Relationship of refractive index to mass density and self-consistency of mixing rules for multicomponent mixtures like ambient aerosols

Abstract

This paper focuses on two important yet poorly addressed aspects of ambient aerosols: relationship of refractive index to mass density (index–density relationship) and consistency of the mixing rules used to calculate these two quantities of a multicomponent mixture like ambient aerosols with the index–density relationship. Combined empirical and theoretical analyses show that a denser material generally tends to have a larger refraction index because the applied electric field induces a greater number of electric dipoles, and that the index–density relationship can be described reasonably well by the Lorentz–Lorenz relation. It is shown that the commonly used volume–mean mixing rule for calculating the effective mass density, the Lorentz–Lorenz mixing rule and the molar refraction mixing rule for calculating effective refractive index form a set of mixing rules that are consistent with the Lorentz–Lorenz relation. The molar fraction mixing rule and the Lorentz–Lorenz mixing rule are shown to be equivalent for the Lorentz–Lorenz mixture while the linear volume-mixing rule is an approximation of the Lorentz–Lorenz mixing rule for quasi-homogeneous mixtures wherein the refractive indices of the constituents do not differ much. The results highlight the need for consistency of the mixing rules for calculating the effective refractive index and mass density with the index–density relationship, which not only provides a theoretical guide for judiciously choosing the mixing rules to calculate effective properties of ambient aerosols but also poses new challenges to develop an effective medium theory that applies to more than one quantity. An empirical power-law expression is obtained from the published data that relates the effective specific refractive index to the effective mass density of aerosol particles.