On the Stochastic Theory of Dissociation and Recombination of Diatomic Molecules in Inert Diluents

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Abstract
A formal stochastic theory is developed to describe the dissociation and recombination of diatomic molecules by inert third bodies, and the manner in which this reaction is coupled with internal relaxation processes. Singular perturbation methods are used to obtain a uniformly valid asymptotic solution to the nonlinear master equation in the limit when the internal relaxation times are short compared with the dissociation time. The solution shows that the reaction begins with a short transient during which the internal distribution function relaxes from the initial state to a ``quasisteady'' state. Following this, the reaction obeys the usual phenomenological equations with well-defined rate coefficients. It is shown that to lowest order the observed rate coefficients are constants during the quasisteady period, and retain their nonequilibrium values as the reaction approaches equilibrium. In higher orders the dissociation and recombination rate coefficients depend on the instantaneous composition of the gas. However, the ratio of the instantaneous values of the dissociation and recombination rate coefficients remains equal to the equilibrium constant. It is also shown that the initial transient causes an observable ``incubation time'' to appear in the reaction. The formula for the incubation time is derived, and applied to the special cases of dissociation behind a shock wave and recombination following flash photolysis. The results are applied to the dissociation and recombination of diatomic molecules possessing rotational, vibrational, and electronic degrees of freedom.