Beyond Beer’s Law: Quasi-Ideal Binary Liquid Mixtures

Abstract

We have recorded attenuated total reflection infrared spectra of binary mixtures in the (quasi-)ideal systems benzene–toluene, benzene–carbon tetrachloride, and benzene–cyclohexane. We used two-dimensional correlation spectroscopy, principal component analysis, and multivariate curve resolution to analyze the data. The 2D correlation proves nonlinearities, also in spectral ranges with no obvious deviations from Beer’s approximation. The number of principal components is much higher than two and multivariate curve resolution carried out under the assumption of the presence of a third component, results in spectra which only show bands of the original components. The results negate the presence of third components, since any complex should have lower symmetry than the individual molecules and thus more and/or different infrared-active bands in the spectra. Based on Lorentz–Lorenz theory and literature values of the optical constants, we show that the nonlinearities and additional principal components are consequences of local field effects and the polarization of matter by light. Lorentz–Lorenz theory is, however, not able to explain, for example, the different blueshifts of the strong A_2u band of benzene in the three mixtures. Obviously, infrared spectroscopy is sensitive to the short-range order around the molecules, which changes with content, their shapes, and their anisotropy.

Graphical Abstract