the Kerr constant is only a fraction of, the values derived from the classical equation. The classical relations between depolarization and intensity and between Kerr constant and depolarization are only approximate. The theory is applied to benzene. It is assumed that the molecules have the same polarizabilities in the liquid and gaseous state. All observations can be explained by assuming a potential barrier of about 8.8 $\mathrm{kT}$ and an anisotropy of the Lorentz force which is in good accordance with the results of the x-ray analysis of the liquid structure.