Quantitative vibrational spectroscopy on liquid mixtures: concentration units matter†
Quantitative vibrational absorption spectroscopies rely on Beer's law relating spectroscopic intensities in a linear fashion to chemical concentrations. To address and clarify contrasting results in the literature about the difference between volume- and mass-based concentrations units used for quantitative spectroscopy on liquid solutions, we performed near-infrared, mid-infrared, and Raman spectroscopy measurements on four different binary solvent mixtures. Using classical least squares (CLS) and partial least squares (PLS) as multivariate analysis methods, we demonstrate that spectroscopic intensities are linearly related to volume-based concentration units rather than more widely used mass-based concentration units such as weight percent. The CLS results show that the difference in root mean square error of prediction (RMSEP) values between CLS models based on mass and volume fractions correlates strongly with the density difference between the two solvents in each binary mixture. This is explained by the fact that density differences are the source of non-linearity between mass and volume fractions in such mixtures. We also show that PLS calibration handles the non-linearity in mass-based models by the inclusion of additional latent variables that describe residual spectroscopic variation beyond the first latent variable (e.g., due to small peak shifts), as observed in the experimental data of all binary solvent mixtures. Using simulation studies, we have quantified the relative errors (up to 10–15%) that are made in PLS modeling when using mass fractions instead of volume fractions. Overall, our results provide conclusive evidence that concentration units based on volume should be preferred for optimal spectroscopic calibration results in academic and industrial practice.