Time dependent diffusion coefficient and the transient dynamics of diffusion controlled bimolecular reactions in liquids: a mode coupling theory analysis

Abstract

As the transient dynamics of many bimolecular reactions occur on ultrafast time scales, this dynamics may not be described accurately by using the standard time independent diffusion coefficient. On the other hand, the full phase space based descriptions are often too complex and cumbersome. Since the key step in many bimolecular reactions is still the mutual diffusion of the two reacting species in the real space, it makes sense to look for a formalism which will include the effects of inertial motion within a diffusion equation based approach. Such a description is presented in this article. The time-dependent diffusion coefficient of a solute molecule in Lennard-Jones liquid is calculated and analyzed on the basis of the mode coupling theory. Not only the usual asymptotic diffusion coefficient, but also the transient diffusion dynamics shows a rich variety with varying curvature of the potential, solute size, or solute interaction strength. The effect of the nascent diffusion on diffusion-influenced bimolecular reaction is examined using the generalized Smoluchowski equation. It is found that there are significant differences in the dynamics from the results obtained with time independent diffusion.