Model for molecular absorption spectroscopy in the 1-100 Torr range in the presence of vibrational depletion - Applied to $\text{CH}_4$ in $\text{N}_2$ and dry air

Abstract

When molecules whose collision induced vibrational decay rates are small are probed by molecular absorption spectroscopic (MAS) techniques the absorption signal can, under certain conditions, be reduced and distorted. The reason has been attributed to the fact that a substantial fraction of the molecules in the interaction region will reside in excited vibrational states, which leads to a depletion of the vibrational ground state. One type of molecule in which this can take place is methane. A model for this phenomenon, based on $\text{CH}_4$ in trace concentrations in either $\text{N}_2$ or dry air in a cylindrical gas cell, detected by mid-infrared light in the 1 - 100 Torr pressure range, is presented. Due to a fast collisional coupling between various rotational states and velocity groups we suggest that depletion in MAS can be modeled adequately by a simple three-level system to which the transport of molecules in the system is coupled as diffusion according to Fick's law, applied to each level individually. The model is verified in a separate work [Hausmaninger T et al., J Quant Spectrosc Radiat Tr. 2017;205:59-70] with good agreement. It predicts that depletion has a strong pressure dependence in the 1 - 30 Torr range, that it is significantly more pronounced in $\text{N}_2$ than in air, and that considerable degrees of depletion can be obtained for mW powers of light (> 10% for powers > 20 mW). The findings indicate that, unless precautions are taken, depletion can adversely affect quantitative assessments performed by MAS. Means of how to reduce depletion are given.