Kinetic cooling in mid-infrared methane photoacoustic spectroscopy: A quantitative analysis via digital twin verification

Abstract

This study presents a detailed quantitative analysis of kinetic cooling in methane photoacoustic spectroscopy, leveraging the capabilities of a digital twin model. Using a quantum cascade laser tuned to 1210.01 cm⁻¹, we investigated the effects of varying nitrogen-oxygen matrix compositions on the photoacoustic signals of 15 ppmV methane. Notably, the photoacoustic signal amplitude decreased with increasing oxygen concentration, even falling below the background signal at oxygen levels higher than approximately 6 %V. This phenomenon was attributed to kinetic cooling, where thermal energy is extracted from the surrounding gas molecules rather than added, as validated by complex vector analysis using a previously published digital twin model. The model accurately reproduced complex signal patterns through simulations, providing insights into the underlying molecular mechanisms by quantifying individual collision contributions. These findings underscore the importance of digital twins in understanding the fundamentals of photoacoustic signal generation at the molecular level.

Keywords: CoNRad; Digital twin; Kinetic cooling; Methane; Photoacoustic spectroscopy; Quantum cascade laser; Relaxation.

Fig. 1

Simplified Jablonski diagram of a two-level system to predict the relaxation cascade of photoacoustic signal generation for methane monitoring in air. The grey shaded area highlights the dyad of CH₄ vibrations v_b.

Fig. 2

Amplitude modulated photoacoustic spectra of 15 ppmV methane in pure N₂ (yellow) and successively substituting N₂ by O₂ (red to green). The purple line depicts the absorption cross-section from HITRAN database.

Fig. 3

The photoacoustic measurement signals for 15 ppmV CH₄ at 13 different N₂:O₂ ratios is presented as a complex vector diagram (blue crosses). The measurement points at the minimum (pure N₂) and maximum (20 %V O₂) concentrations are highlighted in bold, while the background signals are shown as a green point cloud. The colored curved arrows illustrate relaxation processes and do not represent vectors.

Fig. 4

Measured PA signals from Fig. 3 after offset-correction (blue crosses) and DT-simulated signals (red dots) are presented in a complex vector diagram (a) and their absolute values plotted as a function of O₂ concentration (b).

Fig. 5

Representation of the contributions of individual collision reactions to the photoacoustic signal amplitude for selected N₂:O₂ matrix compositions as a bar chart. The red dashed horizontal line indicates the energy of a light quantum in eV. The overlaid white diagonally hatched area illustrates the absolute heat dissipation $q_{100}$.