Effective absorption coefficient and effective thickness in attenuated total reflection spectroscopy.

Area of Science:

• Spectroscopy
• Materials Science
• Physical Chemistry

Background:

• Attenuated total reflection (ATR) spectroscopy is widely used for material characterization.
• Existing methods for relating reflectivity (R) to absorption coefficient (α) are limited to low absorption cases.
• The assumption R∼exp(-αde) uses an effective thickness (de) evaluated for lossless conditions.

Purpose of the Study:

• To develop a more detailed derivation for relating reflectivity to absorption in ATR spectroscopy.
• To define an ATR-effective absorption coefficient (β) and penetration depth (dp).
• To establish a generalized effective thickness (def) applicable to varying absorption strengths.

Main Methods:

• Detailed theoretical derivation of reflectivity (R) in ATR spectroscopy.
• Formulation of R=exp(-βdp/2) and R=exp(-αdef).
• Experimental validation using water, chitosan, and soda-lime glass in the infrared range.

Main Results:

• Introduced ATR-effective absorption coefficient (β) and penetration depth (dp).
• Found β is proportional to 4πε2/λ, where ε2 is the imaginary part of the dielectric function.
• Developed a generalized effective thickness (def) that simplifies to de in the low absorption limit.

Conclusions:

• The derived ATR-effective absorption coefficient is reliable for infrared spectroscopy.
• The new formulation provides accurate characterization across a range of material absorption.
• Experimental data confirm the validity of the new approach for diverse materials.