# Anomalous Humidity Dependence in Photoacoustic Spectroscopy of CO Explained by Kinetic Cooling
## 1 Introduction  
Humidity plays a key role in photoacoustic spectroscopy (PAS) and sensing of many molecules. Water is an efficient quencher that facilitates the conversion of the vibrational energy of other molecules into heat much more rapidly than other collision partners such as N\({}_{2}\) or O\({}_{2}\) typically would [1]. This can be attributed mostly to the high polarity of water and the resulting attractive forces that occur during molecular collisions [2]. Without efficient quenchers, many molecules, in particular small molecules at reduced pressure, relax too slowly to release all of the absorbed energy within one half period of photoacoustic modulation. Therefore, signals usually increase with water concentration, especially in quartz-enhanced PAS (QEPAS), where modulation frequencies are approximately one order of magnitude higher than in conventional PAS, and fast relaxation is accordingly more important. For mid-IR CEPAS of CO, this trend was confirmed, but only for water concentrations above \(\sim\)0.19%v [3, 4]. For smaller concentrations, the opposite trend is observed. The QEPAS signal decreases with increasing humidity and shows a pronounced minimum at \(\sim\)0.19%v (compare Figure 2). Although this peculiar behavior has been observed previously [3, 4], an interpretation or quantitative model of this effect is still pending.  
In this contribution, the humidity dependence of photoacoustic signals from CO excited at the fundamental vibrational frequency can be explained by a kinetic cooling effect that occurs during vibrational-vibrational (V-V) energy transfer from CO to the near-resonant vibration of N\({}_{2}\). Kinetic cooling, which refers to a transient decrease of temperature in response to an excitation, was observed previously in photoacoustic measurements of CO\({}_{2}\)[5; 6; 7] as well as thermal lensing measurements of CD\({}_{4}\) and SO\({}_{2}\)[8]. Additionally, kinetic models for the relaxation of these molecules in different gas matrices were derived [5; 9; 10]. Kinetic cooling was also observed in the photoacoustic signal of CO excited at its fundamental vibrational frequency at 4.6 \(\upmu\)m in nitrogen, however, without discussing the influence of water [11]. In this manuscript, the energy transfer steps in the three component system of CO, N\({}_{2}\), and H\({}_{2}\)O including the V-V transfer from CO to N\({}_{2}\) that causes kinetic cooling are summarized. Competition between endothermic V-V transfer from CO to N\({}_{2}\) and exothermic energy transfer from CO as well as N\({}_{2}\) to H\({}_{2}\)O was identified as the origin of the observed minimum of the photoacoustic signal at a humidity of 0.19%v. A kinetic model for simulating the photoacoustic response from CO in N\({}_{2}\) and H\({}_{2}\)O was introduced. Simulations were compared with experimental QEPAS measurements of CO at varying humidity and pressure recorded using a custom quartz tuning-fork to validate the introduced kinetic model. Further simulations are presented for excitation frequencies of 32.8 kHz and 1.5 kHz, corresponding to typical excitation frequencies for QEPAS and PAS, respectively.