Understanding and Employing (Non-)Linearities in Attenuated Total Reflection Spectroscopy

Area of Science:

• Spectroscopy
• Electromagnetic Theory
• Physical Chemistry

Background:

• Beer's Law relates absorbance to concentration.
• Attenuated Total Reflection (ATR) spectroscopy is widely used.
• Accurate interpretation of spectral data is crucial for quantitative analysis.

Purpose of the Study:

• To compare the accuracy of using the imaginary part of the dielectric function versus the absorption index function in Beer's Law and ATR spectroscopy.
• To evaluate the impact of these functions on ATR correction schemes.
• To provide recommendations for optimizing spectral analysis.

Main Methods:

• Electromagnetic theory interpretation of Beer's Law.
• Series expansion and truncation of the negative logarithm of reflectance for ATR.
• Evaluation of ATR correction schemes (low absorption approximation, Bertie-Eysel formalism).

Main Results:

• A linear relationship between molar concentration and the imaginary part of the dielectric function is more accurate than using the absorption index.
• This improved accuracy extends to ATR absorbance.
• ATR correction schemes using the imaginary part converge faster and yield more accurate results, especially for strong oscillators.

Conclusions:

• The imaginary part of the dielectric function is a more accurate parameter than the absorption index for Beer's Law and ATR spectral analysis.
• Prioritizing the imaginary part in ATR correction schemes enhances accuracy and efficiency.
• These findings are particularly relevant for scalar and isotropic media analysis.