Diffusion-controlled reaction rate to asymmetric reactants under Coulomb interaction

Abstract

The rate constant for diffusion-controlled reactions between asymmetric reactants described by the simple model of Solc and Stockmayer under the influence of Coulomb-type interaction is considered. Using the method of dual series relations, we calculate the rate constant with a high accuracy and obtain some approximate analytical formulas. We compare our results with an approximate analytical formula derived before by the constant-flux approximation and with numerical calculations based on the Brownian dynamics simulation. It is shown that in the case of strong attractive potential the rate constant only slightly depends on the size of the active site and tends to the classical Debye result for isotropically reactive particles with a further increase in the Onsager length. Moreover, it is shown that for small-sized active sites the effect of the interaction potential is to scale the rate constant for neutral reactants by a Boltzmann factor, which was first conjectured by Zhou [Biophys. J. 64, 1711 (1993)].