Nonequilibrium Effects in Recombination—Dissociation Kinetics

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Abstract
It is well known that if a mixture of atoms and diatomic molecules are at thermodynamic equilibrium in a chemically inert, constant-temperature heat bath, the molecular internal degrees of freedom can be characterized by a Maxwell—Boltzmann or equilibrium distribution. If the temperature of this system is suddenly changed, atoms will start to recombine or molecules will start to dissociate in order to restore chemical equilibrium; however, the diatomic molecules will no longer have a Maxwell—Boltzmann distribution. The rate at which these internal energy levels approach equilibrium is influenced by the reaction velocity, the rate at which molecules are created or destroyed. Since it is relatively easy to dissociate highly excited molecules, the rate of reaction is coupled to the rate at which the internal degrees of freedom relax to an equilibrium or Maxwell—Boltzmann distribution. It is very difficult to develop a theory of recombination—dissociation kinetics that explicitly accounts for the coupling of the rate of reaction to the rate of relaxation. Several theoretical techniques have been proposed for solving this problem; however there seem to be certain discrepancies in the theories that are based on these techniques. In the present study, an iterative perturbation procedure, which couples the rate of relaxation to the rate of reaction in a self-consistent manner, is used to derive a nonequilibrium theory of recombination—dissociation kinetics. One of the immediate advantages of this theory is that it includes many of the existing theories as special cases. This theory provides a way of predicting under what conditions it is possible to evaluate atomic recombination coefficients from a knowledge of the dissociation rate constant and the equilibrium constant for the reaction. For a nearest-neighbor transition model of a diatomic molecule, this theory also predicts that the atomic recombination coefficients should decrease as T−2 at sufficiently high temperatures.