Effect of local molecular shape and anisotropic reactivity on the rate of diffusion-controlled reactions

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) approximately 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 theta << 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)/(Rtheta(2)), and therefore, even for small relative thickness d = l(r)/theta, 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.