Rate Equations for the Vibrational Relaxation of CO2 – N2 or CO2− Noble Gas Mixtures— Application to Comparison of Spectrophone Data with Results from Other Experimental Techniques

Abstract

Macroscopic rate equations are formulated for vibrational relaxation in mixtures of CO2 with either N2 or a noble gas. A model is used that assumes the bending and symmetric-stretching modes of CO2 to be in equilibrium with each other and to have a common vibrational temperature. The asymmetric-stretching mode is taken to be described by a different vibrational temperature, which, in the case of CO2−N2 mixtures, is taken to be common with the temperature of the nitrogen vibrational mode. The rate equations are then derived on a phenomenological basis. The resulting phenomenological coefficients can be interpreted in terms of characteristic relaxation times and energy exchange ratios, which are a measure of the relative amounts of energy exchanged by the different vibrational modes in V—V transitions. The equations can be used for any linearized problem. Here they are applied to a spectrophone. The resulting phase-lag equations are used to reinterpret spectrophone data that had been thought to lead to false conclusions. It is shown that the data is in fact compatible with the results from other experiments. Well done and well interpreted spectrophone experiments can possibly yield new information about the energy exchange ratio (and hence the important V—V transitions) for CO2−diluent collisions. It might also be possible to obtain more accurate values for the long V—T relaxation times for CO2 collisions with the heavy noble gases. These possibilities are discussed.