Theory of bimolecular reaction rates limited by anisotropic diffusion

Abstract

The theory of bimolecular diffusion-limited reactions including drift effects is extended to anisotropic diffusion and/or non-spherical reaction volumes. One-dimensional as well as isotropic two-or three-dimensional diffusion are limiting cases of the general theory. It is shown that, in the case of preferentially one-dimensional diffusion, diffusivities in the transverse directions about 10⁷ times smaller than in the direction of fast diffusion may have an essential influence on the reaction kinetics. Such a situation appears to be realized in the diffusion-controlled annihilation of radiation-induced interstitials and vacancies in cadmium. Another interesting conclusion is that the rate of reactions between defects migrating in one dimension but along non-parallel lines (e.g. crowdion-crowdion reactions in f.c.c. metals) or reactions between H centres in alkali halides are controlled by two-dimensional diffusion and not by the much slower one-dimensional diffusion kinetics as has been assumed in the past.