Improved Velocity Distribution Applied to Fokker–Planck–Kramers Equation Treatment for Dynamics of Diffusion-Controlled Reactions in Two Dimensions

Abstract

Abstract The validity of theoretical treatments of short-time dynamics of diffusion-controlled reaction based on the Fokker–Planck–Kramers’ equation (FPKE) has been examined using molecular dynamics (MD) simulation in two-dimensional Lennard–Jones fluids. First, we made Langevin dynamics (LD) simulation assuming that the relative diffusion coefficient is given by the sum of the self-diffusion coefficients and that the potential between the reactants is given by the potential of mean force. The LD and the MD simulation results for the time dependence of the survival probabilities of the reactants agree well. This indicates that the FPKE derived from the Langevin equation can be applied to the problem of diffusion-controlled reaction. The time-dependent Harris theory based on the FPKE and the approximation of the half-range Maxwellian velocity distribution showed disagreements with the MD simulation. Such a limitation of the theory has not been recognized in three-dimensional fluids. In the approximation used in the time-dependent Harris theory, the velocity distribution function is not continuous. We have shown that the agreement between the MD simulation and the theory can be improved when we use a new approximation based on a continuous velocity distribution function.