Pressure- and Temperature-Dependent Combustion Reactions

In combustion systems, many reactions are simple thermal unimolecular isomerizations or dissociations, or the reverse thereof. It is well understood that these reactions typically depend on temperature, pressure and the nature of the bath gas. These kinds of reactions are a subset of the more general behavior that can be described as free radical association reactions that produce highly energized intermediates, which can isomerize or dissociate via multiple chemical pathways. Each reaction rate depends on excitation energy and all of the competing reactions occur in competition with collisional activation and deactivation. These complicated multi-well, multi-channel reaction systems can only be simulated accurately by using master equation techniques. In this paper, master equation calculations are discussed for several examples of reactions important in combustion (and atmospheric chemistry). Current master equation codes are based on statistical RRKM reaction rate constants (including quantum mechanical tunneling) and simplified models for collisional energy transfer. A pragmatic semi-empirical approach is adopted in order to compensate for limited knowledge. The reaction energies needed for RRKM calculations are usually obtained from quantum chemistry calculations, which are often of limited accuracy and may be adjusted empirically. Energy transfer cannot be predicted accurately and must be parameterized by fitting experimental data. For combustion modeling, the master equation results are usually expressed as chemical reactions with rate constants fitted to empirical algebraic equations. However, the results may be expressed more accurately by interpolating from look-up tables. Several current research issues are also mentioned, including the effects of angular momentum conservation, vibrational anharmonicity, slow intramolecular vibrational energy redistribution, and assumptions surrounding the details of collisional energy transfer.