Diffusion-limited reactions in crowded environments

TL;DR

This paper extends the classical diffusion-limited reaction theory to include crowding effects, revealing how excluded-volume interactions and impurities significantly influence encounter rates and induce spatial ordering near absorbers.

Contribution

It introduces a novel extension of the Smoluchowski framework that accounts for crowding and excluded-volume effects in diffusion-limited reactions.

Findings

Encounter rate matches generalized theory at high densities for large absorber-to-diffuser ratios.

Reaction rates decrease and become non-monotonic at intermediate packing densities for small absorber sizes.

Impurities can dramatically slow down reaction dynamics even at low concentrations.

Abstract

Diffusion-limited reactions (DLR) are usually described within the Smoluchowski theory, which neglects interactions between the diffusing components. We propose a first extension of such frame- work that incorporates excluded-volume effects, considering hard diffusing agents in the presence of an absorbing sink. For large values of the absorber-to-diffuser size ratio Rs, the encounter rate obtained from the simulations is in very good agreement with a simple generalization of the Smolu- chowski equation at high densities. Reducing Rs, the rate gets substantially depressed at interme- diate packing and become even non-monotonic for Rs << 1. Concurrently with the saturation of the rate, stationary density waves set in close to the absorbing center. A mean-field, effective-potential analysis of the Smoluchowski equation under crowding sheds light on the subtle link between such ordering and the slowing down of the encounter dynamics. Finally, we show how an infinitesimal amount of non-reacting impurities can equally slow down dramatically the reaction.