Fall-off behavior of the separable exponential Kassel model for thermal unimolecular reactions

Abstract

For thermal unimolecular reactions a fairly realistic model can be constructed by combining the separable exponential model for the collisional activation and deactivation steps with the Kassel model for the reactive steps. The resulting model admits of interesting results which can be expressed analytically. It is argued that the model has a well defined strong collision limit, and an equation for the efficiency factor β̄ for weak colliders is then derived. This factor is a function of the ratio of the rate coefficient κ to its high pressure limiting value κ∞. The model qualitatively, albeit not quantitatively, reproduces the experimental behavior of β̄(κ/κ∞) for methyl isocyanide isomerization in helium at 518 K. Experiments and previous computations both show β̄(κ/κ∞) to decrease at a decreasing rate. The separable exponential-Kassel model gives β̄’s which either increase or decrease with κ/κ∞, but increasing β̄’s occur only for physically unrealistic values of one of the model’s parameters. The model shows that the decreasing rate of decrease of β̄ is related to the small value of the Kassel parameter s for methyl isocyanide isomerization. It predicts that β̄ decreases at an increasing rate for reactions with large s.