Theoretical Calculation and Simulation of Peak Distortion of Absorption Spectra of Complex Mixtures

Attenuated total reflection (ATR) spectroscopy in infrared is a standard tool used in most analytical labs, as it allows a rapid chemical analysis with virtually no sample preparation. However, when the sample contains materials with a high refractive index, special care must be taken as the resulting data may be severely biased. This article reports a theoretical approach to correcting distorted ATR spectra. Starting from Snell's law, Lorenz model and Fresnel's equations are combined to obtain the complex relationship between optical constants. With calculating the real and imaginary parts, that is, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi><mml:mo>(</mml:mo><mml:mi>ν</mml:mi><mml:mo>)</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi><mml:mo>(</mml:mo><mml:mi>ν</mml:mi><mml:mo>)</mml:mo></mml:math>, respectively, of the complex refractive index from the absorption spectrum, a model for mixtures comprising of a liquid and a solid is established. The effects of distortion and potential misinterpretation of the data are discussed. Proof-of-concept experiments with mixtures of carbonaceous materials and toluene confirm the theoretically predicted observations.