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 ͑1993͔͒ studied shock-heated norbornene ͑NB͒ in krypton bath gas using the laser-schlieren technique and observed vibrational relaxation, unimolecular dissociation ͑to 1,3-cyclopentadiene and ethylene͒, 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 coefficients͒. The results cover the temperature range from ϳ300 to 1500 K and the excitation energy range from ϳ1 000 to 18 000 cm Ϫ1 . Three different models ͑based on the exponential step-size distribution͒ for the average downward energy transferred per collision, ͗⌬E͘ 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 ͗⌬E͘ down is temperature dependent. However, all three ͗⌬E͘ 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 Ϫ1 , 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.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

“…For more details of this ''Big-O'' notation, see the Appendix.͔ The discretized ME is an ordinary differential equation ͑ODE͒ that can be integrated from time zero to time t by Monte Carlo methods. [22][23][24][25][26] This approach appears to be good at simulating very complex dynamics, but can be slow to converge. Apart from Monte Carlo integration, an initial population can be integrated by direct time propagation using a stiff ODE integrator.…”

Energy transfer in master equation simulations: A new approach

“…However, in shock tube simulations [34][35][36] and in simulating reactions with very low energy barriers [26] the relevant energies extend all of the way to the bottom of the energy ladder. Furthermore, in 2D (E,J ) master equation simulations, the normalization problems are exacerbated because the 2D density of states is even more sparse and hence exhibits even greater fluctuations than in the one-dimensional (1D) version.…”

“…[44], the reactant was norbornene and the bath gas was krypton. The experiments were later modeled successfully by Barker and King [36], who used a master equation that was similar in many respects to MultiWell.…”

“…In the tests performed here, the model parameters found in our previous work [36] are used with the conventional and new approaches to ascertain the impact of the new approach. As discussed above, the two approaches are expected to give somewhat different results.…”

“…Tests were carried out by using two constant values of the energy transfer parameter α(y) for ClOOCl (small molecule, colliding with N 2 ) and for 1,1,1-trifluoroethane (intermediate size, colliding with Kr). Tests carried out for norbornene (large molecule, colliding with Kr) employed an energy-dependent parameter α(y) found from an analysis [36] of shock tube experimental data [44].…”