Effect of Local Molecular Shape and Anisotropic Reactivity on the Rate of Diffusion-Controlled Reactions

Abstract

The role of distance-dependent anisotropic reactivity and molecular geometry in the vicinity of localized reaction centers in influencing the rate of bimolecular diffusion-controlled reactions is analyzed in detail, both analytically and numerically. The effect of local molecular shape is considered within the model of reflective hemispheres of small radius l h on the surfaces of otherwise spherical molecules of radius R ( l h ≪ R) . The distance-dependent reactivity is modeled by reactive hemispheres of radius l r on top of the reflective hemispheres ( l r ≪ R) . It is shown that the presence of the reflective hemispheres leads to a markedly large increase of the reaction rate. The maximum effect is ∼ R/ l h ≫ 1 times, as described by the ratio of local to average molecular curvature. It is observed for l h ≈ R( l r /R) 1/2 ≫ l r. The effect of thickness of the reaction regions is described within the model of reactive cylinders of height l r and angular radius θ ≪ 1. It is shown that the characteristic parameter in the expansion of the reaction rate as a function of l r /R is l r /( Rθ 2 ) , and therefore, even for small relative thickness d = l r/ θ, its effect on the rate is very strong, i.e., the conventional model of reactive patches, which assumes zero thickness of the reaction region, may considerably underestimate the reaction rate.