The reactions of alkyl peroxy radicals (RO(2)) play a central role in the low-temperature oxidation of hydrocarbons. In this work, we present high-pressure rate estimation rules for the dissociation, concerted elimination, and isomerization reactions of RO(2). These rate rules are derived from a systematic investigation of sets of reactions within a given reaction class using electronic structure calculations performed at the CBS-QB3 level of theory. The rate constants for the dissociation reactions are obtained from calculated equilibrium constants and a literature review of experimental rate constants for the reverse association reactions. For the concerted elimination and isomerization channels, rate constants are calculated using canonical transition state theory. To determine if the high-pressure rate expressions from this work can directly be used in ignition models, we use the QRRK/MSC method to calculate apparent pressure and temperature dependent rate constants for representative reactions of small, medium, and large alkyl radicals with O(2). A comparison of concentration versus time profiles obtained using either the pressure dependent rate constants or the corresponding high-pressure values reveals that under most conditions relevant to combustion/ignition problems, the high-pressure rate rules can be used directly to describe the reactions of RO(2).

The unimolecular reactions of hydroperoxy alkyl radicals (QOOH) play a central role in the low-temperature oxidation of hydrocarbons as they compete with the addition of a second O(2) molecule, which is known to provide chain-branching. In this work we present high-pressure rate estimation rules for the most important unimolecular reactions of the β-, γ-, and δ-QOOH radicals: isomerization to RO(2), cyclic ether formation, and selected β-scission reactions. These rate rules are derived from high-pressure rate constants for a series of reactions of a given reaction class. The individual rate expressions are determined from CBS-QB3 electronic structure calculations combined with canonical transition state theory calculations. Next we use the rate rules, along with previously published rate estimation rules for the reactions of alkyl peroxy radicals (RO(2)), to investigate the potential impact of falloff effects in combustion/ignition kinetic modeling. Pressure effects are examined for the reaction of n-butyl radical with O(2) by comparison of concentration versus time profiles that were obtained using two mechanisms at 10 atm: one that contains pressure-dependent rate constants that are obtained from a QRRK/MSC analysis and another that only contains high-pressure rate expressions. These simulations reveal that under most conditions relevant to combustion/ignition problems, the high-pressure rate rules can be used directly to describe the reactions of RO(2) and QOOH. For the same conditions, we also address whether the various isomers equilibrate during reaction. These results indicate that equilibrium is established between the alkyl, RO(2), and γ- and δ-QOOH radicals.

Reliable estimates of high-pressure-limit reaction rates as a function of temperature are essential for the development of reaction sets that can be used to model complex chemical processes. As these reaction rates depend primarily on the thermodynamic properties of the reactants and the corresponding transition state, this work attempts to predict these properties within the framework of group additivity. Using ab initio calculations at the CBS-Q level, with additional HF/6-31G(d‘) potential energy surfaces (PES) to define the hindrance potential for internal rotations, we calculate heats of formation (Δf H 298), entropies (S 298), and heat capacity values (C p(T)) of species involved in prototypical H abstraction reactions. From these, we derive new group additivity values (GAV) for transition-state-specific moieties. The new GAV allow rapid calculation of reaction rates for entire reaction families with good accuracy. This work presents a detailed description of the methodology and has its focus on H abstraction from alkanes by H and CH3. Subsequent papers will apply this methodology to derive GAV for other reaction families of interest in combustion processes.

This supplemental material contains Cartesian coordinates (Angstroms) for all structures at the CBS-QB3 level of theory.

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Accurate description of reactions between propyl radicals and molecular oxygen is an essential prerequisite for modeling of low-temperature propane oxidation because their multiple reaction pathways either accelerate the oxidation process via chain branching or inhibit it by forming relatively stable products. The CBS-QB3 level of theory was used to construct potential energy surfaces for n-C(3)H(7) + O(2) and i-C(3)H(7) + O(2). High-pressure rate constants were calculated using transition state theory with corrections for tunneling and hindered rotations. These results were used to derive pressure- and temperature-dependent rate constants for the various channels of these reactions under the framework of the Quantum Rice-Ramsperger-Kassel (QRRK) and the modified strong collision (MSC) theories. This procedure resulted in a thermodynamically consistent C(3)H(7) + O(2) submechanism, which was either used directly or as part of a larger extended detailed kinetic mechanism to predict the loss of propyl and the product yields of propylene and HO(2) over a wide range of temperatures, pressures, and residence times. The overall good agreement between predicted and experimental data suggests that this reaction subset is reliable and should be able to properly account for the reactions of propyl radicals with O(2) in propane oxidation. It is also demonstrated that for most conditions of practical interest only a small subset of reactions (e.g., isomerization, concerted elimination of HO(2), and stabilization) controls the oxidation kinetics, which makes it possible to considerably simplify the mechanism. Moreover, we observed strong similarities in the rate coefficients within each reaction class, suggesting the potential for development of relatively simple rate constant estimation rules that could be applied to analogous reactions involving hydrocarbon radicals that are too large to allow accurate detailed electronic structure calculations.

Modeling of low-temperature ethane oxidation requires an accurate description of the reaction of C(2)H(5) + O(2), because its multiple reaction channels either accelerate the oxidation process via chain branching, or inhibit it by forming stable, less reactive products. We have used a steady-state chemical-activation analysis to generate pressure and temperature dependent rate coefficients for the various channels of this system. Input parameters for this analysis were obtained from ab initio calculations at the CBS-QB3 level of theory with bond-additivity corrections, followed by transition state theory calculations with Wigner tunneling corrections. The chemical-activation analysis used QRRK theory to determine k(E) and the modified strong collision (MSC) model to account for collisional deactivation. This procedure resulted in a C(2)H(5) + O(2) submechanism which was either used directly (possibly augmented with a few C(2)H(5) generating and consuming reactions) or as part of a larger extended mechanism to predict the temperature and pressure dependencies of the overall loss of ethyl and of the yields of ethylene, ethylene oxide, HO(2), and OH. A comparison of the predictions using both mechanisms allowed an assessment of the sensitivity of the experimental data to secondary reactions. Except for the time dependent OH profiles, the predictions using the extended mechanism were in good agreement with the observations. By replacing the MSC model with master equation approaches, both steady-state and time dependent, it was confirmed that the MSC assumption is adequate for the analysis of the C(2)H(5) + O(2) reaction. The good overall performance of the C(2)H(5) + O(2) submechanism developed in this study suggests that it provides a good building block for an ethane oxidation mechanism.