Incubation in cyclohexene decomposition at high temperatures

A detailed master equation simulation has been carried out for the thermal unimolecular decomposition of C₆H₁₀ in a shock tube. At the highest temperatures studied experimentally J. H. Kiefer and J. N. Shah, J. Phys. Chem., 91, 3024 (1987)], the average thermal vibrational energy is greater than the reaction threshold and therefore 〈ΔE〉 (up and down steps) is positive for molecules at that energy, rather than negative; the converse is true at lower temperatures. The calculated incubation time, in which the decomposition rate constant rises to 1/e of its steady state value, is found to be only weakly dependent on temperature (at constant pressure) between 1500 K and 2000 K and to depend almost exclusively on 〈ΔE〉_d (down steps, only), and not on collision probability model. Simulations of the experimental data show the magnitude of 〈ΔE〉_d depends weakly on assumed collision probability model, but is nearly independent of temperature. The second moment 〈ΔE〉^½ is found to be independent of both temperature and transition probability model. The experimental data are not very sensitive to the possible energy-dependence of 〈ΔE〉_d for a wide range of assumptions. It is concluded that the observed experimental “delay times” probably can be identified with the incubation time; further experiments are desirable to test this possibility and obtain more direct measures of the incubation time.