NONEQUILIBRIUM EFFECTS IN FREE-RADICAL RECOMBINATION AND ION-MOLECULE REACTION KINETICS

Distortion of the molecular velocity distribution functions from the Maxwellian form and the resulting deviation of the reaction-rate coefficients from the values calculated with the equilibrium assumption of conventional chemical kinetics are considered for two types of reactions in dilute, isothermal, spatially uniform gas mixtures : free-radical recombination reactions and ion-molecule reactions, both proceeding without an activation energy. The reactive collision cross sections used are those derived from the attractive potentials of the reacting pairs, which are inversely proportional to the sixth and the fourth powers of interparticle distances, respectively. The treatment is based on generalized Boltzmann equations which take into account the effects of reactive collisions, as well as elastic collisions, on the change of the velocity distributions with time. For free-radical recombination reactions, a first-order perturbation approximation analogous to that of Chapman and Enskog is used to derive the composition dependence of nonequilibrium effects. This differs from Mahan's earlier calculation; and, contrary to Mahan's result, the present calculation shows that the deviation of the rate coefficient from the equilibrium value remains small for any mole fraction of free radicals and typical values for various molecular parameters. The possible origin of the difference between the two calculations is analyzed. For the ion-molecule reactions, it is first shown that there is no distortion of the Maxwellian distribution by first-order perturbation theory irrespective of the choice of the series expansion. Next it is proved, without using a perturbation scheme, that nonequilibrium effects in the reaction rates vanish exactly for the ion-molecular reactions. The last conclusion is reached without an explicit assumption about the form of the velocity distribution, just as in the case of the transport properties of Maxwellian molecules which interact according to an inverse fourth-power repulsion potential. The reason for small or vanishing nonequilibrium effects in these reactions without activation energy is discussed.