Analytical models for state-specific diatomic dissociation rate coefficients

Abstract

Two analytical models are presented to approximate the temperature dependent, rotationally-averaged vibrational-state-specific dissociation rate coefficient for collisions between diatomic molecules and rare gas atoms at combustion temperatures. The new models are derived by making simplifying approximations to a more detailed theoretical model recently reported in the literature. For accuracy, the first model requires, for a given collision pair, knowledge of the maximum vibrational quantum number, a single vibrational-rotational energy and an interaction parameter for dissociation, all of which are tabulated in this article for collisions of Ar with p-H 2 , O 2 , N 2 , and CO. This is in contrast to the recently reported theoretical model, which requires knowledge of all vibrational-rotational energies below the dissociation threshold, in addition to the interaction parameter for dissociation. The second model is simpler and more general than the first, but less accurate. To completely specify this model, knowledge of only the hard sphere cross section, and the characteristic temperatures for vibration and dissociation is required. The two analytical models are shown to agree well with the published theoretical values, with the accuracy of each model increasing with increasing temperature. The present models provide an accurate and efficient means of computing thousands or millions of rate coefficients for use in numerical simulations of combustion processes that couple kinetic equations with the governing equations of fluid dynamics.

An improved potential energy surface and multi-temperature quasiclassical trajectory calculations of N2 + N2 dissociation reactions

“…10,11 Indeed, several early works found evidence that dissociation caused significant depletion of the high vibrational levels (resulting in non-Boltzmann energy distributions), because molecules in such levels were favored to dissociate. 6,12,13 Finally, still more advanced models, such as the Morse potential model of Johnston and Birks with all transitions allowed, 3 the forced harmonic oscillator (FHO) framework of Adamovich et al, [14][15][16][17] and the information-theoretic approach of Gonzales and Varghese, [18][19][20] permitted both multiquantum transitions and dissociation from any vibrational level. We could also include in this category the analytic model of Macheret and Rich, 21 which assumes classical, impulsive collisions between molecules and a "threshold function" for the minimum translational energy needed for a dissociative collision.…”

A Coupled Vibration-Dissociation Model for Nitrogen from Direct Molecular Simulation

“…Macheret and Adamovich [10] have proposed a forced harmonic oscillator (FHO) model, which allows for multi-quantum jumps using a free-rotation approximation and impulsive collision limit . Finally, information theory (also used in our present work) has been utilized by previous researchers [11,12,13] to formulate dissociation models.…”