Molecular collision cross sections and the effect of water vapour on vibrational relaxation in carbon dioxide

Abstract

Cross sections for the vibrational excitation of carbon dioxide by collision with water vapour have been calculated for collision energies up to 2.5 ev by numerical integration of the appropriate coupled scattering equations. Coupling between five of the molecular vibrational states has been retained. The scattering potential is represented by a spherically symmetric Lennard-Jones function. Chemical forces, which have been suggested by Widom and Bauer in 1953, are not taken into account, but effects arising from the dipole moment of the water molecule have been allowed for in an approximate way by statistically averaging the induced interaction over all orientations of the polar molecule. The cross sections are used to determine the effect of water vapour on vibrational relaxation in carbon dioxide for several water vapour concentrations and temperatures from 300 °K to 1000 °K. It is found that the experimentally observed strong effect of water vapour, the occurrence of sound absorption maxima at more than one frequency and the anomalous temperature dependence of the maximum sound absorption frequencies are all accounted for by the variation of the effective vibrational specific heats with temperature and concentration. In general, comparison with experiment indicates that the cross sections may be low by about a factor of 4. This can be ascribed to the uncertainties in the empirical scattering potential. It is concluded that past disagreement between experiment and theory has arisen in large part from the inadequate theoretical treatment given to the coupling between the various molecular vibrational states.