No abstract

The master equation for unimolecular decomposition and collisional deactivation of an energetic species A formed by chemical reaction was investigated. Particular attention was paid to the validity of the approximation of neglecting upward transitions, i.e., collisional transitions in which energy is added to A. Calculations of κa , the collision frequency ω times the ratio of the rate of decomposition of A to that of deactivation, were performed for the stepladder model for very large and very small ω and for the separable model for small ω. Neglect of upward transitions reduces κa. For the stepladder model the amount by which κa is reduced is greater for large ω than it is for small ω. It was also found that κa is more sensitive to changes in 〈Δε〉−, the average internal energy loss from A in deactivating collisions, when ω is small than it is when ω is large. Thus, when fitting computational results to experimental data, one derives a 〈Δε〉− which is too small if one neglects upward transitions, and the amount by which 〈Δε〉− is too small is considerably greater for large ω than it is for small ω. This result explains both qualitatively and semiquantitatively the discrepancies in 〈Δε〉−’s derived from stepladder model calculations of low pressure and high pressure κa’s for sec-butyl radicals in the presence of rare gas diluents.

An equation of state [Eq. (2) of the text] which has been successfully applied to pure liquids composed of small, nonpolar molecules was generalized to the case of binary mixtures. The generalized equation was used to calculate excess thermodynamic functions for 10 equimolar mixtures, and agreement with experiment was found to be generally good. The partial molar heat of solution of gaseous neon in liquid argon was also calculated, but good agreement with experiment was not obtained in this calculation.

A number of results which pertain to the rate of collisionally induced gas phase dissociation of diatomic molecules were derived. In the standard model for this process collisions bring about random transitions between internal states of the diatom and ultimately lead to dissociation. The rate constant kd for such a model is simply related to λ1, the smallest eigenvalue of a matrix κ which is expressed in terms of rate constants for detailed transitions between states of the diatom. A standard approximation for λ1 is the solution of the linearized characteristic equation for κ. It was shown that the kd so obtained is very nearly the same as the kd obtained from the steady state approximation. If the states of the diatom are assumed to form a continuum, then κ becomes the kernel of an integral operator. Relations between discrete and continuum models were established. It was shown that equivalent diffusion equations which have been derived for the continuum case have analogs in the discrete case. These discrete analogs pertain to stepladder models, models for which transitions are allowed only between adjacent states. It was further shown how discrete (quantum) models and continuum (classical) models are linked by quasicontinuum models which, while still discrete, are formulated in terms of elements of the continuum rather than in terms of individual quantum states. Some of the foregoing results were illustrated by a treatment of the separable exponential model. Parameters α and β for this model have a straightforward physical interpretation. The rate constant and the state distribution for the model are obtainable in closed form via the steady state approximation. Their dependence on α and β is readily interpretable physically. The state distribution for the model was shown to be potentially useful in variational calculations of kd for other models. In such calculations, α and β would be chosen so as to maximize the variational lower bound to λ1 for the model in question.

A Morse oscillator model for recombination of hydrogen and its isotopes was investigated computationally. The model is very similar to one recently studied by Pritchard and co-workers. The aims of the study were the test of certain approximations and the determination of the range of validity of the model. It was found that at low temperatures the steady state approximation is an increasingly accurate and increasingly convenient approximation. A way of estimating the error arising from this approximation was proposed. Other approximations which were tested gave unsatisfactory results. The rate constant vs. temperature curve for the model does not agree well with the experimental curve for hydrogen in argon except insofar as it reproduces the observed levelling-off at high temperatures. For the model this result may be ascribed to increasing relative rates for multiquantum transitions among the levels of the diatom. The model does give the experimentally observed ratios of the rate constants for H-and D-atom recombination. This result indicates that the important factor in determining the isotope ratio is the effect of mass change on the density of states rather than its effect on the collision dynamics.NEIL S. SNIDER. Can. J. Chem. 55, 3464 (1977). On a etudie, a I'aide d'un calculateur, la recombinaison de I'hydrogene et de ses isotopes en prenant comme modele l'oscillateur de Morse. LC modtle est tres proche de celui rtcemment Btudie par Pritchard et ses collaborateurs. LC but de cette etude est de verifier certaines approximations et de determiner la zone oh le modele est valable. I1 apparait qu'a basse temperature I'approximation de 1'Ctat stationnaire est de plus en plus exacte et convenable. On propose une methode d'haluation de I'erreur sur cette approximation. Plusieurs autres approximations n'ont pas donne de bons resultats. La courbe de la constante de vitesse vs. la temptrature pour ce modde ne correspondent pas bien a la courbe expCrimentale pour l'hydrogtne dans I'argon. On peut utiliser cette courbe en autant qu'elle reproduit le palier observe a haute tempQature. LC resultat obtenu pour ce modele peut ttre attribut a l'accroissement des vitesses relatives de transitions multiquantiques parmi les niveaux du diatome. D'ailleurs, le modtle reproduit les rapports qui sont observes expCrimentalen~ent pour les constantes de vitesse pour la combinaison des atomes H et D. Ce resultat suggere que le phknomtne majeur dans la determination du rapport isotopique est I'effet de la variation de masse sur la densitt des ttats plut8t que son effet sur la dynamique des collisions.[Traduit par le journal]