Kinetics of diffusion-limited catalytically-activated reactions: An extension of the Wilemski-Fixman approach

TL;DR

This paper extends the Wilemski-Fixman approach to analyze the kinetics of diffusion-limited catalytically-activated reactions in three-dimensional systems, deriving an analytical expression for the effective reaction rate considering spatial and diffusion parameters.

Contribution

It introduces a novel extension of the classical Wilemski-Fixman method to three-molecular reactions with catalytic subvolumes, providing analytical insights into reaction kinetics.

Findings

Effective reaction constant depends on catalytic subvolume density and particle diffusion.

Analytical expression includes terms related to residence times in finite domains.

Reaction rate exhibits non-trivial dependence on radii and diffusion coefficients.

Abstract

We study kinetics of diffusion-limited catalytically-activated $A + B \to B$ reactions taking place in three dimensional systems, in which an annihilation of diffusive $A$ particles by diffusive traps $B$ may happen only if the encounter of an $A$ with any of the $B$s happens within a special catalytic subvolumen, these subvolumens being immobile and uniformly distributed within the reaction bath. Suitably extending the classical approach of Wilemski and Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. \textbf{58}:4009, 1973) to such three-molecular diffusion-limited reactions, we calculate analytically an effective reaction constant and show that it comprises several terms associated with the residence and joint residence times of Brownian paths in finite domains. The effective reaction constant exhibits a non-trivial dependence on the reaction radii, the mean density of catalytic subvolumens and particles' diffusion coefficients. Finally, we discuss the fluctuation-induced kinetic behavior in such systems.