Diffusion-controlled reactions: an overview

TL;DR

This paper reviews the development of the theory of diffusion-controlled reactions, covering foundational milestones, various reaction models, and emerging approaches with future outlooks.

Contribution

It provides a comprehensive overview of classical and modern theories of diffusion-controlled reactions, including new encounter-based methods and open research challenges.

Findings

Discussion of microscopic origins of reactions

Introduction of encounter-based approach

Outline of open problems and future directions

Abstract

We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski who recognized the importance of diffusion in chemical reactions, we discuss perfect and imperfect surface reactions, their microscopic origins, and the underlying mathematical framework. Single-molecule reaction schemes, anomalous bulk diffusions, reversible binding/unbinding kinetics and many other extensions are presented. An alternative encounter-based approach to diffusion-controlled reactions is introduced, with emphasis on its advantages and potential applications. Some open problems and future perspectives are outlined.