A Note on the Kinetics of Diffusion-mediated Reactions

TL;DR

This paper clarifies the limitations of modeling diffusion-mediated reactions as simple first-order processes, emphasizing the importance of re-encounters and providing insights into the correct theoretical approach.

Contribution

It explains, without mathematics, why the breakup of the encounter complex cannot generally be modeled as a first-order process, highlighting the role of re-encounters in diffusion-mediated reactions.

Findings

First-order approximation valid only in activation-controlled or gas-phase reactions.

Re-encounters are crucial in diffusion-mediated reactions, affecting reaction rate calculations.

Provides references to correct theoretical approaches for calculating reaction rates.

Abstract

The prevalent scheme of a diffusion-mediated bimolecular reaction $A+B\rightarrow P$ is an adaptation of that proposed by Briggs and Haldane for enzyme action [{\em Biochem J.\/}, 19:338--339, 1925]. The purpose of this Note is to explain, {\em by using an argument involving no mathematics\/}, why the breakup of the encounter complex cannot be described, except in special circumstances, in terms of a first-order process $\{AB\}\rightarrow A+B$. Briefly, such a description neglects the occurrence of re-encounters, which lie at the heart of Noyes's theory of diffusion-mediated reactions. The relation $k=\alpha k_{\mbox{\scriptsize e}}$ becomes valid only when $\alpha$ (the reaction probability per encounter) is very much smaller than unity (activation-controlled reactions), or when $\beta$ (the re-encounter probability) is negligible (as happens in a gas-phase reaction). References to some works (by the author and his collaborators) which propound the correct approach for finding $k$ are also supplied.