Refractive Index of Liquid Mixtures: Theory and Experiment

Abstract

An innovative approach is presented to interpret the refractive index of binary liquid mixtures. The concept of refractive index "before mixing" is introduced and shown to be given by the volume-fraction mixing rule of the pure-component refractive indices (Arago-Biot formula). The refractive index of thermodynamically ideal liquid mixtures is demonstrated to be given by the volume-fraction mixing rule of the pure-component squared refractive indices (Newton formula). This theoretical formulation entails a positive change of refractive index upon ideal mixing, which is interpreted in terms of dissimilar London dispersion forces centred in the dissimilar molecules making up the mixture. For real liquid mixtures, the refractive index of mixing and the excess refractive index are introduced in a thermodynamic manner. Examples of mixtures are cited for which excess refractive indices and excess molar volumes show all of the four possible sign combinations, a fact that jeopardises the finding of a general equation linking these two excess properties. Refractive indices of 69 mixtures of water with the amphiphile (R,S)-1-propoxypropan-2-ol are reported at five temperatures in the range 283-303 K. The ideal and real refractive properties of this binary system are discussed. Pear-shaped plots of excess refractive indices against excess molar volumes show that extreme positive values of excess refractive index occur at a substantially lower mole fraction of the amphiphile than extreme negative values of excess molar volume. Analysis of these plots provides insights into the mixing schemes that occur in different composition segments. A nearly linear variation is found when Balankina's ratios between excess and ideal values of refractive indices are plotted against ratios between excess and ideal values of molar volumes. It is concluded that, when coupled with volumetric properties, the new thermodynamic functions defined for the analysis of refractive indices of liquid mixtures give important complementary information on the mixing process over the whole composition range.

Thermodynamic and Acoustic Properties of Mixtures of Dibromomethane + Heptane

“…The thermodynamic approach to the molecular acoustic problems seems very promising. Recently, partial and apparent speeds of sound in binary mixtures were defined and discussed [19]. …”

A review of solid–fluid selection options for optical-based measurements in single-phase liquid, two-phase liquid–liquid and multiphase solid–liquid flows

“…A simple prediction of the RI of a multicomponent liquid can be made using the empirical Arago-Biot (AB) equation (Arago and Biot 1806;Reis et al 2010), which is based on linear volumetric additivity for each component in the mixture:…”

“…Another empirical relation is the Lichtenecker (L) or Lichtenecker-Rother equation (Lichtenecker 1926;Lichtenecker and Rother 1931;Heller 1945) which, as Simpkin (2010) showed, in fact, has a theoretical basis and can be derived from Maxwell's equations: while relatively common Newton (N) equation (Newton 1704;Kurtz and Ward 1936;Reis et al 2010) also has a theoretical foundation:…”

“…14, where V and x are molar volumes and molar fractions, respectively (Sharma et al 2007): The theory behind the RI of liquid mixtures is discussed by Reis et al (2010), who explains that differences between the AB and N equations, which are amongst the simplest of the above relations, stem from the rigorous definitions of RI before and after mixing, respectively. In trying to establish which relation appears better suited for the prediction of the RI of liquid mixtures, we examined comparisons performed by a number of authors.…”

Density and excess properties of N-methyldiethanolamine (MDEA) with 1-hexyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate [hmim][FAP]

“…The calculated values of refractive indices with Lorentz-Lorenz, Gladstone-Dale, and Eykman equations agreed well with the experimental values as the deviation was within the allowable limit (B0.005). In order to calculate the ideal refractive index (n D id ) and excess refractive index (n D E ) of the binary mixtures ([hmim][FAP] with N-methyldiethanolamine (MDEA)) the equations proposed by Reis et al [30] were used. The ideal refractive index is expressed as:…”