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 D(x)=D(y) not equal to D(z) 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+1/2epsilongamma), where gamma=k(0)/4piRD( perpendicular ), epsilon=qER/k(B)T, q is the charge, R is the contact distance, and D( perpendicular ) 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 epsilon<1.