Comparison between molecular dynamics simulations and the Smoluchowski theory of reactions in a hard-sphere liquid

Molecular dynamics simulations of the kinetics of a model of the reaction A+B→B in a dense hard-sphere liquid are compared with the predictions of the Smoluchowski approach to diffusion-influenced reactions. The theory employs the radiation boundary condition at contact with an intrinsic rate constant determined by the low-density collision frequency and the potential of mean force determined by the pair distribution function. Hydrodynamic interactions are ignored and the relative diffusion coefficient is taken as twice the self-diffusion constant. Considering the lack of free parameters and the many-body nature of the problem, the agreement between theory and simulations is surprisingly good over a wide range of B concentrations. Of particular interest is that the above theory provides an exact description of the kinetics at short times.