Deviations from the Beer–Lambert Approximation Investigated Using Two-Dimensional Correlation Infrared Spectroscopy

Abstract

Two-dimensional correlation spectroscopy (2D-COS) is a highly sensitive technique for detecting deviations from the Beer–Lambert approximation through asynchronous spectra. In this study, we apply 2D-COS to examine such deviations in the context of this approximation. While conventional molecular IR spectroscopy literature suggests a linear correlation between absorbance, molar concentration, and sample thickness, a more rigorous analysis, supported by electromagnetic theory, demonstrates that this assumption does not hold, even under ideal conditions. As a result, disproportionate spectral changes, caused by interference effects, give rise to distinct patterns in asynchronous 2D-COS IR spectra. To illustrate this, we investigate the thickness dependence of absorbance in poly(methyl methacrylate) (PMMA) layers deposited on calcium fluoride (CaF₂) and Si. Our findings reveal systematic variations not only in absorbance values but also in band shapes and peak positions. 2D-COS emerges as a powerful tool for identifying and analyzing these patterns.

Graphical abstract

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