# Anomalous Humidity Dependence in Photoacoustic Spectroscopy of CO Explained by Kinetic Cooling
## Materials and Methods  
### Measurement of Humidity Dependent 2f-WM-QEPAS Signals of CO  
The experimental setup for wavelength modulation QEPAS with second harmonic detection (2_f_-WM-QEPAS) is illustrated in Figure 1. A distributed feedback quantum cascade laser (DFB-QCL, Adtech Optics, City of Industry, CA, USA) was operated in continuous wave mode at a wavenumber of 2179.77 cm\({}^{-1}\). The laser wavenumber was sinusoidally modulated at half the QTF resonance frequency \(f_{QTF}\) via a small amplitude current modulation. The laser current was modulated by applying a sinusoidal voltage signal to the analog control input of the laser current driver (QCL OEM300, Wavelength electronics, Bozeman, MT, USA). The modulation amplitude was adjusted to maximize the QEPAS signal for every measurement. The beam was focused to a spot size (1/e\({}^{2}\) radius) of 0.23 mm and directed through the resonator tubes and between the prongs of the quartz tuning fork (QTF). The optical power at the QTF was  
Figure 1: **(Left)** Schematic of the experimental setup for humidity dependent 2_f_-WM-QEPAS measurements of CO in humidified N\({}_{2}\), see text. MFC: mass flow controller, DFB-QCL: Distributed feedback quantum cascade laser. (**Right**) Rendered image of the acoustic detection module and custom tuning fork. 25 mW. The QTF was a custom design for QEPAS with a resonance frequency of 12.46 kHz and a prong spacing of 0.8 mm (see [12], design T08, and [13], design S\({}_{2}\)). The tuning fork including electronic trans-impedance amplification and excitation circuitry was provided as a prototype of a now commercially available QEPAS module (Thorlabs ADM01, Dachau, Germany, compare Figure 1). Two 12.5 mm long stainless steel resonator tubes with a 1.5 mm inner diameter were used as an acoustic resonator [12]. The amplified signal from the QTF was demodulated at the second harmonic of the modulation frequency using a lock-in amplifier (ZI-MFLI, Zurich Instruments, Zurich, Switzerland), yielding the 2_f_-WM-QEPAS signal. The quality factor \(Q\) and resonance frequency \(f_{QTF}\) of the tuning fork were measured by exciting the tuning fork by a sinusoidal voltage of stepped frequency and the modulation frequency of the laser was adjusted to half the resonance frequency for every measurement. After the QEPAS detection module, the beam passed a reference gas cell filled with CO diluted in N\({}_{2}\) at 100 mbar and was finally detected on a mercury-cadmium-telluride (MCT) photodetector (PCI-2 TE-12, Vigo Systems S.A., Poznanska, Poland). The reference gas cell was used to lock the laser wavelength to the resonance wavenumber of the R9 transition of CO at 2179.77 cm\({}^{-1}\) using wavelength modulation locking. To this end, the detector signal was demodulated at the third harmonic of the laser modulation frequency using a lock-in amplifier. The so obtained error signal was used as the input for a digital PI-controller (Digilock 110, Toptica Photonics, Farmington, NY, USA) whose output was applied to the control input of the laser current driver. All measurements were performed in a steady gas flow. A custom built gas mixing unit [14] was used to prepare samples of defined CO concentration and humidity (see electronic supporting information for more details on the gas mixing unit). Defined flow rates of N\({}_{2}\) and CO test gas (100 ppm in N\({}_{2}\), Air Liquide, Paris, France) were set using mass flow controllers (MFC). One stream of nitrogen was humidified using a wash bottle filled with water. To achieve a reproducible humidity, the temperature of the wash bottle was stabilized at 40 \({}^{\circ}\)C in a water bath thermostat [15]. Using the three MFCs, the humidity was varied stepwise while keeping the concentration of CO constant. The overall flow rate was set to 1200 sccm at the MFCs, of which approximately 300 sccm were pumped through the gas cell and the remaining flow was directed through a check valve.