Effect of anisotropic diffusion and external electric field on the rate of diffusion-controlled reactions.

In this paper we investigate theoretically the effect of an external electric field on the rate constant of steady-state bulk diffusion-controlled reactions. We generalize previously derived results for isotropic diffusion in the absence of interparticle interaction [J. Chem. Phys. 87, 4622 (1987)] to the case where translational diffusion is anisotropic. A frequently occurring situation of transverse isotropy where Dx=Dy≠Dz is considered in detail. We derive the first-order expansion for the reaction rate constant in terms of the electric field strength E, k(E)=k(0) (1+1/2εγ), where γ=k(0)/4πRD⊥, ε=qER/kBT, q is the charge, R is the contact distance, and D⊥ is the transverse diffusion coefficient. Numerical calculations show that this first-order expansion works well in the whole range of applicability of the Nernst–Einstein relation, i.e., for ε<1. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]