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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.

We present the full solution of the master equation for the system with reversible isomerization and decomposition channels at low pressures. As an example of such a system we consider the cis-trans isomerization of 2-butene. At high temperatures cis-Zbutene decomposes into butadiene and hydrogen. The effect of isomerization on the decomposition rate coefficient was studied and indicated multiple steady-state behavior. At 1200 K, for example, a true steady state is achieved only after 75% of the product has been formed. This behavior is explained in terms of relaxation to the equilibrium distribution between cis and trans isomers. The first plateau in the rate coefficient corresponds to the irreversible regime of isomerization when two isomers are far from equilibrium, while the second plateau or true steady state is established after equilibrium between isomers has been reached. The effect is not observed at either low temperatures or high pressures.

The decomposition kinetics of n-pentyl radicals in the high temperature regime where steady state distributions are not achieved and reversible isomerization to decomposing 2-pentyl radicals is of importance has been analyzed through the solution of the time-dependent master equation. The reactions are characterized by low activation thresholds and lead to large rate constants that vary with time. Particular attention is paid to branching ratios for direct decomposition of the n-pentyl radical and the decomposition that follows reversible isomerization to the 2-pentyl species. The behavior of the system under a variety of conditions is described and the use of branching ratios as a possible means of characterizing the reactions in a manner that is compatible with present methods for employing kinetic data for simulating complex chemical phenomenon is considered. At higher temperatures, rate constants and branching ratios collapse to limiting values. The combination of limiting and the onset of steady state behavior complicates the situation at lower temperatures. The overall behavior of such systems is highly dependent on the magnitude of the barrier to isomerization. The extent of departures from the high pressure-branching ratios are defined.