Long-time tail effect of the velocity correlation on diffusion-controlled reactions

Abstract

The existence of the long-time tail in the velocity correlation function of a Brownian particle is first discovered from molecular-dynamics simulations and is now well established theoretically and experimentally. In this work, we ask the following question: does this long-time tail have any effect on the kinetics of diffusion-controlled reactions, and if there is any, how the reaction rate is affected, especially in the asymptotic region, t→∞? We will show that this long-time tail can be taken into account by the theory developed recently by Dong and André. The exact asymptotic solutions to the order of t−1/2 are found analytically with Smoluchowski and Collins–Kimball boundary conditions. This allows us to reveal that the long-time tail of the velocity correlation function contributes to the reaction rate an additional term of O(t−1/2) to the long-time limit of the classic Smoluchowski and Collins–Kimball theories.