# Anomalous Humidity Dependence in Photoacoustic Spectroscopy of CO Explained by Kinetic Cooling
## 4 Conclusions  
A kinetic model for the collisional relaxation of CO in N\({}_{2}\) and H\({}_{2}\)O was introduced that quantitatively explains the surprising humidity dependence of photoacoustic signals from CO as measured in PAS and QEPAS experiments. The minimum in photoacoustic amplitude at a humidity of 0.19%v could be attributed to the mutual cancellation of a kinetic cooling effect during V-V transfer from CO to N\({}_{2}\) and exothermal relaxation of CO and N\({}_{2}\) in collision with H\({}_{2}\)O. The comparison of the simulations with experimental data validated the kinetic model and methodology. The detailed  
Figure 5: Simulation of the humidity-dependent photothermal response \(\hat{H}\) of CO in N\({}_{2}\) at wavelength modulated excitation at 32.8 kHz and 1.5 kHz (detection frequency, modulation frequencies were 16.4 kHz and 0.75 kHz, respectively). Simulations were carried out for varying overall pressure. Data were offset as indicated for better visibility.  
treatment of collisional energy transfers responsible for the generation of photoacoustic signals allows for the influence of a variety of experimental parameters such as pressure, humidity, or modulation frequency to be simulated and can hence help identify the preferred operation conditions in sensing applications. The model can be easily adapted, for example, to include oxygen as an important collision partner in ambient measurements, and is equally valid for photoacoustic and photothermal detection [29]. Finally, since the kinetic model yields rates for the collisional relaxation of CO, it can also be used to estimate the saturation intensity of CO at varying humidities and pressures [30; 31; 32]. The presented kinetic model provides an in-depth understanding of the relaxation dynamics of CO and may be used to further improve photoacoustic and photothermal trace gas sensors and thus extend the scope of their applications.  
The following are available online at [[http://www.mdpi.com/2076-3417/10/3/843/s1](http://www.mdpi.com/2076-3417/10/3/843/s1)]([http://www.mdpi.com/2076-3417/10/3/843/s1](http://www.mdpi.com/2076-3417/10/3/843/s1)), MATLAB code used for numeric simulations, original data, supporting information on gas mixing unit and pressure dependent resonance properties of the quartz tuning fork.  
Methodology, J.H.; Software, J.H.; Investigation, J.H. and B.B.; Resources, J.H. and B.B.; Writing--Original draft preparation, J.H.; Writing--Review and editing, B.B. and B.L.; Funding acquisition, B.L. All authors have read and agreed to the published version of the manuscript.  
This work has received funding from the COMET Center CHASE (project No 868615), which is funded within the framework of COMET (Competence Centers for Excellent Technologies) by BMVIT, BMDW, and the Federal Provinces of Upper Austria and Vienna. The COMET program is run by the Austrian Research Promotion Agency (FFG). The authors acknowledge TU Wien University Library for financial support through its Open Access Funding Program.  
The authors want to thank [PERSON], [PERSON], and [PERSON] for providing the QEPAS module and for support with the same.  
The authors declare no conflicts of interest.