A simple reason for non-linear mixture rules in chemical kinetics. Part 1. Vibrational relaxation of diatomic molecules

Abstract

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 non-linearities 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.