High-Pressure-Limit and Pressure-Dependent Rate Rules for Unimolecular Reactions Related to Hydroperoxy Alkyl Radicals in Normal Alkyl Cyclohexane Combustion. 1. Concerted HO₂ Elimination Reaction Class and β-Scission Reaction Class

The reactions of the concerted HO₂ elimination from alkyl peroxy radicals and the β-scission of the C–OOH bond from hydroperoxy alkyl radicals, which lead to the formation of olefins and HO₂ radicals, are two important reaction classes that compete with the second O₂ addition step of hydroperoxy alkyl radicals, which are responsible for the chain branching in the low-temperature oxidation of normal alkyl cycloalkanes. These two reaction classes are also believed to be responsible for the negative temperature coefficient behavior due to the formation of the relatively unreactive HO₂ radical, which has the potential to inhibit ignition of normal alkyl cycloalkanes. In this work, the kinetics of the above two reaction classes in normal alkyl cycloalkanes are studied, where reactions in the concerted elimination class are divided into subclasses depending upon the types of carbons from which the H atom is eliminated and the positions of the reaction center (on the alkyl side chain or on the cycle), and the reactions in the β-scission reaction class are divided into subclasses depending upon the types of the carbons on which the radical is located and the positions of the reaction center. Energy barriers by using quantum chemical methods at the CBS-QB3 level, high-pressure-limit rate constants by using canonical transition state theory, and pressure-dependent rate constants at pressures from 0.01 to 100 atm by using Rice–Ramsberger–Kassel–Marcus/Master Equation theory are calculated for a representative set of reactions from methyl cyclohexane to n-butyl cyclohexane in each subclass, from which high-pressure-limit rate rules and pressure-dependent rate rules for each subclass are derived from the average rate constants of reactions within each subclass. A comparison of the rate constants for the reactions in the two reaction classes calculated in this work is made with the rate constants of the same reactions from available mechanisms published in the literature, where most of the rate constants are approximately estimated from analogous reactions in alkanes or small alkyl cyclohexanes, and it is found that a large difference may exist between them, indicating that the present work, which provides more accurate kinetic parameters and reasonable rate rules for these reaction classes, can be helpful to construct higher-accuracy mechanism models for normal alkyl cyclohexane combustion.