Multi-temperature vibrational energy relaxation rates in CO2

Abstract

Rates of vibrational energy relaxation in carbon dioxide are studied in the framework of the three-temperature kinetic-theory approach. Vibrational–translational transitions in the bending mode and inter-mode exchange of vibrational quanta are considered. In the zero-order approximation of the generalized Chapman–Enskog method, the energy relaxation rates in the coupled symmetric–bending and asymmetric modes are expressed in terms of thermodynamic forces similar to chemical reaction affinities, and a compact representation for the vibrational energy production rates is proposed. Linearized theory is developed, and analytical ratios of linearized relaxation rates to those defined by the original Landau–Teller (LT) theory are obtained. The relaxation rates are calculated using the Schwartz–Slawsky–Herzfeld (SSH) and forced harmonic oscillator models for the vibrational energy transition probabilities in the temperature range 200 K–10 000 K. For inter-mode exchanges, using the SSH theory yields significantly underpredicted relaxation rates. The ranges of applicability for the LT formula and linearized theory are estimated; the original LT formula for inter-mode vibrational energy exchanges is not capable of accounting for the excitation of both vibrational modes; linearized models yield better results. Possible steps for improving the numerically efficient LT model are proposed.