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CHRIS CARRUTHERS and HESHEL TEITELBAUM. Can. J. Chem. 63, 38 1 (1 985). The generalized rate law for the vibrational relaxation of diatomic molecules is extended to include inert collision partners. V-V energy transfer processes are accounted for explicitly as are thermal effects. The molecules are treated as Morse oscillators as far as energetics are concerned; however, the microscopic rate constants are Landau-Teller type. It is found that the phenomenon of non-linear mixture rules arises when experimental data are forced to fit a first-order rate law. The persistence of V-V processes at times well-advanced into the relaxation zone is responsible for deviations from linearity. The nonlinearities are most pronounced at high temperatures, and can be avoided only by using extremely dilute mixtures. Several sources of ambiguity are pointed out. The type of excitation method influences the initial deviation from a Boltzmann distribution and plays a crucial role in determining the importance of V-V processes and hence the degree of non-linearity. 'Thus, when the initial distribution is Boltzmann as in shock waves, the mixture rule is found to be absolutely linear for the vibrational relaxation of diatomic molecules.Several examples, heretofore not recognized as such, are pointed out in the literature.CHRIS CARRUTHERS et HESHEL TEITELBAUM. Can. J. Chem. 63, 381 (1985). Dans le but d'inclure des partenaires inertes impliquks dans des collisions, on a Ctendu la loi gCnCralisCe de vitesse des relaxations vibrationnelles des molCcules diatomiques. On peut interprkter explicitement tant les effets thermiques que les processus de transferts d'knergie V-V. En autant que les Cnergies sont concernCes, on traite les molCcules comme des oscillateurs de Morse; toutefois, les constantes microscopiques de vitesse sont du type Landau-Teller. Lorsqu'on force les donntes expCrimentales a obCir B une loi de vitesse du premier ordre, on observe que le phCnomkne des rkgles de mClanges non-IinCaires se dCveloppe. C'est la persistance des processus V-V, B des temps bien avancCs dans la zone de relaxation, qui provoque des dCviations de la linCaritC. Les non-IinCaritCs sont plus prononcCes B hautes tempCratures et on peut les Cviter uniquement en utilisant des mClanges extrkmement diluCs. On identifie plusieurs sources d'ambiguitk. La mCthode d'excitation influence la deviation initiale, par rapport B la distribution de Boltzmann, et elle joue un r81e crucial dans la dCtermination de I'importance des proccssus V-V et, par conskquent, dans le degrC de non-IinCaritC. Donc, lorsque la distribution initiale est du type Boltzmann, comme dans les ondes de choc, on trouve que la rkgle des mClanges est absolument IinCaire pour la relaxation vibrationnelle des molCcules diatomiques.On a relevC, dans la IittCrature, plusieurs exemples qui n'avaient pas CtC reconnus comme tels.[

CHRIS CARRUTHERS and HESHEL TEITELBAUM. Can. J. Chem. 72, 714 (1994). The master equation is solved numerically for the time dependence of the vibrational level populations of HC1 (treated as a simple harmonic oscillator) during the bimolecular exchange reaction, Br + HCI -+ HBr + C1, taking into account the competition between reaction and vibrational equilibration subject to Landau-Teller T-V excitation. Strong deviations from Boltzmann distributions are found. A wide range of reactant concentrations, diluent concentrations and temperatures were explored. It was found that no significant reaction occurs before the establishment of a steady vibrational population distribution, confirming that the rate coefficient for non-equilibrium bimolecular exchange reactions can be determined from a simple analytical steady state treatment (J. Chem. Soc. Faraday Trans. 87, 229 (1991)). The rate of an isolated elementary bimolecular reaction, A + BC -+ AB + C, under non-equilibrium conditions can deviate seriously from the standard expression, keq [Aj[BC], and is better given by the law where [R] is the concentration of the collisional equilibrator, R, and a and g are constants depending only on temperature. This generalized rate law describes not only the initial rate but also the rate all the way up to completion, in the absence of the reverse reaction.