Fall-off behavior of models of thermal unimolecular reactions

Abstract

Aspects of fall-off behavior for thermal unimolecular reactions were investigated theoretically. The starting point for this investigation was the master equation which describes the generally accepted picture of collisional excitation and reaction. Deviations from simple Lindemann behavior were analyzed in terms of deviations from linearity of the reciprocal of the rate coefficient as a function of reciprocal concentration (or pressure) of collider gas. This function was shown to be always either linear or concave downward under conditions for which the rate of chemical reaction is slow compared to the rate of relaxation of the internal state distribution of the reacting molecules. Analytic results were obtained for two collision models of interest, the stepladder model and the separable exponential model. The strong collision limits for these models were carefully defined, and it was shown that the fall-off behavior becomes more Lindemann-like as the strong collision limit is approached. It was further shown how this characteristic of the approach to the strong collision limit is related to the pressure dependence of weak collision effects.