The Waite-Leibfried theory

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The said allows us to understand the importance of the kinetic approach developed for the first time by Waite and Leibfried [21, 22]. In essence, as is seen from Fig. 1.15 and Fig. 1.26, their approach to the simplest A + B — 0 reaction does not differ from the Smoluchowski one However, coincidence of the two mathematical formalisms in this particular case does not mean that theories are basically identical. Indeed, the Waite-Leibfried equations are derived as some approximation of the exact kinetic equations due to a simplified treatment of the fluctuational spectrum a complete set of the joint correlation functions for kinds of particles is replaced by 

THE HAITE-LEIBFRIED APPROACH TO THE BIMOLECULAR KINETICS (REACTIONS A-t-B B AND A-fB- 0) 

Omstein-Zemike theory of the critical opalescence which operates also with a linear equation for the joint correlation function. 

A new principal element of the Waite-Leibfried theory compared to the Smoluchowski approach is the relation between the effective reaction rate K t) and the intermediate order parameter x — Xab( )0- I its turn, the Smoluchowski approach is just an heuristic attempt to describe the simplest irreversible bimolecular reactions A + B—A + B—and A + B — 0 and cannot be extended for more complicated reactions. The Waite-Leibfried approach is not limited by these simple reactions only it could be applied to the reversible reactions and reaction chains. However, in the latter case the particular linearity in the joint correlation function x = XAB(f, 0 does not always mean linearity of equations since additional non-linearity caused by particle densities can arise. 

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