Universal kinetics of imperfect reactions in confinement

TL;DR

This paper develops a comprehensive analytical framework for understanding the kinetics of imperfect reactions in confined geometries, applicable to various diffusive processes, revealing that reaction time distributions are robust and can be rescaled from perfect reaction models.

Contribution

It provides the first general analytical solution for imperfect reaction kinetics in confinement for any Markovian transport process, including anomalous diffusion, and shows the universality of reaction time distributions.

Findings

Reaction time distribution matches that of perfect reactions after rescaling.

Mean reaction time is independent of transport process in low reactivity regimes.

Numerical simulations confirm theoretical predictions across different geometries.

Abstract

Chemical reactions generically require that particles come into contact. In practice, reaction is often imperfect and can necessitate multiple random encounters between reactants. In confined geometries, despite notable recent advances, there is to date no general analytical treatment of such imperfect transport-limited reaction kinetics. Here, we determine the kinetics of imperfect reactions in confining domains for any diffusive or anomalously diffusive Markovian transport process, and for different models of imperfect reactivity. We show that the full distribution of reaction times is obtained in the large confining volume limit from the knowledge of the mean reaction time only, which we determine explicitly. This distribution for imperfect reactions is found to be identical to that of perfect reactions upon an appropriate rescaling of parameters, which highlights the robustness of our results. Strikingly, this holds true even in the regime of low reactivity where the mean reaction time is independent of the transport process, and can lead to large fluctuations of the reaction time even in simple reaction schemes. We illustrate our results for normal diffusion in domains of generic shape, and for anomalous diffusion in complex environments, where our predictions are confirmed by numerical simulations.