Diffusion controlled reaction rate of molecules with anisotropic reactivity and interaction potential

Abstract

Diffusion controlled reactions of molecules with highly anisotropic reactivity and interaction potential are considered. The limit of high anisotropy corresponds to a small size of both reactivity region ( l r) and potential ( a) ( a is the Onsager radius) in comparison with the characteristic size of molecules, R. A method of calculation of reaction rate constants (RRCs) in this limit is proposed. This method is based on the exact solution of the Smoluchowski equation for a pair of molecules. A simple analytical formula for the RRC of noninteracting molecules is derived. This formula predicts RRC R/l r times larger than the model of reactive patches on the surfaces of molecules. Semiquantitative evaluation of the RRC of interacting molecules (the case of attraction is considered) shows that it strongly depends on whether the interaction potential is smooth or not. For smooth potential (of Coulomb type) the RRC K ∼ ( a/R) 3 as in the model of reactive patches whereas for sharply dependent potentials (of van der Waals type) K ∼ ( a/R) 2. A simple relation between the RRCs of spherical and nonspherical molecules is obtained.