Refractive Index Mixing Rules and Excess Infrared Spectra of Binary Mixtures

Three refractive index mixing rules, Arago-Biot, Lorentz-Lorenz, and Newton, are generalized to complex refractive index and used to define infrared (IR) spectra of the corresponding ideal liquid mixtures. Using the measured optical constants n and k for acetonitrile-water mixtures (Bertie and Lan, 1997) the excess absorbances, A(E) = A(obs) - A(ideal), are calculated. Relying upon the well-established properties of the acetonitrile-water mixtures, the interpretation of the excess absorbances is established that is essentially based on the understanding of a liquid as a set of oscillators. The set depends on the composition of the mixture and comprises oscillators as present in the pure components and oscillators perturbed by hydrogen bonding between unlike molecules. The main features of an excess spectrum can be established assuming chemical equilibria among various oscillators. The most informative parts of the spectrum of a yet unstudied binary system can well be observed and even qualitatively explained from the excess absorbance provided: first, a detailed vibrational study of the components has been done; and, second, it is well understood what actually is subtracted from A(obs). As examples, the binary mixtures of ethynylbenzene and tetrachloroethylene and 2-ethynylpyridine and tetrachloroethylene are considered.