Nanometric determination of the thickness of aqueous samples for accurate molar absorption coefficients of water-soluble molecules in the mid-infrared region

Absorption spectra of aqueous samples measured by transmission need to be acquired using very thin cells (5-50 μm) when targeting the mid-infrared (mid-IR) region, due to the strong background absorbance of liquid water. The thickness of the cell used controls the pathlength of the light through the sample, a value needed for instance to transform absorption spectra into molar absorption coefficient spectra, or to determine solute concentrations from absorption spectra. The most accurate way to determine the thickness of a thin empty cell (i.e., filled with air) is from the period of an interference pattern, known as interference fringes, that arises when the cell is placed perpendicular to the path of light in the spectrometer. However, this same approach is not directly applicable to determine the thickness of a cells filled with an aqueous solution, due partially to the smaller amplitude of the interference fringes but fundamentally caused by its complex waveform, with a wavenumber-dependent oscillation period. Here, using Fresnel equations, we derived analytical expressions to model interference fringes in absorption spectra obtained by transmission, valid also for aqueous samples. We also present a novel Fourier-based analysis of the interference fringes that, in combination with the derived analytical expressions, allowed us to determine the pathlength of aqueous samples with an error below 50 nm. We implemented this novel approach to analyze interference fringes as a Live Script running in the software Matlab. As an application, we measured absorption spectra of a 97 mM solution of MES buffer (at low and high pH) using cells of various nominal thicknesses (6, 25 and 50 μm). The molar absorption coefficient spectrum for the acidic and basic forms of MES, worked out using pathlengths values determined using the present approach, were virtually identical regardless of the nominal thickness of the cells used, indicating that the thickness determined for the cells were consistent and likely very accurate. These results illustrate the performance of the presented method to determine the pathlength of aqueous samples, as well as for its utility to obtain accurate molar absorption coefficient spectra of water-soluble molecules in the mid-IR region.