Master equation analysis of thermal activation reactions: Energy-transfer constraints on falloff behavior in the decomposition of reactive intermediates with low thresholds

This paper deals with the high-temperature decomposition of reactive intermediates with low reaction thresholds. If these intermediates are created in situ, for example, through radical chain processes, their initial molecular distribution functions may be characteristic of the bath temperature and, under certain circumstances, peak at energies above the reaction threshold, Such an ordering of reaction thresholds and distribution functions has some similarities to that found during chemical activation. This leads to consequences that are essenially the inverse (larger rate constants than those deduced from steady-state distributions) of the situation for stable compounds under shock-heated conditions and hence reduces falloff effects. To study this behavior, rate constants for the unimolecular decomposition of allyl, ethyl, n-propyl, and n-hexyl radicals have been determined on the basis of the solution of the time-dependent master equation with specific rate constants from RRKM calculations. The time required for the molecules to attain steady-state distribution functions has been determined as a function of the energy-transfer parameter (the step size down) molecular size (heat capacity), high-pressure rate parameters, temperature, and pressure. At 101 kPa (1 atm) pressure, unimolecular rate constants near 10(7) s(-1) represent a lower boundary, above which steady-state assumptions become increasingly questionable. The effects on rate expressions and branching ratios for decomposition reactions during the pre-steady-state period are described.