Modeling vibrational energy exchange of diatomic molecules using the Morse interatomic potential

Abstract

A model of dissociation of diatomic molecules in intermolecular collisions, for use in Direct Simulation Monte Carlo (DSMC) calculations, has been proposed by Lord. This model, is a development of the exact available energy or vibrationally linked chemistry model of Bird, which models dissociation and chemical reactions directly via Borgnakke–Larsen type energy redistributions between translation and internal modes, dissociation being assumed to occur whenever the vibrational energy of a molecule exceeds its dissociation energy. The model employs the correct energy level scheme of a Morse oscillator and has been shown to yield equilibrium dissociation rate constants for N2 which are in excellent agreement with published values. A shortcoming of the model, however, is that it is purely classical, the molecular vibrational energy being assumed to be continuously distributed. Although this is not a serious defect for the prediction of dissociation, since the dissociation energy is normally many times the largest vibrational energy level spacing, it means that the model is unsuitable for describing vibrational energy exchange at lower collision energies where quantization effects are significant and must be taken into account in a way which satisfies detailed balance at equilibrium. The present paper describes a quantized extension of the earlier model which satisfies this requirement and can therefore be used in conjunction with it. It is shown that the two models become identical at high collision energies.