Vibrational energy transfer in shock-heated norbornene

Abstract

Recently, Kiefer et al. [J. H. Kiefer, S. S. Kumaran, and S. Sundaram, J. Chem. Phys. 99, 3531 (1993)] studied shock-heated norbornene (NB) in krypton bath gas using the laser-schlieren technique and observed vibrational relaxation, unimolecular dissociation (to 1,3-cyclopentadiene and ethylene), and dissociation incubation times. Other workers have obtained an extensive body of high-pressure limit unimolecular reaction rate data at lower temperatures using conventional static and flow reactors. In the present work, we have developed a vibrational energy transfer-unimolecular reaction model based on steady-state RRKM calculations and time-dependent master equation calculations to satisfactorily describe all of the NB data (incubation times, vibrational relaxation times, and unimolecular rate coefficients). The results cover the temperature range from ∼300 to 1500 K and the excitation energy range from ∼1 000 to 18 000 cm−1. Three different models (based on the exponential step-size distribution) for the average downward energy transferred per collision, 〈ΔE〉down were investigated. The experimental data are too limited to enable the identification of a preferred model and it was not possible to determine whether the average 〈ΔE〉down is temperature dependent. However, all three 〈ΔE〉down models depend linearly on vibrational energy and it is concluded that standard unimolecular reaction rate codes must be revised to include energy-dependent microcanonical energy transfer parameters. The choice of energy transfer model affects the deduced reaction critical energy by more than 2 kcal mol−1, however, which shows the importance of energy transfer in determining thermochemistry from unimolecular reaction fall-off data. It is shown that a single set of Arrhenius parameters gives a good fit of all the low temperature data and the shock-tube data extrapolated to the high pressure limit, obviating the need to invoke a change in reaction mechanism from concerted to diradical for high temperature conditions. Some possible future experiments are suggested.