The reaction between ethyl and molecular oxygen II: Further analysis

Abstract

The present investigation is a rather substantial extension and elaboration of our previous work on the same reaction. In this article we accomplish four primary objectives:1. We show quantitatively how sensitive the high-temperature rate coefficient k(T) is to E 02 , the threshold energy of the transition state for direct molecular elimination of HO 2 from ethylperoxy radical (C 2 H 5 O 2 ), thus deducing a value of E 02 = −3.0 kcal/mol (measured from reactants). 2. We derive the result that k 0 (T) ≈ k ∞ (T) in the high-temperature regime, where k 0 (T) is the zero-pressure rate coefficient, and k ∞ (T) is the infinite-pressure rate coefficient for the bimolecular channel. 3. Most importantly, we discuss the three different regimes of the reaction (low-temperature, transition, and high-temperature) in terms of the eigenvectors and eigenvalues of G , the transition matrix of the master equation. The transition regime is shown to be a region of avoided crossing between the two chemically significant eigenvalue curves in which the thermal rate coefficient k(T , p) jumps from one eigenvalue to the other. This jump is accompanied by a "mixing" of the corresponding eigenvectors, through which both eigenvectors deplete the reactant. The onset of the high-temperature regime is triggered by reaching the "stabilization limit" of the ethylperoxy adduct, a limit that is induced by a shift in equilibrium of the stabilization reaction. Our identification of the prompt and secondary HO 2 formed by the reaction with these eigenvalue/eigenvector pairs leads to good agreement between theory and the experiments of Clifford et al. (J Phys Chem A 2000, 104, 11549-11560). 4. Lastly, we describe the master equation results in terms of a set of elementary reactions and phenomenological rate coefficients.

Molecular size dependent falloff rate constants for the recombination reactions of alkyl radicals with O2 and implications for simplified kinetics of alkylperoxy radicals

“…The falloff rate constant calculated either from the dissociation steady state or from the chemical activation steady state has no physical meaning at these conditions. It should be noted that the essentially the same conclusion has been already reached by Miller and Klippenstein [35], but in slightly different manner, for C 2 H 5 + O 2 at high temperatures. Also, the highly related problem of the nonequilibrium factor, f ne , has been well discussed by Gilbert et al [45], Tsang et al [31], and Miller and Klippenstein [64].…”

“…It should be noted that the near-Boltzmann distribution assumption for RO 2 in partial equilibrium with R + O 2 suggested in this study does not conflict with the detailed chemically significant eigenpair analysis by Miller and Klippenstein [35] or their proposed phenomenological rate coefficients. To reproduce the transient behavior, such as the "prompt" HO 2 formation observed by Clifford et al [60], phenomenological rate coefficients are certainly needed.…”

“…12, is not sufficiently larger than the k ∞ (HO 2 ). Although these experimental observations have been fully analyzed in the RRKM/ME calculations by Miller and Klippenstein [35], present analysis gives a simple and intuitive picture for the interpretation of the phenomena when the system is in near partial equilibrium.…”

“…Although the concerted HO 2 elimination and intramolecular hydrogen shift reactions are important channels of the reactions of R + O 2 [27,60,35], these exit channels were ignored for the first attempt to evaluate the molecular-size dependent falloff expression shown below, to avoid the complexity arising from the difference of exit channels among different types of alkyl radicals. The resultant "hypothetical" falloff and low-pressure limiting (LPL) rate constants will be used to elucidate the essential problems and trends caused by the increase in the molecular size.…”

“…The high-pressure limiting (HPL) rate constants have been systematically studied and parameterized [26][27][28][29][30], the Rice-Ramsperger-KasselMarcus (RRKM) theory/master equation (ME) analysis has been successfully extended to the complex multiple-well multiple-channel reactions [31][32][33][34], the falloff behaviors of the many important systems have been well analyzed [35,36], and formulae giving guidance for deciding the validity of the HPL assumption depending on the molecular size have been developed [37]. However, no systematic study has been reported, to the author's knowledge, for the variation of the falloff rate constants by the alkyl substitution or by the increase in the size of the molecule, which is required to construct the reliable kinetic models for various classes and sizes of the hydrocarbons.…”