Spectrophotometric Concentration Analysis Without Molar Absorption Coefficients by Two-Dimensional-Infrared and...

A spectrophotometric method for determining relative concentrations of infrared (IR)-active analytes with unknown concentration and unknown molar absorption coefficient is explored. This type of method may be useful for the characterization of complex/heterogeneous liquids or solids, the study of transient species, and for other scenarios where it might be difficult to gain concentration information by other means. Concentration ratios of two species are obtained from their IR absorption and two-dimensional (2D)-IR diagonal bleach signals using simple ratiometric calculations. A simple calculation framework for deriving concentration ratios from spectral data is developed, extended to IR-pump-probe signals, and applied to the calculation of transition dipole ratios. Corrections to account for the attenuation of the 2D-IR signal caused by population relaxation, spectral overlap, wavelength-dependent pump absorption, inhomogeneous broadening, and laser intensity variations are described. A simple formula for calculating the attenuation of the 2D-IR signal due to sample absorption is deduced and by comparison with 2D-IR signals at varying total sample absorbance found to be quantitatively accurate. 2D-IR and Fourier transform infrared spectroscopy of two carbonyl containing species acetone and N-methyl-acetamide dissolved in D₂O are used to experimentally confirm the validity of the ratiometric calculations. Finally, to address ambiguities over units and scaling of 2D-IR signals, a physical unit of 2D-IR spectral amplitude in mOD/$\sqrt{c{m}^{-1}}$ is proposed.