Product interactions and feedback in diffusion-controlled reactions

TL;DR

This study investigates how interactions involving product species and their diffusion properties influence the rate of diffusion-controlled reactions, revealing complex feedback effects that can either enhance or inhibit reaction rates.

Contribution

It introduces a mean-field approach to model the impact of product interactions and asymmetric diffusion on reaction rates in the classical Smoluchowski framework, addressing a previously overlooked aspect.

Findings

Product interactions significantly alter spatial distributions and reaction rates.

Complex feedback mechanisms can both increase and decrease reaction rates.

Interactions of products can lead to self-regulating or self-amplifying effects.

Abstract

Steric or attractive interactions among reactants or between reactants and inert crowders can substantially influence the total rate of a diffusion-influenced reaction in the liquid phase. However, the role of the product species, that has typically different physical properties than the reactant species, has been disregarded so far. Here we study the effects of reactant-product and product-product interactions as well as asymmetric diffusion properties on the rate of diffusion-controlled reactions in the classical Smoluchowski-setup for chemical transformations at a perfect catalytic sphere. For this we solve the diffusion equation with appropriate boundary conditions coupled by a mean-field approach on the second virial level to account for the particle interactions. We find that all particle spatial distributions and the total rate can change significantly, depending on the diffusion and interaction properties of the accumulated products. Complex competing and self-regulating (homeostatic) or self-amplifying effects are observed for the system, leading to both decrease and increase of the rates, as the presence of interacting products feeds back to the reactant flux and thus the rate with which the products are generated.