Cavity Concept in Dielectric Theory

Abstract

A statistical formulation is presented for the reaction and cavity‐field response functions of an isotropic nonpolar substance. It is shown that the reaction‐field approach can be made consistent to a good approximation with statistically calculated fields by a reasonable choice of the cavity radius a. The cavity radius is a complicated function of density, temperature, and molecular parameters and, in first approximation, is given by expression $$a^{\text{−3}}={\displaystyle {\int }_0^{\infty }}{\text{3r}}^{\text{−4}}\mathrm{\rho (r)dr,}$$ where ρ(r) is the radial distribution function. The value of a³ computed for liquid Xe from x‐ray scattering data according to the latter formula is found to be equal to ½σ³, where σ is the Lennard‐Jones collision diameter; this value is in very good agreement with the Böttcher—Onsager value for a³ calculated on the basis of the macroscopic dielectric constant and polarizability of the free molecule. The dielectric and statistical reaction and cavity‐field functions are compared and discussed.