Infrared spectroscopy of quasi-ideal binary liquid mixtures: The challenges of conventional chemometric regression

Thomas G. Mayerhöfer*, Oleksii Ilchenko, Andrii Kutsyk, Jürgen Popp

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


We have recorded ATR-IR spectra of binary mixtures in the (quasi-)ideal systems Benzene-Toluene, Benzene-Carbon tetrachloride and Benzene-Cyclohexane and performed classical least squares, inverse least squares and principal component regression on the resulting spectra. In contrast to the general expectation, the spectra of ideal mixtures follow only roughly Beer's approximation, in particular stronger bands show shifts and increased intensities for intermediary compositions since the polarization of matter by light cannot be neglected. As a consequence, these conventional regression techniques lead to principle and unavoidable errors, even though some of the classical regression techniques are assumed to be able to cope with nonlinearities. In particular in the system Benzene-Carbon tetrachloride large errors result and the relative average error of the volume fraction determination is about 10 % for all three methods. Especially remarkable is that the multivariate regression methods do not perform better than the classical univariate calibration if for the latter a peak due to an oscillator with comparably low oscillator strength is selected, since for such bands polarization effects are weak and Beer's approximation holds comparably well.

Original languageEnglish
Article number121518
JournalSpectrochimica Acta - Part A: Molecular and Biomolecular Spectroscopy
Number of pages7
Publication statusPublished - 2022


  • Beer's approximation
  • Ideal binary liquid mixtures
  • Lorentz-Lorenz relation


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