Theory of Ion-Ion Recombination

Abstract

A new and basic theory o f ion—ion recombination as a function of gas density is developed from basic microscopic principles. A key equation for the distribution in phase space of ion pairs is derived together with an expression for the resulting rate x o f recombination. Further development of the theory leads to interesting insights into the full variation with N of a ,which is shown to yield the correct limits at low and high N .The recombination rate a is determined by the limiting step of the rate a _rn for ion reaction and of the rate a _tr for ion transport to the reaction zone. A n analytical solution of the time-dependent Debye—Smoluchowski equation, which is a natural consequence o f this theory, is provided for transport—reaction under a general interaction V , for an instantaneous reaction ( a _rn > a _tr ) and for a finite rate ( a _rn ~ a _tr ) of reaction with in a kinetic sink rendered compressible by variation of gas density. Expressions for the transient recombination rates are then derived, and are illustrated . The exhibited time dependence lends itself to eventual experimental verification at high N. A theory that investigates the variation o f a with ion density is also developed. Here the ion—ion interaction V can no longer be assumed ab initio to be pure coulomb but is solved self-consistently with the recombination . Recombination rates for various systems are illustrated as a function of N by a simplified method for the reaction rate. Finally, two theoretical procedures are proposed for the solution o f the general phasespace ion distributions.