Dissociation of diatomic gases

Abstract

The Landau–Zener theory of reactive cross sections has been applied to diatomic molecules dissociating from a ladder of rotational and vibrational states. Although the preexponential factor of the Arrhenius rate expression is shown to be a complex function of the dimensionless activation energy E*/kT, the average over all states in the ladder is well represented by a single factor that varies about as T−n, where the coefficient n is the order of unity. This relation agrees very well with experimental data for dissociation of O2 and N2, for example. While the reactive cross section theory does not agree with experimental rate data when applied only to dissociation from ground state molecules, it gives good agreement when applied to a ladder of rotation–vibration states, since the bulk of the dissociations occur from states within about kT of the dissociation limit. The results validate previous empirical assignment of a single preexponential factor in the Arrhenius expression and justify the extrapolation of the expression well beyond the range of data. The theory is then used to calculate the effect of vibrational nonequilibrium on dissociation rate. For Morse oscillators the results are about the same as for harmonic oscillators, and the dissociation from a ladder of equilibrium rotational and nonequilibrium vibrational states is close to an analytic approximation provided by Hammerling, Kivel, and Teare for harmonic oscillators all dissociating from the ground rotational state.