Universal kinetics of imperfect reactions in confinement

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. Chemical reactions often require multiple random encounters between reactants, but a general, analytical treatment such imperfect transport-limited/influenced reactions in confined spaces has not yet been proposed. Here, the authors predict the full kinetics of these reactions for Markovian processes in large confining volumes.

Automated summary

The authors analyzed the kinetics of imperfect reactions in confining domains for diffusive or anomalous transport processes, and found that the full distribution of reaction times can be obtained from the mean reaction time in large confining volumes. They showed that the distribution of imperfect reactions is similar to that of perfect reactions, even in the regime of low reactivity where there are large fluctuations in reaction time. This was illustrated for both normal diffusion in domains of generic shapes and anomalous diffusion in complex environments, with predictions confirmed by numerical simulations.